Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1333 conjugacy classes of subgroups; only the 991 normal subgroups are shown.
This group has 1333 conjugacy classes of subgroups — too many to draw. Only its 991 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2×C4 | C25 |
| commutator, socle | C22 | C24×C4 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #2906 | C2 | semidirect |
| 5. #2905 | C2 | semidirect |
| 6. C2×#424 | C2 | semidirect |
| 22. #424 | C22 | semidirect |
| 23. #424 | C22 | semidirect |
| 24. #423 | C22 | semidirect |
| 25. C2×C4⋊C8 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#568 | 2 |
| C22×#131 | 2 |
| #3428 | 2 |
| #2906 | 2 |
| #2905 | 2 |
| C2×#424 | 2 |