Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
375 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 183 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 | C42 | C24 |
| socle | C23 | C4×D4 |
| prime radical | C22×D4 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×C8 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C8×Q8 | C2 | semidirect |
| 4. #1583 | C2 | direct (N × H) |
| 5. C2×#334 | C2 | semidirect |
| 6. C2×Q8⋊C8 | C2 | semidirect |
| 8. C2×#322 | C2 | semidirect |
| 14. C8×Q8 | C22 | semidirect |
| 30. #334 | C22 | semidirect |
| 31. Q8⋊C8 | C22 | semidirect |
| 33. #322 | C22 | semidirect |
| 81. C2×Q8 | M16 | semidirect |
| 108. C2×C8 | SD16 | semidirect |
| 134. Q8 | C2×M16 | semidirect |
| 164. C8 | C2×SD16 | semidirect |
| 185. C2 | #1583 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×Q8 | 2 |
| C2×C4×SD16 | 2 |
| C2×#436 | 2 |
| #1583 | 2 |
| C2×#334 | 2 |
| C2×Q8⋊C8 | 2 |
| C2×D4⋊C8 | 2 |
| C2×#322 | 2 |