Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D43 |
| commutator, socle, cosocle | C23×C43 | C25 |
| Fitting | C43×#2840 | C2 |
| hypercenter | #2840 | D43 |
| hypocenter | C43 | #36675 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19142786 | C2 | semidirect |
| 2. #19142679 | C2 | semidirect |
| 3. #19142592 | C2 | semidirect |
| 4. #19137877 | C2 | semidirect |
| 5. #19137812 | C2 | semidirect |
| 6. #19137094 | C2 | semidirect |
| 7. C43×#2840 | C2 | semidirect |
| 8. C22×#10621902 | C22 | semidirect |
| 11. C2×Q8×Dic43 | C22 | semidirect |
| 13. #14582841 | C22 | semidirect |
| 14. #14582826 | C22 | semidirect |
| 16. #14582818 | C22 | semidirect |
| 17. #14582817 | C22 | semidirect |
| 19. #14582810 | C22 | semidirect |
| 24. #14582746 | C22 | semidirect |
| 25. #14582744 | C22 | semidirect |
| 57. C24×C43 | #41 | semidirect |
| 126. #2840 | D43 | semidirect |
| 159. C43 | #36675 | semidirect |
| 189. C24 | #10621902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19142786 | 2 |
| #19142679 | 2 |
| #19142592 | 2 |
| #19137877 | 2 |
| #19137812 | 2 |
| #19137094 | 2 |
| C43×#2840 | 2 |
| #36675 | 43 |