Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
134 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D32×D43 |
| commutator, cosocle | C32×C43 | C23 |
| Frattini | C32 | C22×D43 |
| Fitting | C43×D64 | C2 |
| socle | C2×C43 | C2×D32 |
| hypercenter | D64 | D43 |
| hypocenter | C43 | #13742 |
| LCS | G ▷ C32×C43 ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ D64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19136901 | C2 | semidirect |
| 2. D32×D43 | C2 | semidirect |
| 3. #19132811 | C2 | semidirect |
| 4. #19132810 | C2 | semidirect |
| 5. #19132807 | C2 | semidirect |
| 6. #19132805 | C2 | semidirect |
| 7. C43×D64 | C2 | semidirect |
| 10. Dic688 | C22 | semidirect |
| 15. C43⋊C64 | C22 | semidirect |
| 17. C43×D32 | C22 | semidirect |
| 18. C43×C64 | C22 | semidirect |
| 66. D64 | D43 | semidirect |
| 80. D32 | C2×D43 | semidirect |
| 83. C64 | C2×D43 | semidirect |
| 84. C43 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136901 | 2 |
| D32×D43 | 2 |
| #19132811 | 2 |
| #19132810 | 2 |
| #19132807 | 2 |
| #19132805 | 2 |
| C43×D64 | 2 |
| #13742 | 43 |