Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
450 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 141 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×D19 |
| commutator, socle, cosocle | C23×C19 | C24 |
| Fitting | C2×C4×Q8×C19 | C2 |
| prime radical | C23×D19 | C23 |
| hypercenter | C2×C4×Q8 | D19 |
| hypocenter | C19 | #2637 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11926477 | C2 | semidirect |
| 3. #11926475 | C2 | semidirect |
| 6. #11926463 | C2 | semidirect |
| 9. #11926428 | C2 | semidirect |
| 10. #11926410 | C2 | semidirect |
| 11. C2×C4×Q8×C19 | C2 | semidirect |
| 120. C2×C4×Q8 | D19 | semidirect |
| 161. C19 | #2637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597322 | 2 |
| #11926477 | 2 |
| #11926475 | 2 |
| #11926470 | 2 |
| #11926466 | 2 |
| #11926463 | 2 |
| #11926455 | 2 |
| #11926435 | 2 |
| #11926428 | 2 |
| #11926410 | 2 |
| C2×C4×Q8×C19 | 2 |
| #2637 | 19 |