Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
261 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 75 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 | #390 |
| commutator | C22×C4 | C22×C4 |
| Frattini, cosocle | C23×C4 | C23 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C22×Q16 | C4 | semidirect |
| 14. C2×#107 | C4 | semidirect |
| 15. C2×#103 | C4 | semidirect |
| 100. C22⋊C4 | Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#467 | 2 |
| #1996 | 2 |
| #1808 | 2 |
| C8×C22⋊C4 | 2 |
| #1520 | 2 |