Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 440 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 | C22×D316 | C22 |
| hypercenter | #382 | D79 |
| hypocenter | C79 | #2513 |
| 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. #19098492 | C2 | semidirect |
| 2. #19098490 | C2 | semidirect |
| 6. #19098462 | C2 | semidirect |
| 7. #19098455 | C2 | semidirect |
| 8. #19098452 | C2 | semidirect |
| 9. C4⋊C4×Dic79 | C2 | semidirect |
| 10. C4×Dic79⋊C4 | C2 | semidirect |
| 11. #382×C79 | C2 | semidirect |
| 137. C79 | #2513 | semidirect |
| 146. #382 | D79 | semidirect |