Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
313 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 313 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C42 | C24 |
| socle | C22 | C2×C4×D4 |
| prime radical | C23 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ #431 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1587 | C2 | semidirect |
| 5. #1584 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2983 | 2 |
| #2982 | 2 |
| C2×C4×Q16 | 2 |
| #1587 | 2 |
| #1584 | 2 |
| #1564 | 2 |
| #1479 | 2 |
| #1452 | 2 |