Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
551 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | #399 |
| prime radical | C25 | Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#430 | C2 | semidirect |
| 3. #2091 | C2 | direct (N × H) |
| 4. C2×#338 | C2 | semidirect |
| 9. #430 | C22 | semidirect |
| 14. #338 | C22 | semidirect |
| 117. C2 | #2091 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#430 | 2 |
| C2×#407 | 2 |
| #2091 | 2 |
| C2×#338 | 2 |