Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
248 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 98 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×C127 | #124 |
| commutator, Frattini, cosocle | C2×C42 | C23×C127 |
| socle | C22×C127 | #400 |
| prime radical | C23×C127 | C22⋊Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 114. #10689 | C127 | direct (N × H) |
| 127. C127 | #10689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C127×#1940 | 2 |
| C127×#1838 | 2 |
| C127×#1303 | 2 |
| C127×#1301 | 2 |
| C127×#1275 | 2 |
| #10689 | 127 |