Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
573 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×C22⋊C4 |
| commutator | C24 | C22×C4 |
| Frattini, cosocle | C23×C4 | C23 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#423 | C2 | semidirect |
| 4. C2×#343 | C2 | semidirect |
| 5. #1728 | C2 | semidirect |
| 166. C2×C4 | #100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#423 | 2 |
| C22×#100 | 2 |
| C2×#390 | 2 |
| C2×#343 | 2 |
| #1728 | 2 |