Symbols of the 230 Crystallographic Space Groups
空间群是点对称操作和平移对称操作的对称要素全部可能的组合。点群表示晶体外形上的对称关系，空间群表示晶体结构内部的原子及离子间的对称关系。空间群一共230个，它们分别属于32个点群。晶体结构的对称性不能超出230个空间群的范围，而其外形的对称性和宏观对称性则不能越出32个点群的范围。属于同一点群的各种晶体可以隶属于若干个空间群。
230种晶体学空间群的记号
Symbols of the 230 Crystallographic Space Groups
| 晶系(Crystal system) | 点群 (Point group) | 空间群(Space group) | |||||||||
| 国际符号(HM) | 圣佛利斯符号(Schfl.) | ||||||||||
| 三斜 晶系 | 1 | C1 | P1 | ||||||||
| Ci | P | ||||||||||
| 单斜 晶系 | 2 | P2 | P21 | C2 | |||||||
| m | Pm | Pc | Cm | Cc | |||||||
| 2/m | P2/m | P21/m | C2/m | P2/c | P21/C | C2/c | |||||
| 正交 晶系 | 222 | P222 | P2221 | P21212 | P212121 | C2221 | C222 | F222 | I222 | I212121 | |
| mm2 | Pmm2 | Pmc21 | Pcc2 | Pma2 | Pca21 | Pnc2 | Pmn21 | Pba2 | Pna21 | ||
| Pnn2 | Cmm2 | Cmc21 | Ccc2 | Amm2 | Abm2 | Ama2 | Aba2 | Fmm2 | |||
| Fdd2 | Imm2 | Iba2 | Ima2 | ||||||||
| mmm | Pmmm | Pnnn | Pccm | Pban | Pmma | Pnna | Pmna | Pcca | Pbam | ||
| Pccn | Pbcm | Pnnm | Pmmn | Pbcn | Pbca | Pnma | Cmcm | Cmca | |||
| Cmmm | Cccm | Cmma | Ccca | Fmmm | Fddd | Immm | Ibam | Ibca | |||
| Imma | |||||||||||
| 四方 晶系 | 4 | P4 | P41 | P42 | P43 | I4 | I41 | ||||
| P | I | ||||||||||
| 4/m | P4/m | P42/m | P4/n | P42/n | I4/m | I41/a | |||||
| 422 | P422 | P4212 | P4122 | P41212 | P4222 | P42212 | P4322 | P43212 | I422 | ||
| I4122 | |||||||||||
| 4mm | P4mm | P4bm | P42cm | P42nm | P4cc | P4nc | P42mc | P42bc | I4mm | ||
| I4cm | I41md | I41cd | |||||||||
| 2m | P2m | P2c | P21m | P21c | Pm2 | Pc2 | Pb2 | Pn2 | Im2 | ||
| Ic2 | I2m | I2d | |||||||||
| 4/mmm | P4/mmm | P4/mcc | P4/nbm | P4/nnc | P4/mbm | P4/mnc | P4/nmm | P4/ncc | P42/mmc | ||
| P42/mcm | P42/nbc | P42/nnm | P42/mbc | P42/mnm | P42/nmc | P42/ncm | I4/mmm | I4/mcm | |||
| I41/amd | I41/acd | ||||||||||
| 三方 晶系 | 3 | P3 | P31 | P32 | R3 | ||||||
| P | R | ||||||||||
| 32 | P312 | P321 | P3112 | P3121 | P3212 | P3221 | R32 | ||||
| 3m | P3m1 | P31m | P3c1 | P31c | R3m | R3c | |||||
| m | P1m | P1c | Pm1 | Pc1 | Rm | Rc | |||||
| 六方 晶系 | 6 | P6 | P61 | P65 | P62 | P | P63 | ||||
| P | |||||||||||
| 6/m | P6/m | P63/m | |||||||||
| 622 | P622 | P6122 | P6522 | P6222 | P22 | P6322 | |||||
| 6mm | P6mm | P6cc | P63cm | P63mc | |||||||
| m2 | Pm2 | Pc2 | P2m | P2c | |||||||
| 6/mmm | P6/mmm | P6/mcc | P63/mcm | P63/mmc | |||||||
| 立方 晶系 | 23 | P23 | F23 | I23 | P213 | I213 | |||||
| m | Pm3 | Pn3 | Fm3 | Fd3 | Im3 | Pa3 | Ia3 | ||||
| 432 | P432 | P4232 | F432 | F4132 | I432 | P4332 | P4132 | I4132 | |||
| 3m | P3m | F3m | I3m | P3n | F3c | I3d | |||||
| mm | Pmm | Pnn | Pmn | Pnm | Fmm | Fmc | Fdm | Fdc | Imm | ||
| Iad | |||||||||||
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