Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
392 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 105 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 | C22×C4 | C22×C4 |
| Frattini, cosocle | C2×C42 | C23 |
| prime radical | #2856 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊C8 | C2 | semidirect |
| 3. #1797 | C2 | semidirect |
| 4. C2×#331 | C2 | semidirect |
| 5. #1296 | C2 | semidirect |
| 58. C4⋊C8 | D4 | semidirect |
| 189. C22 | #331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊C8 | 2 |
| #2856 | 2 |
| #1797 | 2 |
| C2×#331 | 2 |
| #1296 | 2 |