Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
593 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 593 conjugacy classes of subgroups — too many to draw. Only its 175 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 | #121 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C23×C4 | C23 |
| socle | C22 | #380 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#344 | C2 | semidirect |
| 4. C2×#341 | C2 | semidirect |
| 5. #1735 | C2 | semidirect |
| 10. C2×#131 | C4 | semidirect |
| 18. #421 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#131 | 2 |
| C2×#421 | 2 |
| C2×#344 | 2 |
| C2×#341 | 2 |
| #1735 | 2 |