Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
190 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C16 | #322 |
| commutator | C8 | C8×C16 |
| Frattini, cosocle | C2×#1397 | C22 |
| socle | C2 | #93990 |
| prime radical | C23 | #1398 |
| LCS | G ▷ C8 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16 ◁ C2×#1397 ◁ G | |
| LECS | G ▷ C2×#1397 ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. M128 | C8 | semidirect |
| 26. C2×C64 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#7511 | 2 |
| #149496 | 2 |