Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1279 conjugacy classes of subgroups; only the 687 normal subgroups are shown.
This group has 1279 conjugacy classes of subgroups — too many to draw. Only its 687 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24 | C24 |
| commutator, Frattini, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2859 | C2 | direct (N × H) |
| 78. C2×C4 | #125 | semidirect |
| 98. C4 | C2×#125 | semidirect |
| 100. C2 | #2859 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#125 | 2 |
| #2859 | 2 |
| C2×#389 | 2 |
| C2×#384 | 2 |
| C2×#382 | 2 |
| C2×C43 | 2 |