Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3550 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D61 |
| commutator, socle, cosocle | C23×C61 | C25 |
| Fitting | C61×#2840 | C2 |
| prime radical | C25×D61 | C22 |
| hypercenter | #2840 | D61 |
| hypocenter | C61 | C2×#2840 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21454072 | C2 | semidirect |
| 2. #21454071 | C2 | semidirect |
| 3. #393×D61 | C2 | semidirect |
| 5. C61×#2840 | C2 | semidirect |
| 7. C22×Q8×D61 | C22 | semidirect |
| 9. #16839675 | C22 | semidirect |
| 10. #16839674 | C22 | semidirect |
| 11. #16839673 | C22 | semidirect |
| 14. #95×D61 | C22 | semidirect |
| 15. C61×#393 | C22 | semidirect |
| 18. C24×D61 | Q8 | semidirect |
| 21. C22×Dic122 | C23 | semidirect |
| 27. #14519684 | C23 | semidirect |
| 29. C22×Q8×C61 | C23 | semidirect |
| 31. #95×C61 | C23 | semidirect |
| 33. C24×C61 | C2×Q8 | semidirect |
| 40. C23×D61 | C2×Q8 | semidirect |
| 87. #2840 | D61 | direct (N × H) |
| 94. D61 | #2840 | direct (N × H) |
| 101. #393 | C2×D61 | semidirect |
| 106. C61 | C2×#2840 | semidirect |
| 114. C22×Q8 | C22×D61 | semidirect |
| 121. #95 | C22×D61 | semidirect |
| 131. C24 | Q8×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454072 | 2 |
| #21454071 | 2 |
| #393×D61 | 2 |
| #379×D61 | 2 |
| C61×#2840 | 2 |
| C2×#2840 | 61 |