Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2615 conjugacy classes of subgroups; only the 823 normal subgroups are shown.
This group has 2615 conjugacy classes of subgroups — too many to draw. Only its 823 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C23 |
| commutator, Frattini, cosocle | C23 | C25 |
| prime radical | C26 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4⋊C4 | C2 | semidirect |
| 4. C2×#397 | C2 | direct (N × H) |
| 5. C22×#95 | C2 | semidirect |
| 6. C22×#95 | C2 | semidirect |
| 13. C22×C4⋊C4 | C22 | semidirect |
| 18. #397 | C22 | direct (N × H) |
| 19. C2×#95 | C22 | semidirect |
| 20. C2×#95 | C22 | semidirect |
| 43. C2×C4⋊C4 | C23 | semidirect |
| 48. #95 | C23 | semidirect |
| 49. #95 | C23 | semidirect |
| 130. C22 | #397 | direct (N × H) |
| 146. C2 | C2×#397 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4 | 2 |
| C23×C22⋊C4 | 2 |
| C2×#397 | 2 |
| C22×#95 | 2 |