Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1781 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 1781 conjugacy classes of subgroups — too many to draw. Only its 635 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 | C22 | C22×C42 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#95 | C2 | semidirect |
| 3. C4⋊#95 | C2 | semidirect |
| 4. C22⋊#95 | C2 | semidirect |
| 5. C4×#95 | C2 | semidirect |
| 9. C2×C4×D4 | C4 | semidirect |
| 26. C23×C4 | C2×C4 | semidirect |
| 33. C2×C4⋊C4 | C2×C4 | semidirect |
| 35. C2×C22⋊C4 | C2×C4 | semidirect |
| 37. C2×C42 | C2×C4 | semidirect |
| 41. #95 | D4 | direct (N × H) |
| 98. D4 | #95 | direct (N × H) |
| 117. C2×C4 | C4×D4 | semidirect |
| 124. C22 | C2×#95 | semidirect |
| 140. C4 | C2×#95 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D4 | 2 |
| C22×#95 | 2 |
| C4⋊#95 | 2 |
| C22⋊#95 | 2 |
| C4×#95 | 2 |