Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
3769 conjugacy classes of subgroups; only the 631 normal subgroups are shown.
This group has 3769 conjugacy classes of subgroups — too many to draw. Only its 631 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C24 |
| commutator, Frattini, socle, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C4 | C2 | semidirect |
| 2. C2×#525 | C2 | semidirect |
| 3. #2849 | C2 | semidirect |
| 4. #2848 | C2 | semidirect |
| 5. #2847 | C2 | semidirect |
| 6. #2846 | C2 | semidirect |
| 7. C4×#120 | C2 | semidirect |
| 8. #2280 | C2 | semidirect |
| 10. C22×#41 | C22 | semidirect |
| 17. C2×#123 | C22 | semidirect |
| 18. C2×C22⋊Q8 | C22 | semidirect |
| 19. C2×#121 | C22 | semidirect |
| 22. C2×C4×D4 | C22 | semidirect |
| 23. C2×#117 | C22 | semidirect |
| 24. #386 | C22 | semidirect |
| 25. #385 | C22 | semidirect |
| 26. #381 | C22 | semidirect |
| 27. #380 | C22 | semidirect |
| 30. C4×C22⋊C4 | C22 | semidirect |
| 36. C22×Q8 | C23 | semidirect |
| 39. C22×D4 | C23 | semidirect |
| 46. C23×C4 | D4 | semidirect |
| 52. C23×C4 | C23 | semidirect |
| 60. C2×C4⋊C4 | C23 | semidirect |
| 61. C2×C4⋊C4 | C23 | semidirect |
| 65. C2×C22⋊C4 | C23 | semidirect |
| 66. C2×C42 | C23 | semidirect |
| 67. #95 | C23 | semidirect |
| 75. C24 | #41 | semidirect |
| 140. C2×C4 | #120 | semidirect |
| 153. C22 | #525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4 | 2 |
| C2×#525 | 2 |
| #2849 | 2 |
| #2848 | 2 |
| #2847 | 2 |
| #2846 | 2 |
| C4×#120 | 2 |
| #2280 | 2 |