Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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×D431 |
| commutator, socle, cosocle | C22×C431 | C24 |
| Fitting | C4⋊Q8×C431 | C2 |
| prime radical | C2×D1724 | C22 |
| hypercenter | C4⋊Q8 | D431 |
| hypocenter | C431 | #554 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28352180 | C2 | semidirect |
| 2. #28352169 | C2 | semidirect |
| 3. #28352165 | C2 | semidirect |
| 4. C4×Dic862 | C2 | semidirect |
| 7. C4⋊C4×D431 | C2 | semidirect |
| 8. C4⋊Q8×C431 | C2 | semidirect |
| 27. D1724 | Q8 | semidirect |
| 53. C431 | #554 | semidirect |
| 55. C4⋊Q8 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352180 | 2 |
| #28352169 | 2 |
| #28352165 | 2 |
| C4×Dic862 | 2 |
| C4×D1724 | 2 |
| #28352151 | 2 |
| C4⋊C4×D431 | 2 |
| C4⋊Q8×C431 | 2 |
| #554 | 431 |