Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
3311 conjugacy classes of subgroups; only the 583 normal subgroups are shown.
This group has 3311 conjugacy classes of subgroups — too many to draw. Only its 583 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×#120 | C2 | semidirect |
| 2. #2679 | C2 | direct (N × H) |
| 3. C2×#394 | C2 | semidirect |
| 4. C2×#390 | C2 | semidirect |
| 5. C26 | C22 | semidirect |
| 9. C2×#120 | C22 | semidirect |
| 10. C22×C4⋊C4 | C22 | semidirect |
| 11. C22×C22⋊C4 | C22 | semidirect |
| 12. C22×C22⋊C4 | C22 | semidirect |
| 13. C22×C42 | C22 | semidirect |
| 14. #394 | C22 | semidirect |
| 15. #390 | C22 | semidirect |
| 16. C2×#95 | C22 | semidirect |
| 21. C25 | C23 | semidirect |
| 26. C22×D4 | D4 | semidirect |
| 33. C2×C4⋊C4 | C23 | semidirect |
| 36. C2×C22⋊C4 | C23 | semidirect |
| 37. C2×C22⋊C4 | C23 | semidirect |
| 39. C2×C42 | C23 | semidirect |
| 40. #95 | C23 | semidirect |
| 60. C2×D4 | C2×D4 | semidirect |
| 115. C2 | #2679 | 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 |
| #2679 | 2 |
| C2×#394 | 2 |
| C2×#390 | 2 |