Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
2414 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | #95 |
| commutator | C23 | C2×C42×C41 |
| Frattini, cosocle | C25 | C23×C41 |
| prime radical | C26×C41 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C26×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1304 | C2 | direct (N × H) |
| 5. C22×C22⋊C4×C41 | C4 | semidirect |
| 7. C41×#379 | C4 | semidirect |
| 23. C2×C22⋊C4×C41 | C2×C4 | semidirect |
| 95. C2×#1304 | C41 | direct (N × H) |
| 122. #1304 | C2×C41 | direct (N × H) |
| 129. C2×C41 | #1304 | direct (N × H) |
| 133. C22×C22⋊C4 | C4×C41 | semidirect |
| 135. #379 | C4×C41 | semidirect |
| 137. C41 | C2×#1304 | direct (N × H) |
| 152. C2×C22⋊C4 | C2×C4×C41 | semidirect |
| 255. C2 | C41×#1304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#379 | 2 |
| C41×#1304 | 2 |
| C2×#1304 | 41 |