Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
692 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #379 |
| commutator | C42 | C22×C4×C41 |
| Frattini, cosocle | C2×C42 | C23×C41 |
| prime radical | C41×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C41×#1559 | C2 | semidirect |
| 5. C41×#1506 | C2 | semidirect |
| 7. C41×#559 | C4 | semidirect |
| 8. Q82×C41 | C4 | semidirect |
| 124. #8492 | C41 | direct (N × H) |
| 141. #1559 | C2×C41 | semidirect |
| 143. #1506 | C2×C41 | semidirect |
| 149. #559 | C4×C41 | semidirect |
| 150. Q82 | C4×C41 | semidirect |
| 165. C41 | #8492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3550 | 2 |
| C41×#1963 | 2 |
| C41×#1559 | 2 |
| C41×#1536 | 2 |
| C41×#1506 | 2 |
| #8492 | 41 |