Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
524 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 165 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×D251 |
| commutator, socle, cosocle | C23×C251 | C24 |
| Fitting | C43×C251 | C2 |
| prime radical | C22×D1004 | C22 |
| hypercenter | C43 | D251 |
| hypocenter | C251 | #2861 |
| LCS | G ▷ C23×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22548707 | C2 | semidirect |
| 3. #30631593 | C2 | semidirect |
| 5. #30631578 | C2 | semidirect |
| 6. C43×C251 | C2 | semidirect |
| 68. C251 | #2861 | semidirect |
| 75. C43 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548707 | 2 |
| C2×#22548703 | 2 |
| #30631593 | 2 |
| #30631589 | 2 |
| #30631578 | 2 |
| C43×C251 | 2 |
| #2861 | 251 |