Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
191 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×C22⋊C4 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C22×C8 | C23 |
| socle | C2 | #1752 |
| prime radical | C2×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C2×M32 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2110 | C2 | semidirect |
| 4. C2×#347 | C2 | semidirect |
| 6. #1378 | C2 | semidirect |
| 7. #1377 | C2 | semidirect |
| 10. #504 | C4 | semidirect |
| 20. #350 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3407 | 2 |
| #2117 | 2 |
| #2110 | 2 |
| C2×#347 | 2 |
| #1765 | 2 |
| #1378 | 2 |
| #1377 | 2 |