Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
707 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 707 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C23×C4 | C23 |
| socle | C22 | C2×#95 |
| prime radical | C25 | D4 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×H(3,ℤ/4) | C2 | semidirect |
| 10. C2×#117 | C4 | semidirect |
| 15. C22×C42 | C4 | semidirect |
| 19. C2×C22⋊C8 | C4 | semidirect |
| 23. C4×C22⋊C4 | C4 | semidirect |
| 43. C22×C8 | C2×C4 | semidirect |
| 63. C2×C42 | C2×C4 | semidirect |
| 129. C42 | C22⋊C4 | semidirect |
| 202. C22 | H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#117 | 2 |
| C2×#407 | 2 |
| #2280 | 2 |
| C2×H(3,ℤ/4) | 2 |