Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
178 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 63 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 | #120 |
| commutator | C42 | C22×C4 |
| Frattini, cosocle | C2×C42 | C23 |
| socle | C22 | #385 |
| prime radical | C23 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. #332 | C4 | semidirect |
| 26. #332 | C4 | semidirect |
| 27. #332 | C4 | semidirect |
| 28. #332 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2986 | 2 |
| #1994 | 2 |
| #1574 | 2 |
| #1544 | 2 |
| #1276 | 2 |