Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #1677 |
| commutator, Frattini, cosocle | C2×C4×C8 | C23 |
| prime radical | C23 | #472 |
| LCS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ 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 |
|---|---|
| #13187 | 2 |
| #13181 | 2 |
| #13162 | 2 |
| #12890 | 2 |
| #7271 | 2 |
| #7269 | 2 |
| #7161 | 2 |