Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
759 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 759 conjugacy classes of subgroups — too many to draw. Only its 271 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 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C23 | C22×D4 |
| prime radical | C25 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#427 | C2 | semidirect |
| 4. #1809 | C2 | semidirect |
| 5. #1735 | C2 | semidirect |
| 8. C22×M16 | C4 | semidirect |
| 14. C2×#107 | C22 | semidirect |
| 15. C2×#106 | C22 | semidirect |
| 20. #340 | C22 | semidirect |
| 76. C2×C8 | C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×M16 | 2 |
| C2×#427 | 2 |
| #2280 | 2 |
| #1809 | 2 |
| #1735 | 2 |