The space group of a crystal uniquely determines the Bravais lattice and the point group. The point group does not uniquely determine the Bravais lattice.
Space Group | Bravais lattice | Point group | |
1 P1 | Triclinic | 1 | C1 |
2 P1 | Triclinic | 1 | S2 = Ci |
3 P2 | Simple Monoclinic | 2 | C2 |
4 P21 | Simple Monoclinic | 2 | C2 |
5 C2 | Base-Centered Monoclinic | 2 | C2 |
6 Pm | Simple Monoclinic | m | C1h = Cs |
7 Pc | Simple Monoclinic | m | C1h = Cs |
8 Cm | Base-Centered Monoclinic | m | C1h = Cs |
9 Cc | Base-Centered Monoclinic | m | C1h = Cs |
10 P2/m | Simple Monoclinic | $\frac{2}{m}$ | C2h |
11 P21/m | Simple Monoclinic | $\frac{2}{m}$ | C2h |
12 C2/m | Base-Centered Monoclinic | $\frac{2}{m}$ | C2h |
13 P2/c | Simple Monoclinic | $\frac{2}{m}$ | C2h |
14 P21/c | Simple Monoclinic | $\frac{2}{m}$ | C2h |
15 C2/c | Base-Centered Monoclinic | $\frac{2}{m}$ | C2h |
16 P222 | Simple Orthorhombic | 222 | V = D2 |
17 P2221 | Simple Orthorhombic | 222 | V = D2 |
18 P21212 | Simple Orthorhombic | 222 | V = D2 |
19 P212121 | Simple Orthorhombic | 222 | V = D2 |
20 C2221 | Base-Centered Orthorhombic | 222 | V = D2 |
21 C222 | Base-Centered Orthorhombic | 222 | V = D2 |
22 F222 | Face-Centered Orthorhombic | 222 | V = D2 |
23 I222 | Body-Centered Orthorhombic | 222 | V = D2 |
24 I212121 | Body-Centered Orthorhombic | 222 | V = D2 |
25 Pmm2 | Simple Orthorhombic | mm2 | C2v |
26 Pmc21 | Simple Orthorhombic | mm2 | C2v |
27 Pcc2 | Simple Orthorhombic | mm2 | C2v |
28 Pma2 | Simple Orthorhombic | mm2 | C2v |
29 Pca21 | Simple Orthorhombic | mm2 | C2v |
30 Pnc2 | Simple Orthorhombic | mm2 | C2v |
31 Pmn21 | Simple Orthorhombic | mm2 | C2v |
32 Pba2 | Simple Orthorhombic | mm2 | C2v |
33 Pna21 | Simple Orthorhombic | mm2 | C2v |
34 Pnn2 | Simple Orthorhombic | mm2 | C2v |
35 Cmm2 | Base-Centered Orthorhombic | mm2 | C2v |
36 Cmc21 | Base-Centered Orthorhombic | mm2 | C2v |
37 Ccc2 | Base-Centered Orthorhombic | mm2 | C2v |
38 Amm2 | Base-Centered Orthorhombic | mm2 | C2v |
39 Aem2 | Base-Centered Orthorhombic | mm2 | C2v |
40 Ama2 | Base-Centered Orthorhombic | mm2 | C2v |
41 Aea2 | Base-Centered Orthorhombic | mm2 | C2v |
42 Fmm2 | Face-Centered Orthorhombic | mm2 | C2v |
43 Fdd2 | Face-Centered Orthorhombic | mm2 | C2v |
44 Imm2 | Body-Centered Orthorhombic | mm2 | C2v |
45 Iba2 | Body-Centered Orthorhombic | mm2 | C2v |
46 Ima2 | Body-Centered Orthorhombic | mm2 | C2v |
47 Pmmm | Simple Orthorhombic | mmm | Vh = D2h |
48 Pnnn | Simple Orthorhombic | mmm | Vh = D2h |
49 Pccm | Simple Orthorhombic | mmm | Vh = D2h |
50 Pban | Simple Orthorhombic | mmm | Vh = D2h |
51 Pmma | Simple Orthorhombic | mmm | Vh = D2h |
