Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14579129 |
| commutator, cosocle | C42×C79 | C23 |
| Frattini | C42 | C22×D79 |
| Fitting | #460×C79 | C2 |
| socle | C22×C79 | #120 |
| hypercenter | #460 | D79 |
| hypocenter | C79 | #1621 |
| LCS | G ▷ C42×C79 ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19099235 | C2 | semidirect |
| 2. #19098939 | C2 | semidirect |
| 3. #19098755 | C2 | semidirect |
| 4. #19098306 | C2 | semidirect |
| 5. Q8⋊(C79⋊C8) | C2 | semidirect |
| 6. #19098290 | C2 | semidirect |
| 7. #460×C79 | C2 | semidirect |
| 56. Q8×C79 | D8 | semidirect |
| 108. C79 | #1621 | semidirect |
| 111. #460 | D79 | semidirect |
| 164. Q8 | #11929609 | semidirect |