Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
529 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 529 conjugacy classes of subgroups — too many to draw. Only its 186 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 | C4⋊#95 |
| commutator | C42 | C2×C42 |
| Frattini, cosocle | C22×C42 | C23 |
| prime radical | C24 | #127 |
| LCS | G ▷ C42 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C4×#107 | C4 | semidirect |
| 12. C4×#106 | C4 | semidirect |
| 13. #1452 | C4 | semidirect |
| 15. #1450 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20818 | 2 |
| #17323 | 2 |
| #7945 | 2 |