Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
268 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #331 |
| commutator | C42 | C2×C8×C61 |
| Frattini, cosocle | C43 | C22×C61 |
| socle | C2×C61 | #1270 |
| prime radical | C61×#532 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ C43×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C61×#1276 | C2 | semidirect |
| 10. C4⋊Q8×C61 | C8 | semidirect |
| 11. #127×C61 | C8 | semidirect |
| 67. #7106 | C61 | direct (N × H) |
| 82. #1276 | C2×C61 | semidirect |
| 92. C61 | #7106 | direct (N × H) |
| 95. C4⋊Q8 | C8×C61 | semidirect |
| 96. #127 | C8×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#1962 | 2 |
| C61×#1276 | 2 |
| #7106 | 61 |