Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2414 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D42 | C2 | semidirect |
| 2. #2679 | C2 | semidirect |
| 3. #2537 | C2 | semidirect |
| 4. #2408 | C2 | semidirect |
| 5. C4×#127 | C2 | semidirect |
| 6. C23×D4 | C22 | semidirect |
| 9. C2×#121 | C22 | semidirect |
| 10. C2×#120 | C22 | semidirect |
| 11. C2×C4×D4 | C22 | semidirect |
| 12. C2×C4×D4 | C22 | semidirect |
| 13. #394 | C22 | semidirect |
| 14. #392 | C22 | semidirect |
| 15. #390 | C22 | semidirect |
| 16. #390 | C22 | semidirect |
| 17. #384 | C22 | semidirect |
| 18. #380 | C22 | semidirect |
| 19. #379 | C22 | semidirect |
| 20. C43 | C22 | semidirect |
| 28. #127 | D4 | semidirect |
| 53. C2×D4 | C2×D4 | semidirect |
| 54. C2×D4 | C2×D4 | semidirect |
| 68. C42 | C2×D4 | semidirect |
| 102. C4 | D42 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D42 | 2 |
| #2679 | 2 |
| #2537 | 2 |
| #2408 | 2 |
| C4×#127 | 2 |