Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
134 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C22×D61 |
| commutator, socle | C2×C61 | C22×C32 |
| Fitting | C61×M128 | C2 |
| prime radical | C22×D61 | C32 |
| cosocle | C32×C61 | C23 |
| hypercenter | M128 | D61 |
| hypocenter | C61 | C2×M128 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C32 ◁ M128 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21444030 | C2 | semidirect |
| 3. #21444029 | C2 | semidirect |
| 4. C64×D61 | C2 | semidirect |
| 5. C61×M128 | C2 | semidirect |
| 12. #16839481 | C22 | semidirect |
| 14. C61×C64 | C22 | semidirect |
| 60. M128 | D61 | direct (N × H) |
| 65. D61 | M128 | direct (N × H) |
| 74. C64 | C2×D61 | semidirect |
| 75. C61 | C2×M128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D61 | 2 |
| #21444030 | 2 |
| #21444029 | 2 |
| C64×D61 | 2 |
| C61×M128 | 2 |
| C2×M128 | 61 |