Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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×D241 |
| commutator, socle, cosocle | C22×C241 | C24 |
| Fitting | #117×C241 | C2 |
| prime radical | C2×C22⋊D241 | C22 |
| hypercenter | #117 | D241 |
| hypocenter | C241 | #556 |
| LCS | G ▷ C22×C241 ▷ C241 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21440641 | C2 | semidirect |
| 2. #21440636 | C2 | semidirect |
| 3. #21440635 | C2 | semidirect |
| 5. #21440622 | C2 | semidirect |
| 6. #21440621 | C2 | semidirect |
| 7. C4×Dic482 | C2 | semidirect |
| 8. #21440607 | C2 | semidirect |
| 10. #21440600 | C2 | semidirect |
| 11. #117×C241 | C2 | semidirect |
| 72. C241 | #556 | semidirect |
| 84. #117 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440641 | 2 |
| #21440636 | 2 |
| #21440635 | 2 |
| #21440628 | 2 |
| #21440622 | 2 |
| #21440621 | 2 |
| C4×Dic482 | 2 |
| #21440607 | 2 |
| C4×C22⋊D241 | 2 |
| #21440600 | 2 |
| #117×C241 | 2 |
| #556 | 241 |