Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
157 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 157 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23 |
| socle | C2 | #2065 |
| prime radical | C2×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2155 | C2 | semidirect |
| 2. #2150 | C2 | semidirect |
| 6. #1945 | C2 | semidirect |
| 7. #1388 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2155 | 2 |
| #2150 | 2 |
| #2145 | 2 |
| #2143 | 2 |
| #1974 | 2 |
| #1945 | 2 |
| #1388 | 2 |