Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
414 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72286339 |
| commutator | C2×C32 | C22×C8 |
| Frattini, cosocle | #7330 | C23 |
| prime radical | #33981 | C8 |
| LCS | G ▷ C2×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×#1311 ◁ #149495 ◁ G | |
| LECS | G ▷ #7330 ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72231932 | C2 | semidirect |
| 2. #72225405 | C2 | semidirect |
| 4. #72224654 | C2 | semidirect |
| 16. #94509 | C22 | semidirect |
| 19. #93877 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72231932 | 2 |
| #72225405 | 2 |
| #72225310 | 2 |
| #72224654 | 2 |