Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
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×D457 |
| commutator, socle, cosocle | C22×C457 | C24 |
| Fitting | C22⋊Q8×C457 | C2 |
| hypercenter | C22⋊Q8 | D457 |
| hypocenter | C457 | #562 |
| LCS | G ▷ C22×C457 ▷ C457 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28410542 | C2 | semidirect |
| 2. #28410541 | C2 | semidirect |
| 3. #28410538 | C2 | semidirect |
| 4. #28410537 | C2 | semidirect |
| 5. #28410537 | C2 | semidirect |
| 6. #28410535 | C2 | semidirect |
| 7. #28410534 | C2 | semidirect |
| 8. #28410532 | C2 | semidirect |
| 9. #28410530 | C2 | semidirect |
| 10. #28410528 | C2 | semidirect |
| 11. #28410527 | C2 | semidirect |
| 12. #28410526 | C2 | semidirect |
| 13. #28410525 | C2 | semidirect |
| 14. #28410525 | C2 | semidirect |
| 15. C22⋊Q8×C457 | C2 | semidirect |
| 109. C457 | #562 | semidirect |
| 121. C22⋊Q8 | D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410542 | 2 |
| #28410541 | 2 |
| #28410538 | 2 |
| #28410537 | 2 |
| #28410535 | 2 |
| #28410534 | 2 |
| #28410532 | 2 |
| #28410530 | 2 |
| #28410528 | 2 |
| #28410527 | 2 |
| #28410526 | 2 |
| #28410525 | 2 |
| C22⋊Q8×C457 | 2 |
| #562 | 457 |