Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C61 | C24 |
| commutator | C22 | C24×C4×C61 |
| Frattini, cosocle | C2×C4 | C25×C61 |
| socle | C23×C61 | C23×C4 |
| prime radical | C25×C61 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C61×#2905 | C2 | direct (N × H) |
| 4. C2×C61×#424 | C2 | semidirect |
| 5. C2×C61×#423 | C2 | semidirect |
| 19. C61×#424 | C22 | semidirect |
| 20. C61×#423 | C22 | semidirect |
| 21. C2×C4⋊C8×C61 | C22 | semidirect |
| 51. C4⋊C8×C61 | C23 | semidirect |
| 118. C2×#2905 | C61 | direct (N × H) |
| 137. #2905 | C2×C61 | direct (N × H) |
| 138. C2×#424 | C2×C61 | semidirect |
| 139. C2×#423 | C2×C61 | semidirect |
| 142. C2×C61 | #2905 | direct (N × H) |
| 158. #424 | C22×C61 | semidirect |
| 159. #423 | C22×C61 | semidirect |
| 160. C2×C4⋊C8 | C22×C61 | semidirect |
| 161. C61 | C2×#2905 | direct (N × H) |
| 191. C4⋊C8 | C23×C61 | semidirect |
| 276. C2 | C61×#2905 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×M16×C61 | 2 |
| C22×#117×C61 | 2 |
| C61×#2905 | 2 |
| C2×C61×#424 | 2 |
| C2×C61×#423 | 2 |
| C2×#2905 | 61 |