Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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×D41 |
| commutator, socle, cosocle | C22×C41 | C24 |
| Fitting | C4⋊Q8×C41 | C2 |
| prime radical | C22×D41 | C23 |
| hypercenter | C4⋊Q8 | D41 |
| hypocenter | C41 | #544 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13050163 | C2 | semidirect |
| 2. #13050162 | C2 | semidirect |
| 3. #13050156 | C2 | semidirect |
| 4. #13050155 | C2 | semidirect |
| 5. #13050154 | C2 | semidirect |
| 11. C4⋊Q8×C41 | C2 | semidirect |
| 48. C4×D41 | Q8 | semidirect |
| 69. C41 | #544 | semidirect |
| 72. C4⋊Q8 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050163 | 2 |
| #13050162 | 2 |
| #13050156 | 2 |
| #13050155 | 2 |
| #13050154 | 2 |
| #13050142 | 2 |
| #13050140 | 2 |
| #13050122 | 2 |
| #13050121 | 2 |
| C4⋊C4×D41 | 2 |
| C4⋊Q8×C41 | 2 |
| #544 | 41 |