Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1746 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C4×Q8×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C61×#3390 | C2 | direct (N × H) |
| 49. C2×Q16×C61 | Q8 | semidirect |
| 120. Q16×C61 | C2×Q8 | semidirect |
| 179. C2×#3390 | C61 | direct (N × H) |
| 196. #3390 | C2×C61 | direct (N × H) |
| 205. C2×C61 | #3390 | direct (N × H) |
| 244. C61 | C2×#3390 | direct (N × H) |
| 248. C2×Q16 | Q8×C61 | semidirect |
| 319. Q16 | C2×Q8×C61 | semidirect |
| 393. C2 | C61×#3390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C61×#557 | 2 |
| C61×#3390 | 2 |
| C2×C61×#501 | 2 |
| C2×C61×#499 | 2 |
| C2×C61×#479 | 2 |
| C2×C61×#477 | 2 |
| C2×C61×#446 | 2 |
| C2×C61×#441 | 2 |
| C2×C4×Q16×C61 | 2 |
| C2×#3390 | 61 |