Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D251 |
| commutator, socle, cosocle | C22×C251 | C24 |
| Fitting | #117×C251 | C2 |
| prime radical | C2×C22⋊D251 | C22 |
| hypercenter | #117 | D251 |
| hypocenter | C251 | #556 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22548714 | C2 | semidirect |
| 2. #22548709 | C2 | semidirect |
| 3. #22548708 | C2 | semidirect |
| 5. #22548695 | C2 | semidirect |
| 6. #22548694 | C2 | semidirect |
| 7. C4×Dic502 | C2 | semidirect |
| 8. #22548680 | C2 | semidirect |
| 10. #22548673 | C2 | semidirect |
| 11. #117×C251 | C2 | semidirect |
| 72. C251 | #556 | semidirect |
| 84. #117 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22548714 | 2 |
| #22548709 | 2 |
| #22548708 | 2 |
| #22548701 | 2 |
| #22548695 | 2 |
| #22548694 | 2 |
| C4×Dic502 | 2 |
| #22548680 | 2 |
| C4×C22⋊D251 | 2 |
| #22548673 | 2 |
| #117×C251 | 2 |
| #556 | 251 |