Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
944 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Frattini | C23 | C23×D79 |
| Fitting | C22×#41×C79 | C2 |
| hypercenter | C22×#41 | D79 |
| hypocenter | C79 | #2388 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C22⋊D79 | C2 | semidirect |
| 2. #19098482 | C2 | semidirect |
| 3. #19098477 | C2 | semidirect |
| 4. #19098474 | C2 | semidirect |
| 5. #19098471 | C2 | semidirect |
| 6. C4×C22⋊Dic79 | C2 | semidirect |
| 7. C22×#41×C79 | C2 | semidirect |
| 41. C22×C4×C79 | D4 | semidirect |
| 52. C22×D79 | #41 | semidirect |
| 65. C2×Dic79 | #41 | semidirect |
| 89. C79 | #2388 | semidirect |
| 90. C22×#41 | D79 | semidirect |
| 125. C22×C4 | C22⋊D79 | semidirect |