Finite Group DatabasebetaFinite Group DatabasebetaOrder 10048.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D157 |
| commutator, socle, cosocle | C22×C157 | C24 |
| Fitting | C22⋊Q8×C157 | C2 |
| hypercenter | C22⋊Q8 | D157 |
| hypocenter | C157 | #562 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19097761 | C2 | semidirect |
| 2. #19097760 | C2 | semidirect |
| 3. #19097757 | C2 | semidirect |
| 4. #19097756 | C2 | semidirect |
| 5. #19097756 | C2 | semidirect |
| 6. #19097754 | C2 | semidirect |
| 7. #19097753 | C2 | semidirect |
| 8. #19097751 | C2 | semidirect |
| 9. #19097749 | C2 | semidirect |
| 10. #19097747 | C2 | semidirect |
| 11. #19097746 | C2 | semidirect |
| 12. #19097745 | C2 | semidirect |
| 13. #19097744 | C2 | semidirect |
| 14. #19097744 | C2 | semidirect |
| 15. C22⋊Q8×C157 | C2 | semidirect |
| 109. C157 | #562 | semidirect |
| 121. C22⋊Q8 | D157 | semidirect |