Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1737 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 1737 conjugacy classes of subgroups — too many to draw. Only its 463 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#121 | C2 | semidirect |
| 2. #2815 | C2 | semidirect |
| 3. #2619 | C2 | semidirect |
| 4. #2617 | C2 | semidirect |
| 5. #2504 | C2 | semidirect |
| 6. #2433 | C2 | semidirect |
| 7. #2403 | C2 | semidirect |
| 8. #2280 | C2 | semidirect |
| 10. C23×D4 | C22 | semidirect |
| 12. C2×#127 | C22 | semidirect |
| 16. C2×#121 | C22 | semidirect |
| 17. C2×#121 | C22 | semidirect |
| 18. C2×#120 | C22 | semidirect |
| 19. C2×#117 | C22 | semidirect |
| 20. C22×C4⋊C4 | C22 | semidirect |
| 21. C22×C22⋊C4 | C22 | semidirect |
| 22. #397 | C22 | semidirect |
| 23. #394 | C22 | semidirect |
| 24. #392 | C22 | semidirect |
| 25. #392 | C22 | semidirect |
| 26. #390 | C22 | semidirect |
| 27. #386 | C22 | semidirect |
| 28. #382 | C22 | semidirect |
| 29. #381 | C22 | semidirect |
| 30. #380 | C22 | semidirect |
| 32. C4×C22⋊C4 | C22 | semidirect |
| 45. C23×C4 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#121 | 2 |
| #2815 | 2 |
| #2619 | 2 |
| #2617 | 2 |
| #2504 | 2 |
| #2433 | 2 |
| #2403 | 2 |
| #2280 | 2 |