Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
240 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #99 |
| commutator | C23 | C2×C16×C61 |
| Frattini, cosocle | C2×C22⋊C8 | C22×C61 |
| socle | C22×C61 | #323 |
| prime radical | C24×C61 | C2×C8 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C22×C4×C61 ◁ C2×C22⋊C8×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 31. C22×C4×C61 | C16 | semidirect |
| 68. #7055 | C61 | direct (N × H) |
| 100. C61 | #7055 | direct (N × H) |
| 124. C22×C4 | C16×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#1817 | 2 |
| C61×#1314 | 2 |
| #7055 | 61 |