Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2391 conjugacy classes of subgroups; only the 647 normal subgroups are shown.
This group has 2391 conjugacy classes of subgroups — too many to draw. Only its 647 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. C22×#121 | C2 | semidirect |
| 2. C22×C4×D4 | C2 | semidirect |
| 3. #2537 | C2 | direct (N × H) |
| 4. C2×#394 | C2 | semidirect |
| 5. C2×#384 | C2 | semidirect |
| 6. C2×#380 | C2 | semidirect |
| 11. C2×#121 | C22 | semidirect |
| 13. C2×C4×D4 | C22 | semidirect |
| 20. #394 | C22 | semidirect |
| 21. #384 | C22 | semidirect |
| 22. #380 | C22 | semidirect |
| 29. C22×D4 | D4 | semidirect |
| 52. C2×C42 | D4 | semidirect |
| 70. C2×D4 | C2×D4 | semidirect |
| 95. C42 | C2×D4 | semidirect |
| 129. C2×C4 | #121 | semidirect |
| 155. C4 | C2×#121 | semidirect |
| 157. C2 | #2537 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#121 | 2 |
| C22×C4×D4 | 2 |
| #2537 | 2 |
| C2×#394 | 2 |
| C2×#384 | 2 |
| C2×#380 | 2 |