Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
3367 conjugacy classes of subgroups; only the 575 normal subgroups are shown.
This group has 3367 conjugacy classes of subgroups — too many to draw. Only its 575 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C23 |
| commutator | C22 | C22×C42 |
| Frattini, socle, cosocle | C24 | C24 |
| prime radical | C26 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×C22⋊C4 | C2 | semidirect |
| 4. C22⋊#95 | C2 | semidirect |
| 7. C24×C4 | C4 | semidirect |
| 11. C22×C42 | C22 | semidirect |
| 12. #379 | C4 | direct (N × H) |
| 14. C2×#95 | C22 | semidirect |
| 33. C2×C22⋊C4 | C2×C4 | semidirect |
| 43. C24 | C42 | semidirect |
| 58. C22×C4 | C22⋊C4 | semidirect |
| 61. C22×C4 | C22×C4 | semidirect |
| 100. C22 | C4×C22⋊C4 | semidirect |
| 109. C4 | #379 | 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 |
| C2×#379 | 2 |
| C2×C4×C22⋊C4 | 2 |
| C22⋊#95 | 2 |