Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
555 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #2789 |
| commutator, Frattini, cosocle | C23×C4 | C24 |
| socle | C2 | #17210 |
| prime radical | C24 | C22×Q8 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2103 | 2 |
| #11345 | 2 |
| #11332 | 2 |
| #11319 | 2 |
| #11295 | 2 |
| #11248 | 2 |
| #11235 | 2 |
| #11230 | 2 |