Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
582 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 582 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 | #398×C79 | C2 |
| prime radical | #19098473 | C2 |
| hypercenter | #398 | D79 |
| hypocenter | C79 | #2603 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #398 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579156 | C2 | semidirect |
| 2. C2×#14579123 | C2 | semidirect |
| 3. #19098489 | C2 | semidirect |
| 4. #19098480 | C2 | semidirect |
| 6. #19098464 | C2 | semidirect |
| 7. #19098455 | C2 | semidirect |
| 8. #19098441 | C2 | semidirect |
| 9. #19098434 | C2 | semidirect |
| 10. #19098408 | C2 | semidirect |
| 11. #398×C79 | C2 | semidirect |
| 62. C4×Dic79 | D4 | semidirect |
| 144. C79 | #2603 | semidirect |
| 147. #398 | D79 | semidirect |