52 Pnna | Simple Orthorhombic | mmm | Vh = D2h |
53 Pmna | Simple Orthorhombic | mmm | Vh = D2h |
54 Pcca | Simple Orthorhombic | mmm | Vh = D2h |
55 Pbam | Simple Orthorhombic | mmm | Vh = D2h |
56 Pccn | Simple Orthorhombic | mmm | Vh = D2h |
57 Pbcm | Simple Orthorhombic | mmm | Vh = D2h |
58 Pnnm | Simple Orthorhombic | mmm | Vh = D2h |
59 Pmmn | Simple Orthorhombic | mmm | Vh = D2h |
60 Pbcn | Simple Orthorhombic | mmm | Vh = D2h |
61 Pbca | Simple Orthorhombic | mmm | Vh = D2h |
62 Pnma | Simple Orthorhombic | mmm | Vh = D2h |
63 Cmcm | Base-Centered Orthorhombic | mmm | Vh = D2h |
64 Cmce | Base-Centered Orthorhombic | mmm | Vh = D2h |
65 Cmmm | Base-Centered Orthorhombic | mmm | Vh = D2h |
66 Cccm | Base-Centered Orthorhombic | mmm | Vh = D2h |
67 Cmme | Base-Centered Orthorhombic | mmm | Vh = D2h |
68 Ccce | Base-Centered Orthorhombic | mmm | Vh = D2h |
69 Fmmm | Face-Centered Orthorhombic | mmm | Vh = D2h |
70 Fddd | Face-Centered Orthorhombic | mmm | Vh = D2h |
71 Immm | Body-Centered Orthorhombic | mmm | Vh = D2h |
72 Ibam | Body-Centered Orthorhombic | mmm | Vh = D2h |
73 Ibca | Body-Centered Orthorhombic | mmm | Vh = D2h |
74 Imma | Body-Centered Orthorhombic | mmm | Vh = D2h |
75 P4 | Simple Tetragonal | 4 | C4 |
76 P41 | Simple Tetragonal | 4 | C4 |
77 P42 | Simple Tetragonal | 4 | C4 |
78 P43 | Simple Tetragonal | 4 | C4 |
79 I4 | Body-Centered Tetragonal | 4 | C4 |
80 I41 | Body-Centered Tetragonal | 4 | C4 |
81 P4 | Simple Tetragonal | 4 | S4 |
82 I4 | Body-Centered Tetragonal | 4 | S4 |
83 P4/m | Simple Tetragonal | $\frac{4}{m}$ | C4h |
84 P42/m | Simple Tetragonal | $\frac{4}{m}$ | C4h |
85 P4/n | Simple Tetragonal | $\frac{4}{m}$ | C4h |
86 P42/n | Simple Tetragonal | $\frac{4}{m}$ | C4h |
87 I4/m | Body-Centered Tetragonal | $\frac{4}{m}$ | C4h |
88 I41/a | Body-Centered Tetragonal | $\frac{4}{m}$ | C4h |
89 P422 | Simple Tetragonal | 422 | D4 |
90 P4212 | Simple Tetragonal | 422 | D4 |
91 P4122 | Simple Tetragonal | 422 | D4 |
92 P41212 | Simple Tetragonal | 422 | D4 |
93 P4222 | Simple Tetragonal | 422 | D4 |
94 P42212 | Simple Tetragonal | 422 | D4 |
95 P4322 | Simple Tetragonal | 422 | D4 |
96 P43212 | Simple Tetragonal | 422 | D4 |
97 I422 | Body-Centered Tetragonal | 422 | D4 |
98 I4122 | Body-Centered Tetragonal | 4mm | C4v |
99 P4mm | Simple Tetragonal | 4mm | C4v |
100 P4bm | Simple Tetragonal | 4mm | C4v |
101 P42cm | Simple Tetragonal | 4mm | C4v |
102 P42nm | Simple Tetragonal | 4mm | C4v |
103 P4cc | Simple Tetragonal | 4mm | C4v |
104 P4nc | Simple Tetragonal | 4mm | C4v |
105 P42mc | Simple Tetragonal | 4mm | C4v |
106 P42bc | Simple Tetragonal | 4mm | C4v |
107 I4mm | Body-Centered Tetragonal | 4mm | C4v |
