Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1272 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 449 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. C2×#560 | C2 | semidirect |
| 2. #2860 | C2 | semidirect |
| 3. #2823 | C2 | semidirect |
| 4. #2699 | C2 | semidirect |
| 5. #2697 | C2 | semidirect |
| 6. #2486 | C2 | semidirect |
| 7. #2416 | C2 | semidirect |
| 8. #2408 | C2 | semidirect |
| 9. C4×#127 | C2 | semidirect |
| 13. C2×#126 | C22 | semidirect |
| 16. C2×#121 | C22 | semidirect |
| 19. C2×C4×D4 | C22 | semidirect |
| 20. C22×C4⋊C4 | C22 | semidirect |
| 21. #398 | C22 | semidirect |
| 23. #396 | C22 | semidirect |
| 25. #394 | C22 | semidirect |
| 29. #390 | C22 | semidirect |
| 30. #389 | C22 | semidirect |
| 31. #388 | C22 | semidirect |
| 32. #386 | C22 | semidirect |
| 33. #384 | C22 | semidirect |
| 34. #381 | C22 | semidirect |
| 36. #380 | C22 | semidirect |
| 38. C43 | C22 | semidirect |
| 49. #127 | D4 | semidirect |
| 94. C2×D4 | C2×D4 | semidirect |
| 122. C42 | C2×D4 | semidirect |
| 178. C4 | #560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#560 | 2 |
| #2860 | 2 |
| #2823 | 2 |
| #2699 | 2 |
| #2697 | 2 |
| #2486 | 2 |
| #2416 | 2 |
| #2408 | 2 |
| C4×#127 | 2 |