Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
985 conjugacy classes of subgroups; only the 359 normal subgroups are shown.
This group has 985 conjugacy classes of subgroups — too many to draw. Only its 359 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22⋊C4 |
| commutator | C22 | C22×C42 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C23 | C2×C22⋊C4 |
| prime radical | C23×D4 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×M16 | C2 | semidirect |
| 4. C4×#100 | C2 | direct (N × H) |
| 5. C2×#343 | C2 | semidirect |
| 17. C2×#100 | C4 | direct (N × H) |
| 20. C4×M16 | C22 | semidirect |
| 23. #343 | C22 | semidirect |
| 42. C2×M16 | C2×C4 | semidirect |
| 61. #100 | C2×C4 | direct (N × H) |
| 107. M16 | C22×C4 | semidirect |
| 151. C2×C4 | #100 | direct (N × H) |
| 188. C4 | C2×#100 | direct (N × H) |
| 194. C2 | C4×#100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D4 | 2 |
| C22×#100 | 2 |
| C2×C4×M16 | 2 |
| C4×#100 | 2 |
| C2×#343 | 2 |