Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
357 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 135 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 | C22⋊C4 |
| commutator | C2×C4 | C22×C8 |
| Frattini, cosocle | C2×C42 | C23 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1271 | C2 | direct (N × H) |
| 41. C2×C4⋊C4 | C8 | semidirect |
| 93. C4⋊C4 | C2×C8 | semidirect |
| 168. C2 | #1271 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#389 | 2 |
| C2×#336 | 2 |
| #1271 | 2 |