Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
905 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 905 conjugacy classes of subgroups — too many to draw. Only its 199 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C24 | C24 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#399 | C2 | semidirect |
| 2. C2×#396 | C2 | semidirect |
| 4. C2×#389 | C2 | semidirect |
| 5. #1444 | C2 | semidirect |
| 6. #1439 | C2 | semidirect |
| 8. C4⋊#95 | C2 | semidirect |
| 55. C2×C4⋊C4 | D4 | semidirect |
| 56. C2×C4⋊C4 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#399 | 2 |
| C2×#396 | 2 |
| C2×#390 | 2 |
| C2×#389 | 2 |
| #1444 | 2 |
| #1439 | 2 |
| #1438 | 2 |
| C4⋊#95 | 2 |