Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
163 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | #99 |
| commutator | C2×C4 | C2×C32 |
| Frattini, cosocle | C2×C4⋊C16 | C22 |
| socle | C22 | #1314 |
| prime radical | C22×D4 | C16 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4⋊C16 ◁ G | |
| LECS | G ▷ C2×C4⋊C16 ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #7362 | C2 | semidirect |
| 49. C2×D4 | C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13189 | 2 |
| #7362 | 2 |