108 I4cm | Body-Centered Tetragonal | 4mm | C4v |
109 I41md | Body-Centered Tetragonal | 4mm | C4v |
110 I41cd | Body-Centered Tetragonal | 4mm | C4v |
111 P42m | Simple Tetragonal | 42m | Vd = D2d |
112 P42c | Simple Tetragonal | 42m | Vd = D2d |
113 P421m | Simple Tetragonal | 42m | Vd = D2d |
114 P421c | Simple Tetragonal | 42m | Vd = D2d |
115 P4m2 | Simple Tetragonal | 42m | Vd = D2d |
116 P4c2 | Simple Tetragonal | 42m | Vd = D2d |
117 P4b2 | Simple Tetragonal | 42m | Vd = D2d |
118 P4n2 | Simple Tetragonal | 42m | Vd = D2d |
119 I4m2 | Body-Centered Tetragonal | 42m | Vd = D2d |
120 I4c2 | Body-Centered Tetragonal | 42m | Vd = D2d |
121 I42m | Body-Centered Tetragonal | 42m | Vd = D2d |
122 I42d | Body-Centered Tetragonal | 42m | Vd = D2d |
123 P4/mmm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
124 P4/mcc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
125 P4/nbm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
126 P4/nnc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
127 P4/mbm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
128 P4/mnc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
129 P4/nmm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
130 P4/ncc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
131 P42/mmc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
132 P42/mcm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
133 P42/nbc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
134 P42/nnm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
135 P42/mbc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
136 P42/mnm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
137 P42/nmc | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
138 P42/ncm | Simple Tetragonal | $\frac{4}{m}mm$ | D4h |
139 I4/mmm | Body-Centered Tetragonal | $\frac{4}{m}mm$ | D4h |
140 I4/mcm | Body-Centered Tetragonal | $\frac{4}{m}mm$ | D4h |
141 I41/amd | Body-Centered Tetragonal | $\frac{4}{m}mm$ | D4h |
142 I41/acd | Body-Centered Tetragonal | $\frac{4}{m}mm$ | D4h |
143 P3 | Hexagonal | 3 | C3 |
144 P31 | Hexagonal | 3 | C3 |
145 P32 | Hexagonal | 3 | C3 |
146 R3 | Rhombohedral | 3 | C3 |
147 P3 | Hexagonal | 3 | S6 = C6i |
148 R3 | Rhombohedral | 3 | S6 = C6i |
149 P312 | Hexagonal | 32 | D3 |
150 P321 | Hexagonal | 32 | D3 |
151 P3112 | Hexagonal | 32 | D3 |
152 P3121 | Hexagonal | 32 | D3 |
153 P3212 | Hexagonal | 32 | D3 |
154 P3221 | Hexagonal | 32 | D3 |
155 R32 | Rhombohedral | 32 | D3 |
156 P3m1 | Hexagonal | 3m | C3v |
157 P31m | Hexagonal | 3m | C3v |
158 P3c1 | Hexagonal | 3m | C3v |
159 P31c | Hexagonal | 3m | C3v |
160 R3m | Rhombohedral | 3m | C3v |
161 R3c | Rhombohedral | 3m | C3v |
