Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
909 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 909 conjugacy classes of subgroups — too many to draw. Only its 239 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 | #120 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C2×#120 |
| prime radical | C2×#532 | C2 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 2. #3428 | C2 | semidirect |
| 3. #2896 | C2 | semidirect |
| 4. C2×#413 | C2 | semidirect |
| 5. #1888 | C2 | semidirect |
| 6. #1887 | C2 | semidirect |
| 7. #1886 | C2 | semidirect |
| 8. #1885 | C2 | semidirect |
| 9. C2×#339 | C2 | semidirect |
| 14. #532 | C4 | semidirect |
| 46. C2×#41 | C2×C4 | semidirect |
| 65. C4⋊Q8 | C2×C4 | semidirect |
| 67. #127 | C2×C4 | semidirect |
| 70. #124 | C2×C4 | semidirect |
| 71. #124 | C2×C4 | semidirect |
| 82. #117 | D4 | semidirect |
| 86. C2×C4⋊C4 | D4 | semidirect |
| 95. C2×C42 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#532 | 2 |
| #3428 | 2 |
| #2896 | 2 |
| C2×#413 | 2 |
| #1888 | 2 |
| #1887 | 2 |
| #1886 | 2 |
| #1885 | 2 |
| C2×#339 | 2 |