Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1764 conjugacy classes of subgroups.
The subgroup lattice has 968 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #182043 |
| commutator | C22×C8 | C22×C42 |
| Frattini, cosocle | C4×M32 | C24 |
| socle | C2 | #72285281 |
| prime radical | #3444 | M16 |
| LCS | G ▷ C22×C8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ #346 ◁ #479908 ◁ G | |
| LECS | G ▷ C4×M32 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72319824 | C2 | semidirect |
| 2. #72319535 | C2 | semidirect |
| 3. #72319527 | C2 | semidirect |
| 4. #72319502 | C2 | semidirect |
| 6. #72286160 | C2 | semidirect |
| 7. #72217231 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72319824 | 2 |
| #72319535 | 2 |
| #72319527 | 2 |
| #72319502 | 2 |
| #72287401 | 2 |
| #72286160 | 2 |
| #72217231 | 2 |
| #72216670 | 2 |