Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
518 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×#6923 |
| commutator, socle | C22×C61 | C43 |
| Fitting | C82×C61 | C4 |
| prime radical | C22×D61 | C2×C42 |
| cosocle | C42×D61 | C23 |
| hypercenter | C82 | #6923 |
| hypocenter | C61 | #7844 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #92420⋊C8 | C4 | semidirect |
| 12. #16840603 | C4 | semidirect |
| 15. C8×#92418 | C4 | semidirect |
| 16. C8×#92418 | C4 | semidirect |
| 17. C82×C61 | C4 | semidirect |
| 96. C82 | #6923 | semidirect |
| 97. C61 | #7844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461532 | 2 |
| C4×#14519831 | 2 |
| #21461015 | 2 |
| #21461013 | 2 |
| C82×D61 | 2 |
| #7844 | 61 |