Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
262 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| socle | C2 | C2×#476 |
| prime radical | C2×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3160 | C2 | semidirect |
| 3. #2231 | C2 | semidirect |
| 4. #2230 | C2 | semidirect |
| 5. #2155 | C2 | semidirect |
| 6. C2×#364 | C2 | semidirect |
| 14. #499 | C22 | semidirect |
| 15. #498 | C22 | semidirect |
| 25. #365 | C22 | semidirect |
| 26. #364 | C22 | semidirect |
| 27. #364 | C22 | semidirect |
| 32. #135 | Q8 | semidirect |
| 34. C2×Q16 | Q8 | semidirect |
| 36. C2×D8 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3160 | 2 |
| C2×#443 | 2 |
| #2231 | 2 |
| #2230 | 2 |
| #2155 | 2 |
| C2×#364 | 2 |
| #2145 | 2 |