Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1273 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1273 conjugacy classes of subgroups — too many to draw. Only its 411 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. #2842 | C2 | semidirect |
| 2. #2752 | C2 | semidirect |
| 3. #2678 | C2 | semidirect |
| 4. #2539 | C2 | semidirect |
| 5. #2471 | C2 | semidirect |
| 6. #2403 | C2 | semidirect |
| 7. #2403 | C2 | semidirect |
| 8. #2309 | C2 | semidirect |
| 9. #2308 | C2 | semidirect |
| 12. C2×#123 | C22 | semidirect |
| 13. C2×#121 | C22 | semidirect |
| 14. C2×#120 | C22 | semidirect |
| 15. C2×#120 | C22 | semidirect |
| 16. C2×#120 | C22 | semidirect |
| 17. C2×#117 | C22 | semidirect |
| 18. C22×C22⋊C4 | C22 | semidirect |
| 19. #399 | C22 | semidirect |
| 20. #399 | C22 | semidirect |
| 21. #397 | C22 | semidirect |
| 22. #396 | C22 | semidirect |
| 23. #394 | C22 | semidirect |
| 26. #392 | C22 | semidirect |
| 27. #390 | C22 | semidirect |
| 28. #390 | C22 | semidirect |
| 29. #390 | C22 | semidirect |
| 30. #388 | C22 | semidirect |
| 31. #387 | C22 | semidirect |
| 32. #386 | C22 | semidirect |
| 33. #386 | C22 | semidirect |
| 34. #386 | C22 | semidirect |
| 35. #386 | C22 | semidirect |
| 36. #381 | C22 | semidirect |
| 40. #379 | C22 | semidirect |
| 41. C4×C22⋊C4 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2842 | 2 |
| #2752 | 2 |
| #2678 | 2 |
| #2539 | 2 |
| #2471 | 2 |
| #2403 | 2 |
| #2309 | 2 |
| #2308 | 2 |