Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
496 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 209 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×D239 |
| commutator | C22×C239 | C23×C4 |
| Fitting | #391×C239 | C2 |
| socle, prime radical, cosocle | C23×C239 | C24 |
| hypercenter | #391 | D239 |
| hypocenter | C239 | #2369 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #21439958 | C4 | semidirect |
| 44. Dic239⋊C4 | Q8 | semidirect |
| 109. C239 | #2369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439958 | 2 |
| #29504679 | 2 |
| #29504676 | 2 |
| #29504669 | 2 |
| #29504667 | 2 |
| C4×Dic239⋊C4 | 2 |
| #29504623 | 2 |
| #391×C239 | 2 |
| #2369 | 239 |