Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
608 conjugacy classes of subgroups; only the 314 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 314 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator | C2×C4 | C22×C42 |
| Frattini, cosocle | C2×C42 | C24 |
| socle | C22 | C2×#376 |
| prime radical | C24 | #117 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #8142 | C2 | semidirect |
| 13. #1455 | C4 | semidirect |
| 14. #1453 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20367 | 2 |
| #17334 | 2 |
| #8142 | 2 |
| #7861 | 2 |
| #7856 | 2 |