162 P31m | Hexagonal | 3m | D3d |
163 P31c | Hexagonal | 3m | D3d |
164 P3m1 | Hexagonal | 3m | D3d |
165 P3c1 | Hexagonal | 3m | D3d |
166 R3m | Rhombohedral | 3m | D3d |
167 R3c | Rhombohedral | 3m | D3d |
168 P6 | Hexagonal | 6 | C6 |
169 P61 | Hexagonal | 6 | C6 |
170 P65 | Hexagonal | 6 | C6 |
171 P62 | Hexagonal | 6 | C6 |
172 P64 | Hexagonal | 6 | C6 |
173 P63 | Hexagonal | 6 | C6 |
174 P6 | Hexagonal | 6 | C3h = S3 |
175 P6/m | Hexagonal | $\frac{6}{m}$ | C6h |
176 P63/m | Hexagonal | $\frac{6}{m}$ | C6h |
177 P622 | Hexagonal | 622 | D6 |
178 P6122 | Hexagonal | 622 | D6 |
179 P6522 | Hexagonal | 622 | D6 |
180 P6222 | Hexagonal | 622 | D6 |
181 P6422 | Hexagonal | 622 | D6 |
182 P6322 | Hexagonal | 622 | D6 |
183 P6mm | Hexagonal | 6mm | C6v |
184 P6cc | Hexagonal | 6mm | C6v |
185 P63cm | Hexagonal | 6mm | C6v |
186 P63mc | Hexagonal | 6mm | C6v |
187 P6m2 | Hexagonal | 6m2 | D3h |
188 P6c2 | Hexagonal | 6m2 | D3h |
189 P62m | Hexagonal | 6m2 | D3h |
190 P62c | Hexagonal | 6m2 | D3h |
191 P6/mmm | Hexagonal | $\frac{6}{m}mm$ | D6h |
192 P6/mcc | Hexagonal | $\frac{6}{m}mm$ | D6h |
193 P63/mcm | Hexagonal | $\frac{6}{m}mm$ | D6h |
194 P63/mmc | Hexagonal | $\frac{6}{m}mm$ | D6h |
195 P23 | Simple Cubic | 23 | T |
196 F23 | Face-Centered Cubic | 23 | T |
197 I23 | Body-Centered Cubic | 23 | T |
198 P213 | Simple Cubic | 23 | T |
199 I213 | Body-Centered Cubic | 23 | T |
200 Pm3 | Simple Cubic | m3 | Th |
201 Pn3 | Simple Cubic | m3 | Th |
202 Fm3 | Face-Centered Cubic | m3 | Th |
203 Fd3 | Face-Centered Cubic | m3 | Th |
204 Im3 | Body-Centered Cubic | m3 | Th |
205 Pa3 | Simple Cubic | m3 | Th |
206 Ia3 | Body-Centered Cubic | m3 | Th |
207 P432 | Simple Cubic | 432 | O |
208 P4232 | Simple Cubic | 432 | O |
209 F432 | Face-Centered Cubic | 432 | O |
210 F4132 | Face-Centered Cubic | 432 | O |
211 I432 | Body-Centered Cubic | 432 | O |
212 P4332 | Simple Cubic | 432 | O |
213 P4132 | Simple Cubic | 432 | O |
214 I4132 | Body-Centered Cubic | 432 | O |
215 P43m | Simple Cubic | 43m | Td |
216 F43m | Face-Centered Cubic | 43m | Td |
217 I43m | Body-Centered Cubic | 43m | Td |
218 P43n | Simple Cubic | 43m | Td |
219 F43c | Face-Centered Cubic | 43m | Td |
220 I43d | Body-Centered Cubic | 43m | Td |
221 Pm3m | Simple Cubic | m3m | Oh |
222 Pn3n | Simple Cubic | m3m | Oh |
223 Pm3n | Simple Cubic | m3m | Oh |
224 Pn3m | Simple Cubic | m3m | Oh |
225 Fm3m | Face-Centered Cubic | m3m | Oh |
226 Fm3c | Face-Centered Cubic | m3m | Oh |
227 Fd3m | Face-Centered Cubic | m3m | Oh |
228 Fd3c | Face-Centered Cubic | m3m | Oh |
229 Im3m | Body-Centered Cubic | m3m | Oh |
230 Ia3d | Body-Centered Cubic | m3m | Oh |
P - Primitive |