Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
429 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 183 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 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle, prime radical | C23 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C4×Q16 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q16 | 2 |
| #2295 | 2 |
| C42×Q8 | 2 |
| #1927 | 2 |
| #1918 | 2 |
| #1878 | 2 |
| #1865 | 2 |
| C4×#106 | 2 |
| C4×#103 | 2 |
| #1744 | 2 |