Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
10894 conjugacy classes of subgroups; only the 3815 normal subgroups are shown.
This group has 10894 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 | #63091 |
| 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. #21460630 | C2 | semidirect |
| 2. #21460600 | C2 | semidirect |
| 3. #21460593 | C2 | semidirect |
| 4. C2×#16840567 | C2 | semidirect |
| 5. C61×#3573 | C2 | semidirect |
| 7. #16840598 | C22 | semidirect |
| 8. C2×#14519823 | C22 | semidirect |
| 10. #16840579 | C22 | semidirect |
| 11. #16840574 | C22 | semidirect |
| 12. #16840567 | C22 | semidirect |
| 13. #16840567 | C22 | semidirect |
| 14. #16840562 | C22 | semidirect |
| 15. C2×#14519805 | C22 | semidirect |
| 16. C2×#14519799 | C22 | semidirect |
| 17. C22×D488 | C22 | semidirect |
| 19. C61×#568 | C22 | semidirect |
| 20. C2×#131×C61 | C22 | semidirect |
| 22. #14519824 | C23 | semidirect |
| 24. #14519823 | C23 | semidirect |
| 27. C2×#11758222 | C23 | semidirect |
| 29. C22×D244 | C23 | semidirect |
| 31. #14519810 | C23 | semidirect |
| 32. #14519805 | C23 | semidirect |
| 33. #14519799 | C23 | semidirect |
| 34. #14519799 | C23 | semidirect |
| 35. C2×Dic244 | C23 | semidirect |
| 36. C2×#11758190 | C23 | semidirect |
| 37. C2×D488 | C23 | semidirect |
| 38. C2×D488 | C23 | semidirect |
| 42. #131×C61 | C23 | semidirect |
| 43. #131×C61 | C23 | semidirect |
| 44. C2×M16×C61 | C23 | semidirect |
| 45. C22×C8×C61 | C23 | semidirect |
| 99. #3573 | D61 | semidirect |
| 116. #568 | C2×D61 | semidirect |
| 117. C2×#131 | C2×D61 | semidirect |
| 118. C61 | #63091 | semidirect |
| 140. #131 | C22×D61 | semidirect |
| 141. #131 | C22×D61 | semidirect |
| 142. C2×M16 | C22×D61 | semidirect |
| 143. C22×C8 | C22×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460630 | 2 |
| #21460600 | 2 |
| #21460593 | 2 |
| C2×#16840567 | 2 |
| C61×#3573 | 2 |
| #63091 | 61 |