Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | #11999 |
| commutator | C2×C16 | C22×C16 |
| Frattini, cosocle | #7329 | C23 |
| socle | C2 | #72227188 |
| prime radical | C23 | #7456 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8 ◁ C4×C16 ◁ C4×M64 ◁ C8×M64 ◁ G | |
| LECS | G ▷ #7329 ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227187 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227187 | 2 |
| #72225395 | 2 |
| #72216226 | 2 |