Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
713 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 713 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×C22⋊C4 |
| commutator | C23 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C25 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #1901 | C2 | semidirect |
| 4. #1821 | C2 | semidirect |
| 5. #1784 | C2 | semidirect |
| 18. C2×#101 | C22 | semidirect |
| 25. #343 | C22 | semidirect |
| 143. C23 | #101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Q8 | 2 |
| C2×#407 | 2 |
| #1901 | 2 |
| #1821 | 2 |
| #1784 | 2 |