Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
10698 conjugacy classes of subgroups; only the 3815 normal subgroups are shown.
This group has 10698 conjugacy classes of subgroups — too many to draw. Only its 3815 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C24×D244 |
| commutator, cosocle | C4×C61 | C26 |
| Frattini | C4 | C25×D61 |
| Fitting | C61×#3573 | C2 |
| socle | C2×C61 | C24×D4 |
| hypercenter | #3573 | D61 |
| hypocenter | C61 | #63093 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ #585 ◁ #3573 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21460632 | C2 | semidirect |
| 2. #21460607 | C2 | semidirect |
| 3. #21460593 | C2 | semidirect |
| 4. C2×#16840579 | C2 | semidirect |
| 5. C61×#3573 | C2 | semidirect |
| 6. #16840598 | C22 | semidirect |
| 8. C2×#14519824 | C22 | semidirect |
| 10. #16840579 | C22 | semidirect |
| 11. #16840579 | C22 | semidirect |
| 12. #16840574 | C22 | semidirect |
| 13. #16840567 | C22 | semidirect |
| 14. #16840562 | C22 | semidirect |
| 15. C2×#14519810 | C22 | semidirect |
| 16. C2×#14519799 | C22 | semidirect |
| 17. C22×Dic244 | C22 | semidirect |
| 19. C61×#568 | C22 | semidirect |
| 20. C2×#131×C61 | C22 | semidirect |
| 98. #3573 | D61 | semidirect |
| 115. #568 | C2×D61 | semidirect |
| 116. C2×#131 | C2×D61 | semidirect |
| 117. C61 | #63093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460632 | 2 |
| #21460607 | 2 |
| #21460593 | 2 |
| C2×#16840579 | 2 |
| C61×#3573 | 2 |
| #63093 | 61 |