Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
2879 conjugacy classes of subgroups; only the 2063 normal subgroups are shown.
This group has 2879 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, prime radical | C25 | C23 |
| 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 |
|---|---|---|
| 4. C2×C4×C4⋊C4 | C2 | direct (N × H) |
| 10. C22×C4⋊C4 | C4 | direct (N × H) |
| 13. C22×C42 | C4 | semidirect |
| 16. C4×C4⋊C4 | C22 | direct (N × H) |
| 33. C2×C4⋊C4 | C2×C4 | direct (N × H) |
| 36. C2×C42 | C2×C4 | semidirect |
| 51. C22×C4 | C42 | semidirect |
| 52. C22×C4 | C4⋊C4 | direct (N × H) |
| 64. C4⋊C4 | C22×C4 | direct (N × H) |
| 66. C42 | C22×C4 | semidirect |
| 83. C2×C4 | C2×C42 | semidirect |
| 84. C2×C4 | C2×C4⋊C4 | direct (N × H) |
| 92. C22 | C4×C4⋊C4 | direct (N × H) |
| 105. C4 | C22×C42 | semidirect |
| 106. C4 | C22×C4⋊C4 | direct (N × H) |
| 107. C2 | C2×C4×C4⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4 | 2 |
| C23×C42 | 2 |
| C2×C4×C4⋊C4 | 2 |
| C22×#95 | 2 |