Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
119 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 119 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C16 | D4 |
| commutator | C4 | C22×C16 |
| Frattini, cosocle | C4×C8 | C23 |
| socle | C22 | C8×D4 |
| prime radical | C2×D4 | C2×C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16 ◁ C4×C16 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×C16 | C2 | semidirect |
| 4. #1367 | C2 | semidirect |
| 5. Q8⋊C16 | C2 | semidirect |
| 7. C8×C16 | C2 | semidirect |
| 47. SD16 | C16 | direct (N × H) |
| 67. C16 | SD16 | direct (N × H) |
| 70. Q8 | C2×C16 | semidirect |
| 86. C8 | C2×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C16 | 2 |
| D4×C16 | 2 |
| C8×SD16 | 2 |
| #1367 | 2 |
| Q8⋊C16 | 2 |
| D4⋊C16 | 2 |
| C8×C16 | 2 |