Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C22×C79 | C23×C4 |
| Fitting | #391×C79 | C2 |
| socle, prime radical, cosocle | C23×C79 | C24 |
| hypercenter | #391 | D79 |
| hypocenter | C79 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #14579159 | C4 | semidirect |
| 48. C4×Dic79 | Q8 | semidirect |
| 96. Dic79 | C4×Q8 | semidirect |
| 97. Dic79 | C4⋊Q8 | semidirect |
| 104. C79 | C4×C4⋊Q8 | semidirect |