Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
3066 conjugacy classes of subgroups; only the 1818 normal subgroups are shown.
This group has 3066 conjugacy classes of subgroups — too many to draw. Only its 1818 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22×C4 | C25 |
| commutator, socle | C23 | C24×C4 |
| prime radical | C25 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #20793 | C2 | semidirect |
| 17. #1843 | C22 | semidirect |
| 18. #1842 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2905 | 2 |
| C22×#424 | 2 |
| #33996 | 2 |
| #20793 | 2 |