Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 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 | C2×#127×C79 | C2 |
| hypercenter | C2×#127 | D79 |
| hypocenter | C79 | #2431 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11929623 | C2 | semidirect |
| 2. C2×#14579148 | C2 | semidirect |
| 3. C2×#14579132 | C2 | semidirect |
| 4. #19098471 | C2 | semidirect |
| 5. #19098469 | C2 | semidirect |
| 6. #19098466 | C2 | semidirect |
| 7. #19098443 | C2 | semidirect |
| 8. C4×(C2×D79)⋊C4 | C2 | semidirect |
| 9. C2×#127×C79 | C2 | semidirect |
| 37. C2×Dic158 | D4 | semidirect |
| 52. C2×C4×D79 | D4 | semidirect |
| 69. C2×D4×C79 | D4 | semidirect |
| 97. C2×C4×C79 | #41 | semidirect |
| 149. C79 | #2431 | semidirect |
| 151. C2×#127 | D79 | semidirect |
| 202. C2×D4 | C22⋊D79 | semidirect |
| 262. C2×C4 | #11929623 | semidirect |