Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
562 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 137 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 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #382×C79 | C2 |
| prime radical | #19098473 | C2 |
| hypercenter | #382 | D79 |
| hypocenter | C79 | #2636 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579155 | C2 | semidirect |
| 2. C2×C4×D316 | C2 | semidirect |
| 3. #19098503 | C2 | semidirect |
| 4. #19098500 | C2 | semidirect |
| 5. #19098485 | C2 | semidirect |
| 6. #19098481 | C2 | semidirect |
| 7. #19098480 | C2 | semidirect |
| 9. #19098441 | C2 | semidirect |
| 10. #19098437 | C2 | semidirect |
| 11. #382×C79 | C2 | semidirect |
| 70. C42×C79 | D4 | semidirect |
| 144. C79 | #2636 | semidirect |
| 155. #382 | D79 | semidirect |
| 214. C42 | D316 | semidirect |