Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2189 conjugacy classes of subgroups; only the 527 normal subgroups are shown.
This group has 2189 conjugacy classes of subgroups — too many to draw. Only its 527 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 |
| prime radical | C22×#120 | C2 |
| 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 |
|---|---|---|
| 2. C23×C22⋊C4 | C2 | semidirect |
| 3. #2622 | C2 | direct (N × H) |
| 4. C2×#397 | C2 | semidirect |
| 5. C2×#394 | C2 | semidirect |
| 6. C2×#386 | C2 | semidirect |
| 7. C2×#385 | C2 | semidirect |
| 8. C2×#379 | C2 | semidirect |
| 15. C22×C4⋊C4 | C22 | semidirect |
| 22. C22×C22⋊C4 | C22 | semidirect |
| 23. C22×C22⋊C4 | C22 | semidirect |
| 24. #397 | C22 | semidirect |
| 25. #394 | C22 | semidirect |
| 26. #386 | C22 | semidirect |
| 27. #385 | C22 | semidirect |
| 28. #379 | C22 | semidirect |
| 29. C2×#95 | C22 | semidirect |
| 30. C2×#95 | C22 | semidirect |
| 53. C2×C4⋊C4 | C23 | semidirect |
| 66. C2×C22⋊C4 | C23 | semidirect |
| 67. #95 | C23 | semidirect |
| 68. #95 | C23 | semidirect |
| 191. C2 | #2622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#120 | 2 |
| C23×C22⋊C4 | 2 |
| #2622 | 2 |
| C2×#397 | 2 |
| C2×#394 | 2 |
| C2×#386 | 2 |
| C2×#385 | 2 |
| C2×#379 | 2 |