Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
505 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 505 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 | C22×#41 | C22 |
| 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 |
| 2. C2×#424 | C2 | semidirect |
| 5. #2098 | C2 | direct (N × H) |
| 6. C2×H(3,ℤ/4) | C2 | semidirect |
| 13. #430 | C22 | semidirect |
| 16. #424 | C22 | semidirect |
| 24. H(3,ℤ/4) | C22 | semidirect |
| 202. C2 | #2098 | 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×#424 | 2 |
| C2×#421 | 2 |
| C2×#408 | 2 |
| #2098 | 2 |
| C2×H(3,ℤ/4) | 2 |