Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
125 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 125 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #357 |
| commutator | C2×C16 | C2×C8 |
| Frattini, cosocle | C2×C4×C16 | C22 |
| socle | C22 | #1331 |
| prime radical | C23 | #359 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4×C16 ◁ G | |
| LECS | G ▷ C2×C4×C16 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13169 | 2 |
| #7465 | 2 |
| #7160 | 2 |