Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
570 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 162 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 | #2826 |
| commutator, Frattini, cosocle | C23×C4 | C24 |
| prime radical | C24 | 2−1+4 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ 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 |
| #11336 | 2 |
| #11331 | 2 |
| #11308 | 2 |
| #11297 | 2 |
| #11253 | 2 |
| #11252 | 2 |
| #11239 | 2 |
| #11214 | 2 |