Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
616 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#99 |
| commutator | C24 | C22×C4×C61 |
| Frattini, cosocle | C22×D4 | C23×C61 |
| prime radical | C22×D4×C61 | C23 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×C4×D4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C23×Q8×C61 | C4 | semidirect |
| 15. C61×#385 | C4 | semidirect |
| 16. C61×#380 | C4 | semidirect |
| 47. #99×C61 | Q8 | semidirect |
| 143. #13296 | C61 | direct (N × H) |
| 180. C23×Q8 | C4×C61 | semidirect |
| 190. #385 | C4×C61 | semidirect |
| 191. #380 | C4×C61 | semidirect |
| 195. C61 | #13296 | direct (N × H) |
| 223. #99 | Q8×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2409 | 2 |
| C61×#1800 | 2 |
| C4×#99×C61 | 2 |
| C61×#1390 | 2 |
| #13296 | 61 |