Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
271 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | H(3,ℤ/4) |
| commutator | C22×C8 | C42 |
| Frattini, cosocle | C2×#405 | C22 |
| socle | C22 | #1289 |
| prime radical | C24 | #103 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 ◁ G | |
| LECS | G ▷ C2×#405 ▷ C22×C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #12784 | 2 |
| #10867 | 2 |
| #8601 | 2 |