Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
298 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22⋊C4 |
| commutator | C2×C4 | C22×C8 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C23 | C2×C22⋊C4 |
| prime radical | C24 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1272 | C2 | semidirect |
| 5. #1271 | C2 | semidirect |
| 33. C22⋊Q8 | C8 | semidirect |
| 61. C2×Q8 | C2×C8 | semidirect |
| 96. C4⋊C4 | C2×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊Q8 | 2 |
| C4×C22⋊C8 | 2 |
| C2×#336 | 2 |
| #1272 | 2 |
| #1271 | 2 |