Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
4291 conjugacy classes of subgroups; only the 751 normal subgroups are shown.
This group has 4291 conjugacy classes of subgroups — too many to draw. Only its 751 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C24 |
| commutator, Frattini, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ 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. C22×#121 | C2 | semidirect |
| 3. C22×#120 | C2 | semidirect |
| 4. #2847 | C2 | direct (N × H) |
| 5. C2×#386 | C2 | semidirect |
| 6. C2×#380 | C2 | semidirect |
| 9. C23×D4 | C22 | semidirect |
| 13. C24×C4 | C22 | semidirect |
| 15. C2×#121 | C22 | semidirect |
| 17. C2×#120 | C22 | semidirect |
| 18. C22×C4⋊C4 | C22 | semidirect |
| 20. C22×C22⋊C4 | C22 | semidirect |
| 21. #386 | C22 | semidirect |
| 22. #380 | C22 | semidirect |
| 23. C2×#95 | C22 | semidirect |
| 26. C25 | D4 | semidirect |
| 35. C22×D4 | C23 | semidirect |
| 41. C23×C4 | D4 | semidirect |
| 50. C2×C4⋊C4 | C23 | semidirect |
| 54. C2×C22⋊C4 | C23 | semidirect |
| 55. #95 | C23 | semidirect |
| 68. C24 | C2×D4 | semidirect |
| 91. C22×C4 | C2×D4 | semidirect |
| 114. C23 | #121 | semidirect |
| 132. C2×C4 | #120 | semidirect |
| 147. C22 | C2×#121 | semidirect |
| 154. C4 | C2×#120 | semidirect |
| 157. C2 | #2847 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4 | 2 |
| C22×#121 | 2 |
| C22×#120 | 2 |
| #2847 | 2 |
| C2×#386 | 2 |
| C2×#380 | 2 |