Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
446 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 446 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, socle | C22 | D42 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C2×#472 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2948 | C2 | semidirect |
| 3. #2946 | C2 | semidirect |
| 4. #2912 | C2 | semidirect |
| 5. #1972 | C2 | semidirect |
| 6. #1951 | C2 | semidirect |
| 7. #1931 | C2 | semidirect |
| 8. #1883 | C2 | semidirect |
| 9. #1856 | C2 | semidirect |
| 10. #1773 | C2 | semidirect |
| 11. #1765 | C2 | semidirect |
| 17. #472 | C4 | semidirect |
| 49. AGL(1,ℤ/8) | C2×C4 | semidirect |
| 55. C2×D8 | C2×C4 | semidirect |
| 57. #131 | C2×C4 | semidirect |
| 80. #108 | C2×C4 | semidirect |
| 97. #100 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#472 | 2 |
| #2948 | 2 |
| #2946 | 2 |
| #2912 | 2 |
| #1972 | 2 |
| #1951 | 2 |
| #1931 | 2 |
| #1883 | 2 |
| #1856 | 2 |
| #1773 | 2 |
| #1765 | 2 |