Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C41 |
| prime radical | C41×#392 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×#117×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1740 | C2 | semidirect |
| 3. C41×#1464 | C2 | semidirect |
| 4. C41×#1351 | C2 | semidirect |
| 6. C2×#124×C41 | C4 | semidirect |
| 10. C41×#395 | C4 | semidirect |
| 11. C41×#394 | C4 | semidirect |
| 18. C41×#376 | C4 | semidirect |
| 155. #11758 | C41 | direct (N × H) |
| 187. #1740 | C2×C41 | semidirect |
| 188. #1464 | C2×C41 | semidirect |
| 189. #1351 | C2×C41 | semidirect |
| 199. C2×#124 | C4×C41 | semidirect |
| 203. #395 | C4×C41 | semidirect |
| 204. #394 | C4×C41 | semidirect |
| 211. #376 | C4×C41 | semidirect |
| 216. C41 | #11758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2610 | 2 |
| C41×#1740 | 2 |
| C41×#1464 | 2 |
| C41×#1351 | 2 |
| C41×#1343 | 2 |
| #11758 | 41 |