Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
741 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 741 conjugacy classes of subgroups — too many to draw. Only its 239 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 | C43 |
| Frattini, prime radical, cosocle | C25 | C23 |
| socle | C23 | C2×C22⋊C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C25 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C22×C42 | C4 | semidirect |
| 12. C4×C22⋊C4 | C4 | semidirect |
| 14. C2×#95 | C4 | semidirect |
| 15. #342 | C4 | direct (N × H) |
| 67. C22×C4 | C42 | semidirect |
| 80. C22⋊C4 | C42 | semidirect |
| 159. C4 | #342 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊C4 | 2 |
| C2×#342 | 2 |