Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
414 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 127 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 | #1333 |
| commutator | C16 | C22×C16 |
| Frattini, cosocle | #1311 | C23 |
| socle | C22 | C2×#1333 |
| prime radical | C22×D16 | C8 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C82 ◁ C2×#1311 ◁ G | |
| LECS | G ▷ #1311 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #149502 | C2 | semidirect |
| 3. #122919 | C2 | semidirect |
| 4. #93757 | C2 | semidirect |
| 17. #7332 | C22 | semidirect |
| 19. #7099 | C22 | semidirect |
| 57. C2×D16 | C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#12045 | 2 |
| #149502 | 2 |
| #122919 | 2 |
| #93757 | 2 |