Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2514 conjugacy classes of subgroups; only the 1178 normal subgroups are shown.
This group has 2514 conjugacy classes of subgroups — too many to draw. Only its 1178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, prime radical, cosocle | C24 | C25 |
| commutator | C23 | C24×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C42×Q8 | C4 | semidirect |
| 30. #383 | Q8 | direct (N × H) |
| 88. C42 | C4×Q8 | semidirect |
| 94. Q8 | #383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×Q8 | 2 |
| #14688 | 2 |
| #13936 | 2 |
| Q8×#95 | 2 |
| C4×#383 | 2 |