Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
5481 conjugacy classes of subgroups; only the 3135 normal subgroups are shown.
This group has 5481 conjugacy classes of subgroups — too many to draw. Only its 3135 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 | C22 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×2−1+4 | C2 | semidirect |
| 2. #3497 | C2 | semidirect |
| 3. #3487 | C2 | semidirect |
| 4. #3486 | C2 | semidirect |
| 5. #3449 | C2 | semidirect |
| 6. C2×#519 | C2 | semidirect |
| 9. C2×2−1+4 | C22 | semidirect |
| 11. C22×#41 | C22 | semidirect |
| 13. C23×Q8 | C22 | semidirect |
| 14. #550 | C22 | semidirect |
| 15. D4×Q8 | C22 | semidirect |
| 16. #548 | C22 | semidirect |
| 17. #537 | C22 | semidirect |
| 18. #536 | C22 | semidirect |
| 19. #535 | C22 | semidirect |
| 21. #532 | C22 | semidirect |
| 22. #525 | C22 | semidirect |
| 23. #519 | C22 | semidirect |
| 24. C2×C4×Q8 | C22 | semidirect |
| 34. C22×Q8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×2−1+4 | 2 |
| #3497 | 2 |
| #3487 | 2 |
| #3486 | 2 |
| #3449 | 2 |
| C2×#519 | 2 |