Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
497 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 497 conjugacy classes of subgroups — too many to draw. Only its 167 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, Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C2×#121 |
| prime radical | C22×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#108 | C2 | semidirect |
| 2. #2911 | C2 | semidirect |
| 3. C2×#424 | C2 | semidirect |
| 7. #2064 | C2 | semidirect |
| 8. #2063 | C2 | semidirect |
| 9. #1742 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#108 | 2 |
| #2911 | 2 |
| C2×#424 | 2 |
| #2896 | 2 |
| C2×#416 | 2 |
| C2×#413 | 2 |
| #2064 | 2 |
| #2063 | 2 |
| #1742 | 2 |