Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
900 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C22×C22⋊C4×C79 | C2 |
| hypercenter | C22×C22⋊C4 | D79 |
| hypocenter | C79 | #2539 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579144 | C2 | semidirect |
| 2. C2×#14579135 | C2 | semidirect |
| 3. C2×#14579130 | C2 | semidirect |
| 4. #19098499 | C2 | semidirect |
| 5. #19098472 | C2 | semidirect |
| 6. #19098463 | C2 | semidirect |
| 7. C4×C22⋊Dic79 | C2 | semidirect |
| 8. C22×C22⋊C4×C79 | C2 | semidirect |
| 9. C22×D316 | C22 | semidirect |
| 15. C2×C4⋊Dic79 | C22 | semidirect |
| 16. C2×Dic79⋊C4 | C22 | semidirect |
| 19. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D79)⋊C4 | C22 | semidirect |
| 21. C2×C4×Dic79 | C22 | semidirect |
| 22. C79⋊#95 | C22 | semidirect |
| 43. C22⋊Dic79 | D4 | semidirect |
| 56. C22×C4×C79 | D4 | semidirect |
| 130. C79 | #2539 | semidirect |
| 134. C22×C22⋊C4 | D79 | semidirect |
| 179. C22×C4 | C22⋊D79 | semidirect |