Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | #7385 |
| commutator | C32 | C2×C32 |
| Frattini, cosocle | #93664 | C22 |
| socle | C2 | #72226997 |
| prime radical | #2262 | C16 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8 ◁ C2×C16 ◁ C4×C32 ◁ C8×C32 ◁ #93664 ◁ G | |
| LECS | G ▷ #93664 ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225398 | C2 | semidirect |
| 3. #72225071 | C2 | semidirect |
| 44. Q64 | C32 | semidirect |
| 46. D32 | C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225398 | 2 |
| #72225356 | 2 |
| #72225071 | 2 |