Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
6916 conjugacy classes of subgroups.
The subgroup lattice has 1720 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×C22⋊C4 |
| commutator | C23 | C23×C42 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C22 | C22×C4×C22⋊C4 |
| prime radical | C23×#41 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4×M16 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #6370009 | C2 | semidirect |
| 5. #183093 | C2 | semidirect |
| 6. M16×#99 | C2 | semidirect |
| 7. #182085 | C2 | semidirect |
| 8. #182081 | C2 | semidirect |
| 9. #181483 | C2 | semidirect |
| 16. C2×#2971 | C4 | semidirect |
| 17. C2×#2970 | C4 | semidirect |
| 19. C2×#2965 | C4 | semidirect |
| 22. C2×Q8×M16 | C4 | semidirect |
| 23. C2×D4×M16 | C4 | semidirect |
| 25. C2×#2920 | C4 | semidirect |
| 28. C22×C4×M16 | C4 | semidirect |
| 41. #20481 | C22 | semidirect |
| 43. #20476 | C22 | semidirect |
| 49. #17366 | C4 | semidirect |
| 50. #17365 | C4 | semidirect |
| 51. #17364 | C4 | semidirect |
| 55. #17361 | C4 | semidirect |
| 56. #17361 | C4 | semidirect |
| 57. #17357 | C4 | semidirect |
| 59. #8161 | C22 | semidirect |
| 60. #8160 | C22 | semidirect |
| 61. C8×#99 | C22 | semidirect |
| 63. #7928 | C22 | semidirect |
| 64. #7926 | C22 | semidirect |
| 119. C2×#446 | C2×C4 | semidirect |
| 120. C2×#446 | C2×C4 | semidirect |
| 121. C2×C8×Q8 | C2×C4 | semidirect |
| 129. C2×#436 | C2×C4 | semidirect |
| 131. C2×#435 | C2×C4 | semidirect |
| 133. C2×C8×D4 | C2×C4 | semidirect |
| 153. C2×#432 | C2×C4 | semidirect |
| 154. C2×#432 | C2×C4 | semidirect |
| 159. C2×#431 | C2×C4 | semidirect |
| 160. C2×#431 | C2×C4 | semidirect |
| 184. C2×C4×M16 | C2×C4 | semidirect |
| 185. C2×C4×M16 | C2×C4 | semidirect |
| 191. C22×#97 | C2×C4 | semidirect |
| 193. C22×C4×C8 | C2×C4 | semidirect |
| 236. #1467 | C2×C4 | semidirect |
| 237. #1467 | C2×C4 | semidirect |
| 238. #1466 | C2×C4 | semidirect |
| 239. #1466 | C2×C4 | semidirect |
| 242. #1464 | C2×C4 | semidirect |
| 243. #1464 | C2×C4 | semidirect |
| 246. #1461 | C2×C4 | semidirect |
| 247. #1460 | C2×C4 | semidirect |
| 250. #1458 | C2×C4 | semidirect |
| 251. #1458 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×#41 | 2 |
| C2×#20723 | 2 |
| #6370009 | 2 |
| #6342561 | 2 |
| #183093 | 2 |
| M16×#99 | 2 |
| #182085 | 2 |
| #182081 | 2 |
| #181483 | 2 |