Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
502 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | D16 |
| commutator, Frattini, cosocle | C16 | C24×C61 |
| prime radical | C22×D16×C61 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C22×C4×C61 ◁ C22×C8×C61 ◁ C22×C16×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q32×C61 | C2 | semidirect |
| 3. C2×C61×SD64 | C2 | direct (N × H) |
| 4. C22×C32×C61 | C2 | semidirect |
| 8. C2×Q32×C61 | C22 | semidirect |
| 12. C61×SD64 | C22 | direct (N × H) |
| 13. C2×C32×C61 | C22 | semidirect |
| 22. Q32×C61 | C23 | semidirect |
| 27. C32×C61 | C23 | semidirect |
| 55. C22×SD64 | C61 | direct (N × H) |
| 58. C22×C61 | SD64 | direct (N × H) |
| 63. C22×Q32 | C2×C61 | semidirect |
| 65. C2×SD64 | C2×C61 | direct (N × H) |
| 66. C22×C32 | C2×C61 | semidirect |
| 68. C2×C61 | C2×SD64 | direct (N × H) |
| 73. C2×Q32 | C22×C61 | semidirect |
| 77. SD64 | C22×C61 | direct (N × H) |
| 78. C2×C32 | C22×C61 | semidirect |
| 79. C61 | C22×SD64 | direct (N × H) |
| 88. Q32 | C23×C61 | semidirect |
| 93. C32 | C23×C61 | semidirect |
| 123. C22 | C61×SD64 | direct (N × H) |
| 129. C2 | C2×C61×SD64 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q32×C61 | 2 |
| C22×D16×C61 | 2 |
| C2×C61×SD64 | 2 |
| C22×C32×C61 | 2 |
| C22×SD64 | 61 |