Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2622 conjugacy classes of subgroups.
The subgroup lattice has 308 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C61 | C23 |
| commutator | C22 | C24×C4×C61 |
| Frattini, cosocle | C23 | C25×C61 |
| socle, prime radical | C24×C61 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#125×C61 | C2 | direct (N × H) |
| 9. C2×#125×C61 | C4 | direct (N × H) |
| 37. #125×C61 | C2×C4 | direct (N × H) |
| 120. C2×C4×C61 | #125 | direct (N × H) |
| 130. C2×C4×#125 | C61 | direct (N × H) |
| 147. C4×C61 | C2×#125 | direct (N × H) |
| 149. C4×#125 | C2×C61 | direct (N × H) |
| 156. C2×C61 | C4×#125 | direct (N × H) |
| 162. C2×#125 | C4×C61 | direct (N × H) |
| 183. C61 | C2×C4×#125 | direct (N × H) |
| 191. #125 | C2×C4×C61 | direct (N × H) |
| 274. C2×C4 | #125×C61 | direct (N × H) |
| 300. C4 | C2×#125×C61 | direct (N × H) |
| 301. C2 | C4×#125×C61 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#125×C61 | 2 |
| C4×#125×C61 | 2 |
| C2×C61×#389 | 2 |
| C2×C61×#387 | 2 |
| C2×C61×#382 | 2 |
| C2×C4×C4⋊C4×C61 | 2 |
| C2×C43×C61 | 2 |
| C2×C4×#125 | 61 |