Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
619 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 619 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#493 | C2 | semidirect |
| 2. C2×#466 | C2 | semidirect |
| 3. C2×#466 | C2 | semidirect |
| 4. C2×C4×D8 | C2 | semidirect |
| 5. #2428 | C2 | semidirect |
| 6. #2041 | C2 | semidirect |
| 7. #1999 | C2 | semidirect |
| 8. #1970 | C2 | semidirect |
| 9. #1942 | C2 | semidirect |
| 10. #1879 | C2 | semidirect |
| 11. C8×C22⋊C4 | C2 | semidirect |
| 59. C2×D8 | D4 | semidirect |
| 89. #107 | D4 | semidirect |
| 171. C22⋊C4 | D8 | semidirect |
| 245. C8 | #121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#493 | 2 |
| C2×#466 | 2 |
| C2×C4×D8 | 2 |
| #2428 | 2 |
| #2041 | 2 |
| #1999 | 2 |
| #1970 | 2 |
| #1942 | 2 |
| #1879 | 2 |
| C8×C22⋊C4 | 2 |