Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
480 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 480 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×D251 |
| commutator, socle, cosocle | C23×C251 | C24 |
| Fitting | #390×C251 | C2 |
| prime radical | C22×D4×C251 | C22 |
| hypercenter | #390 | D251 |
| hypocenter | C251 | #2804 |
| LCS | G ▷ C23×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30631626 | C2 | semidirect |
| 2. #30631599 | C2 | semidirect |
| 3. #30631593 | C2 | semidirect |
| 5. #30631562 | C2 | semidirect |
| 35. C2×D4×C251 | Q8 | semidirect |
| 86. C251 | #2804 | semidirect |
| 114. C2×D4 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631626 | 2 |
| #30631599 | 2 |
| #30631593 | 2 |
| #30631567 | 2 |
| #30631562 | 2 |
| #390×C251 | 2 |
| #2804 | 251 |