Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
259 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #427 |
| commutator | C22×C8 | C22×C4 |
| Frattini, cosocle | C2×C4×C8 | C23 |
| socle | C22 | #1568 |
| prime radical | C24 | #108 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 ◁ C2×#405 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#1373 | C2 | semidirect |
| 5. C2×#1369 | C2 | semidirect |
| 6. #7161 | C2 | semidirect |
| 7. #7160 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2166 | 2 |
| #12790 | 2 |
| #12600 | 2 |
| C2×#1373 | 2 |
| C2×#1369 | 2 |
| #7161 | 2 |
| #7160 | 2 |