Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
540 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 90 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×Q8 | C23×C61 |
| prime radical | C2×2−1+4×C61 | C22 |
| LCS | G ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C61 ◁ C22×Q8×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#2809 | C2 | semidirect |
| 4. C61×#1394 | C2 | semidirect |
| 5. C61×#1394 | C2 | semidirect |
| 139. #13379 | C61 | direct (N × H) |
| 157. #2809 | C2×C61 | semidirect |
| 160. #1394 | C2×C61 | semidirect |
| 161. #1394 | C2×C61 | semidirect |
| 181. C61 | #13379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2809 | 2 |
| C61×#1793 | 2 |
| C61×#1394 | 2 |
| #13379 | 61 |