Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
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×D443 |
| commutator, socle, cosocle | C22×C443 | C24 |
| Fitting | C22⋊Q8×C443 | C2 |
| hypercenter | C22⋊Q8 | D443 |
| hypocenter | C443 | #562 |
| LCS | G ▷ C22×C443 ▷ C443 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28381876 | C2 | semidirect |
| 2. #28381875 | C2 | semidirect |
| 3. #28381872 | C2 | semidirect |
| 4. #28381871 | C2 | semidirect |
| 5. #28381871 | C2 | semidirect |
| 6. #28381869 | C2 | semidirect |
| 7. #28381868 | C2 | semidirect |
| 8. #28381866 | C2 | semidirect |
| 9. #28381864 | C2 | semidirect |
| 10. #28381862 | C2 | semidirect |
| 11. #28381861 | C2 | semidirect |
| 12. #28381860 | C2 | semidirect |
| 13. #28381859 | C2 | semidirect |
| 14. #28381859 | C2 | semidirect |
| 15. C22⋊Q8×C443 | C2 | semidirect |
| 109. C443 | #562 | semidirect |
| 121. C22⋊Q8 | D443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28381876 | 2 |
| #28381875 | 2 |
| #28381872 | 2 |
| #28381871 | 2 |
| #28381869 | 2 |
| #28381868 | 2 |
| #28381866 | 2 |
| #28381864 | 2 |
| #28381862 | 2 |
| #28381861 | 2 |
| #28381860 | 2 |
| #28381859 | 2 |
| C22⋊Q8×C443 | 2 |
| #562 | 443 |