Finite Group DatabasebetaFinite Group DatabasebetaOrder 10048.
236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C4×D4×C157 | C2 |
| hypercenter | C4×D4 | D157 |
| hypocenter | C157 | #555 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19097771 | C2 | semidirect |
| 2. #19097757 | C2 | semidirect |
| 3. #19097745 | C2 | semidirect |
| 4. #19097742 | C2 | semidirect |
| 5. C4×D628 | C2 | semidirect |
| 6. #19097730 | C2 | semidirect |
| 7. #19097729 | C2 | semidirect |
| 8. C4×D4×C157 | C2 | semidirect |
| 57. C157 | #555 | semidirect |
| 64. C4×D4 | D157 | semidirect |