Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
1133 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 1133 conjugacy classes of subgroups — too many to draw. Only its 635 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, prime radical, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 34. C4⋊Q8 | Q8 | direct (N × H) |
| 38. C4×Q8 | Q8 | semidirect |
| 86. Q8 | C4⋊Q8 | direct (N × H) |
| 116. C4 | Q82 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q82 | 2 |
| #2868 | 2 |
| #2567 | 2 |
| #2551 | 2 |
| Q8×C4⋊C4 | 2 |
| C4×C4⋊Q8 | 2 |
| C42×Q8 | 2 |