Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1631 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 1631 conjugacy classes of subgroups — too many to draw. Only its 463 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 |
| prime radical | C26 | C22 |
| 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. #2842 | C2 | semidirect |
| 2. #2840 | C2 | semidirect |
| 3. #2626 | C2 | semidirect |
| 4. #2437 | C2 | semidirect |
| 7. C2×C22⋊Q8 | C22 | semidirect |
| 10. #399 | C22 | semidirect |
| 11. #399 | C22 | semidirect |
| 12. #396 | C22 | semidirect |
| 13. #396 | C22 | semidirect |
| 14. #393 | C22 | semidirect |
| 15. #393 | C22 | semidirect |
| 16. #385 | C22 | semidirect |
| 17. #380 | C22 | semidirect |
| 23. C25 | Q8 | semidirect |
| 27. C22×Q8 | C23 | semidirect |
| 30. C2×C4⋊C4 | C23 | semidirect |
| 31. C2×C4⋊C4 | C23 | semidirect |
| 40. #95 | C23 | semidirect |
| 41. #95 | C23 | semidirect |
| 42. #95 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2842 | 2 |
| #2840 | 2 |
| #2626 | 2 |
| #2437 | 2 |
| C2×#379 | 2 |