Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
627 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 231 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C23 | C22×D4 |
| prime radical | C2×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C43 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×SD16 | C2 | semidirect |
| 3. C4×C4⋊Q8 | C2 | semidirect |
| 5. #1968 | C2 | semidirect |
| 7. #1956 | C2 | semidirect |
| 8. #1844 | C2 | semidirect |
| 9. C42×C8 | C2 | semidirect |
| 16. #492 | C4 | direct (N × H) |
| 39. C2×SD16 | C2×C4 | semidirect |
| 43. C4⋊Q8 | C2×C4 | semidirect |
| 68. C4×C8 | C2×C4 | semidirect |
| 69. C4×C8 | D4 | semidirect |
| 111. C42 | SD16 | semidirect |
| 149. C8 | C4×D4 | semidirect |
| 165. C4 | C4×SD16 | semidirect |
| 166. C4 | #492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#492 | 2 |
| C2×C4×SD16 | 2 |
| C4×C4⋊Q8 | 2 |
| C4×#127 | 2 |
| #1968 | 2 |
| #1957 | 2 |
| #1956 | 2 |
| #1844 | 2 |
| C42×C8 | 2 |