Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C2×C4 | C2×C42 |
| Frattini, cosocle | C2×C42 | C23 |
| prime radical | C2×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C43 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1767 | C2 | semidirect |
| 3. C4×C4⋊C8 | C2 | semidirect |
| 5. #1296 | C2 | semidirect |
| 21. #331 | C4 | semidirect |
| 49. C4⋊C8 | C2×C4 | semidirect |
| 50. C4⋊C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#127 | 2 |
| #1767 | 2 |
| C4×C4⋊C8 | 2 |
| C2×#331 | 2 |
| #1296 | 2 |