Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
3358 conjugacy classes of subgroups.
The subgroup lattice has 320 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 |
|---|---|---|
| 3. C4×C4⋊Q8×C61 | C2 | direct (N × H) |
| 10. C2×C4⋊Q8×C61 | C4 | direct (N × H) |
| 41. C4⋊Q8×C61 | C2×C4 | direct (N × H) |
| 56. C2×C42×C61 | Q8 | semidirect |
| 103. C42×C61 | C2×Q8 | semidirect |
| 123. C2×C4×C61 | C4×Q8 | semidirect |
| 124. C2×C4×C61 | C4⋊Q8 | direct (N × H) |
| 136. C2×C4×C4⋊Q8 | C61 | direct (N × H) |
| 152. C4×C61 | C2×C4×Q8 | semidirect |
| 153. C4×C61 | C2×C4⋊Q8 | direct (N × H) |
| 156. C4×C4⋊Q8 | C2×C61 | direct (N × H) |
| 162. C2×C61 | C4×C4⋊Q8 | direct (N × H) |
| 169. C2×C4⋊Q8 | C4×C61 | direct (N × H) |
| 189. C61 | C2×C4×C4⋊Q8 | direct (N × H) |
| 201. C4⋊Q8 | C2×C4×C61 | direct (N × H) |
| 216. C2×C42 | Q8×C61 | semidirect |
| 263. C42 | C2×Q8×C61 | semidirect |
| 283. C2×C4 | C4×Q8×C61 | semidirect |
| 284. C2×C4 | C4⋊Q8×C61 | direct (N × H) |
| 311. C4 | C2×C4×Q8×C61 | semidirect |
| 312. C4 | C2×C4⋊Q8×C61 | direct (N × H) |
| 313. C2 | C4×C4⋊Q8×C61 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Q8×C61 | 2 |
| C22×C4×Q8×C61 | 2 |
| C4×C4⋊Q8×C61 | 2 |
| C2×C61×#391 | 2 |
| C2×C61×#389 | 2 |
| C2×C61×#384 | 2 |
| C2×C4×C4⋊C4×C61 | 2 |
| C2×C43×C61 | 2 |
| C2×C4×C4⋊Q8 | 61 |