Finite Group DatabasebetaFinite Group DatabasebetaOrder 10048.
206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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 | #125×C157 | C2 |
| prime radical | C22×D157 | C23 |
| hypercenter | #125 | D157 |
| hypocenter | C157 | #544 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19097771 | C2 | semidirect |
| 2. #19097770 | C2 | semidirect |
| 3. #19097770 | C2 | semidirect |
| 4. #19097762 | C2 | semidirect |
| 5. #19097761 | C2 | semidirect |
| 11. #125×C157 | C2 | semidirect |
| 44. C4×D157 | Q8 | semidirect |
| 68. C157 | #544 | semidirect |
| 75. #125 | D157 | semidirect |