Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
318 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3417 | C2 | semidirect |
| 2. #3293 | C2 | semidirect |
| 3. #2247 | C2 | semidirect |
| 4. #2222 | C2 | semidirect |
| 5. #2214 | C2 | semidirect |
| 6. #2195 | C2 | semidirect |
| 7. #2178 | C2 | semidirect |
| 8. #2170 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3417 | 2 |
| #3293 | 2 |
| #2247 | 2 |
| #2222 | 2 |
| #2214 | 2 |
| #2195 | 2 |
| #2178 | 2 |
| #2170 | 2 |