Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
4749 conjugacy classes of subgroups.
The subgroup lattice has 481 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×C42 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C22×C8 | C25 |
| socle | C24 | C2×#97 |
| prime radical | C25 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×#12666 | C2 | direct (N × H) |
| 14. C2×#2150 | C4 | semidirect |
| 16. C22×C4⋊C16 | C4 | semidirect |
| 17. C22×C4⋊C16 | C4 | semidirect |
| 20. C2×C4×M32 | C4 | semidirect |
| 22. C22×#346 | C4 | semidirect |
| 23. C22×C4×C16 | C4 | semidirect |
| 27. #12666 | C22 | direct (N × H) |
| 69. #2150 | C2×C4 | semidirect |
| 71. C2×C4⋊C16 | C2×C4 | semidirect |
| 72. C2×C4⋊C16 | C2×C4 | semidirect |
| 75. C4×M32 | C2×C4 | semidirect |
| 77. C2×#346 | C2×C4 | semidirect |
| 78. C2×C4×C16 | C2×C4 | semidirect |
| 128. C2×M32 | C4⋊C4 | semidirect |
| 139. C22×C16 | C4⋊C4 | semidirect |
| 168. C4⋊C16 | C22×C4 | semidirect |
| 169. C4⋊C16 | C22×C4 | semidirect |
| 171. #346 | C22×C4 | semidirect |
| 172. C4×C16 | C22×C4 | semidirect |
| 264. M32 | C2×C4⋊C4 | semidirect |
| 269. C2×C16 | C2×C4⋊C4 | semidirect |
| 306. C22×C4 | #347 | semidirect |
| 385. C16 | C22×C4⋊C4 | semidirect |
| 415. C2×C4 | C2×#347 | semidirect |
| 454. C22 | #12666 | direct (N × H) |
| 468. C4 | C22×#347 | semidirect |
| 476. C2 | C2×#12666 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#2150 | 2 |
| C23×#347 | 2 |
| C22×C4×M32 | 2 |
| C22×#1770 | 2 |
| C2×#12666 | 2 |
| C22×#1375 | 2 |