Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
939 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 939 conjugacy classes of subgroups — too many to draw. Only its 263 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 | C2×C22⋊C4 |
| prime radical | C2×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#423 | C2 | semidirect |
| 3. C22×#104 | C2 | semidirect |
| 4. C2×C43 | C2 | semidirect |
| 5. #1962 | C2 | direct (N × H) |
| 10. #532 | C4 | semidirect |
| 12. C2×C4⋊Q8 | C4 | semidirect |
| 13. C2×#127 | C4 | semidirect |
| 14. C2×#124 | C4 | semidirect |
| 21. #423 | C22 | semidirect |
| 24. C2×#104 | C22 | semidirect |
| 26. C43 | C22 | semidirect |
| 46. C4⋊Q8 | C2×C4 | semidirect |
| 48. #127 | C2×C4 | semidirect |
| 50. #124 | C2×C4 | semidirect |
| 67. C2×C42 | D4 | semidirect |
| 127. C42 | C2×D4 | semidirect |
| 154. C2×C4 | #104 | semidirect |
| 187. C4 | C2×#104 | semidirect |
| 194. C2 | #1962 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#532 | 2 |
| C2×#423 | 2 |
| C22×#104 | 2 |
| C2×C43 | 2 |
| #1962 | 2 |