Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
995 conjugacy classes of subgroups; only the 535 normal subgroups are shown.
This group has 995 conjugacy classes of subgroups — too many to draw. Only its 535 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 | C24 |
| commutator, Frattini, socle, cosocle | C23 | C25 |
| prime radical | C24 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2864 | C2 | semidirect |
| 2. #2859 | C2 | semidirect |
| 4. C4×#125 | C2 | semidirect |
| 86. C2×C4 | #125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2864 | 2 |
| #2859 | 2 |
| #2851 | 2 |
| C4×#125 | 2 |
| #2296 | 2 |
| #2285 | 2 |
| C2×C43 | 2 |