Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
952 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 185 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×#41×C79 | C2 |
| hypercenter | C22×#41 | D79 |
| hypocenter | C79 | #2431 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579157 | C2 | semidirect |
| 2. C2×#14579150 | C2 | semidirect |
| 3. C2×#14579135 | C2 | semidirect |
| 4. #19098471 | C2 | semidirect |
| 5. #19098470 | C2 | semidirect |
| 6. #19098466 | C2 | semidirect |
| 7. #19098442 | C2 | semidirect |
| 8. C4×C22⋊Dic79 | C2 | semidirect |
| 9. C22×#41×C79 | C2 | semidirect |
| 57. C2×Q8×C79 | D4 | semidirect |
| 63. C2×D4×C79 | D4 | semidirect |
| 69. C22×C4×C79 | D4 | semidirect |
| 112. C2×Dic79 | #41 | semidirect |
| 149. C79 | #2431 | semidirect |
| 150. C22×#41 | D79 | semidirect |
| 188. C2×Q8 | C22⋊D79 | semidirect |
| 202. C2×D4 | C22⋊D79 | semidirect |
| 211. C22×C4 | C22⋊D79 | semidirect |