Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
221 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23 | #1368 |
| commutator | C16 | C22×C16 |
| Frattini, cosocle | #1311 | C23 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ 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 |
|---|---|---|
| 3. #93877 | C2 | direct (N × H) |
| 38. C2×C32 | C16 | semidirect |
| 78. C32 | C2×C16 | semidirect |
| 125. C2 | #93877 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#7330 | 2 |
| C2×#7099 | 2 |
| #93877 | 2 |