Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
907 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 907 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
| prime radical | C23×D4 | C22 |
| 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. #2842 | C2 | semidirect |
| 2. #2735 | C2 | semidirect |
| 3. #2707 | C2 | semidirect |
| 4. #2611 | C2 | semidirect |
| 5. #2526 | C2 | semidirect |
| 6. #2483 | C2 | semidirect |
| 8. #2312 | C2 | semidirect |
| 11. C2×#125 | C22 | semidirect |
| 15. #400 | C22 | semidirect |
| 17. #398 | C22 | semidirect |
| 19. #397 | C22 | semidirect |
| 20. #396 | C22 | semidirect |
| 21. #396 | C22 | semidirect |
| 24. #389 | C22 | semidirect |
| 26. #388 | C22 | semidirect |
| 27. #388 | C22 | semidirect |
| 28. #388 | C22 | semidirect |
| 29. #387 | C22 | semidirect |
| 32. #385 | C22 | semidirect |
| 33. #381 | C22 | semidirect |
| 34. #380 | C22 | semidirect |
| 40. C4×C22⋊C4 | C22 | semidirect |
| 41. #376 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2842 | 2 |
| #2735 | 2 |
| #2707 | 2 |
| #2611 | 2 |
| #2526 | 2 |
| #2483 | 2 |
| #2405 | 2 |
| #2312 | 2 |
| #2309 | 2 |