Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
279 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C24 |
| prime radical | C2×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ 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. C2×#498 | C2 | semidirect |
| 3. #2230 | C2 | direct (N × H) |
| 4. C2×#365 | C2 | semidirect |
| 5. C2×#364 | C2 | semidirect |
| 12. #498 | C22 | semidirect |
| 20. #365 | C22 | semidirect |
| 21. #364 | C22 | semidirect |
| 27. #135 | Q8 | semidirect |
| 29. C2×Q16 | Q8 | semidirect |
| 31. C2×D8 | Q8 | semidirect |
| 69. Q16 | C2×Q8 | semidirect |
| 73. D8 | C2×Q8 | semidirect |
| 140. C2 | #2230 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#498 | 2 |
| C2×#443 | 2 |
| #2230 | 2 |
| C2×#365 | 2 |
| C2×#364 | 2 |
| C2×#360 | 2 |