Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
371 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 131 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C22 | C2×#95 |
| prime radical | C24 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1303 | C2 | semidirect |
| 10. #432 | C4 | semidirect |
| 11. #432 | C4 | semidirect |
| 14. #431 | C4 | semidirect |
| 16. #423 | C4 | semidirect |
| 53. C4⋊C8 | C2×C4 | semidirect |
| 54. C4⋊C8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2920 | 2 |
| C2×C4×C4⋊C4 | 2 |
| #1303 | 2 |