Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
518 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24 |
| prime radical | #2856 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#460 | C2 | semidirect |
| 2. C2×#431 | C2 | semidirect |
| 4. C4×C22⋊Q8 | C2 | semidirect |
| 5. #2034 | C2 | semidirect |
| 6. #2000 | C2 | semidirect |
| 7. #1982 | C2 | semidirect |
| 8. #1968 | C2 | semidirect |
| 9. #1948 | C2 | semidirect |
| 10. #1934 | C2 | semidirect |
| 11. #1803 | C2 | semidirect |
| 92. C4⋊C8 | D4 | semidirect |
| 143. C22×C4 | SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#460 | 2 |
| C2×#431 | 2 |
| #2856 | 2 |
| C4×C22⋊Q8 | 2 |
| #2034 | 2 |
| #2000 | 2 |
| #1982 | 2 |
| #1968 | 2 |
| #1948 | 2 |
| #1934 | 2 |
| #1803 | 2 |