Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
179 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 179 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #1697 |
| commutator, Frattini, cosocle | C2×C4×C8 | C23 |
| socle | C2 | #10658 |
| prime radical | C23 | #473 |
| LCS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13188 | 2 |
| #13182 | 2 |
| #13161 | 2 |
| #12891 | 2 |
| #7272 | 2 |
| #7270 | 2 |
| #7160 | 2 |