Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
412 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C2×C16 | C24 |
| commutator | C2 | C23×C32 |
| socle | C22 | C23×C16 |
| prime radical | C22×D4 | C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16 ◁ G | |
| LECS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D4×C32 | C2 | semidirect |
| 3. #13639 | C2 | semidirect |
| 4. C2×C22⋊C32 | C2 | semidirect |
| 7. C22×C32 | C22 | semidirect |
| 13. C4⋊C32 | C22 | semidirect |
| 15. C22⋊C32 | C22 | semidirect |
| 16. C4×C32 | C22 | semidirect |
| 65. C2×D4 | C32 | semidirect |
| 96. C23 | C2×C32 | semidirect |
| 99. D4 | C2×C32 | semidirect |
| 107. C2×C4 | C2×C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C16 | 2 |
| D4×C32 | 2 |
| #13639 | 2 |
| C2×C22⋊C32 | 2 |