Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
4767 conjugacy classes of subgroups; only the 2063 normal subgroups are shown.
This group has 4767 conjugacy classes of subgroups — too many to draw. Only its 2063 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C22 |
| commutator | C2 | C23×C42 |
| Frattini, cosocle | C23 | C25 |
| socle | C25 | C23 |
| prime radical | C26 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×C42 | C2 | semidirect |
| 4. C2×C4×C22⋊C4 | C2 | direct (N × H) |
| 5. C22×#95 | C2 | semidirect |
| 8. C24×C4 | C4 | semidirect |
| 13. C22×C22⋊C4 | C4 | direct (N × H) |
| 16. C22×C42 | C22 | semidirect |
| 17. C4×C22⋊C4 | C22 | direct (N × H) |
| 18. C2×#95 | C22 | semidirect |
| 32. C23×C4 | C2×C4 | semidirect |
| 33. C23×C4 | C2×C4 | semidirect |
| 39. C2×C22⋊C4 | C2×C4 | direct (N × H) |
| 42. C2×C42 | C23 | semidirect |
| 43. #95 | C23 | semidirect |
| 49. C24 | C42 | semidirect |
| 65. C22×C4 | C22⋊C4 | direct (N × H) |
| 68. C22×C4 | C22×C4 | semidirect |
| 69. C22×C4 | C22×C4 | semidirect |
| 74. C22⋊C4 | C22×C4 | direct (N × H) |
| 83. C23 | C2×C42 | semidirect |
| 100. C2×C4 | C2×C22⋊C4 | direct (N × H) |
| 103. C2×C4 | C23×C4 | semidirect |
| 109. C22 | C4×C22⋊C4 | direct (N × H) |
| 111. C22 | C22×C42 | semidirect |
| 121. C4 | C22×C22⋊C4 | direct (N × H) |
| 123. C2 | C2×C4×C22⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4 | 2 |
| C23×C22⋊C4 | 2 |
| C23×C42 | 2 |
| C2×C4×C22⋊C4 | 2 |
| C22×#95 | 2 |