Finite Group DatabasebetaFinite Group DatabasebetaOrder 29632.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D463 |
| commutator, socle, cosocle | C22×C463 | C24 |
| Fitting | C22⋊Q8×C463 | C2 |
| hypercenter | C22⋊Q8 | D463 |
| hypocenter | C463 | #562 |
| LCS | G ▷ C22×C463 ▷ C463 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28414648 | C2 | semidirect |
| 2. #28414647 | C2 | semidirect |
| 3. #28414644 | C2 | semidirect |
| 4. #28414643 | C2 | semidirect |
| 5. #28414643 | C2 | semidirect |
| 6. #28414641 | C2 | semidirect |
| 7. #28414640 | C2 | semidirect |
| 8. #28414638 | C2 | semidirect |
| 9. #28414636 | C2 | semidirect |
| 10. #28414634 | C2 | semidirect |
| 11. #28414633 | C2 | semidirect |
| 12. #28414632 | C2 | semidirect |
| 13. #28414631 | C2 | semidirect |
| 14. #28414631 | C2 | semidirect |
| 15. C22⋊Q8×C463 | C2 | semidirect |
| 109. C463 | #562 | semidirect |
| 121. C22⋊Q8 | D463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414648 | 2 |
| #28414647 | 2 |
| #28414644 | 2 |
| #28414643 | 2 |
| #28414641 | 2 |
| #28414640 | 2 |
| #28414638 | 2 |
| #28414636 | 2 |
| #28414634 | 2 |
| #28414633 | 2 |
| #28414632 | 2 |
| #28414631 | 2 |
| C22⋊Q8×C463 | 2 |
| #562 | 463 |