Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1059 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 1059 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C24 | C24 |
| commutator | C23 | C23×C4 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#385 | C2 | semidirect |
| 4. #1441 | C2 | semidirect |
| 5. #1439 | C2 | semidirect |
| 6. C4⋊#95 | C2 | semidirect |
| 17. #390 | C4 | semidirect |
| 51. C2×C4⋊C4 | C2×C4 | semidirect |
| 52. C2×C4⋊C4 | D4 | semidirect |
| 61. C2×C22⋊C4 | C2×C4 | semidirect |
| 64. C2×C42 | C2×C4 | semidirect |
| 87. C2×D4 | C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#390 | 2 |
| C2×#386 | 2 |
| C2×#385 | 2 |
| #1441 | 2 |
| #1439 | 2 |
| C4⋊#95 | 2 |