Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
285 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 159 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 | #117 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C2×C8 | C24 |
| socle | C22 | #432 |
| prime radical | C24 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2165 | C2 | direct (N × H) |
| 3. C2×#364 | C2 | semidirect |
| 5. C2×#347 | C2 | semidirect |
| 16. #364 | C22 | semidirect |
| 18. #347 | C22 | semidirect |
| 127. C2 | #2165 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×M16 | 2 |
| #2165 | 2 |
| C2×#364 | 2 |
| C2×#349 | 2 |
| C2×#347 | 2 |