Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
958 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C23×C4 | C23×C41 |
| prime radical | C41×#2404 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2273 | C2 | semidirect |
| 3. C41×#1789 | C2 | semidirect |
| 4. C41×#1462 | C2 | semidirect |
| 5. C41×#1284 | C2 | semidirect |
| 12. C41×#393 | C4 | semidirect |
| 13. C41×#392 | C4 | semidirect |
| 25. C22×Q8×C41 | C2×C4 | semidirect |
| 28. C22×D4×C41 | C2×C4 | semidirect |
| 46. C2×C42×C41 | D4 | semidirect |
| 54. #95×C41 | C2×C4 | semidirect |
| 127. C23×C41 | #104 | semidirect |
| 160. #9475 | C41 | direct (N × H) |
| 192. #2273 | C2×C41 | semidirect |
| 193. #1789 | C2×C41 | semidirect |
| 194. #1462 | C2×C41 | semidirect |
| 195. #1284 | C2×C41 | semidirect |
| 210. #393 | C4×C41 | semidirect |
| 211. #392 | C4×C41 | semidirect |
| 219. C41 | #9475 | direct (N × H) |
| 224. C22×Q8 | C2×C4×C41 | semidirect |
| 227. C22×D4 | C2×C4×C41 | semidirect |
| 245. C2×C42 | D4×C41 | semidirect |
| 253. #95 | C2×C4×C41 | semidirect |
| 326. C23 | #104×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2404 | 2 |
| C41×#2273 | 2 |
| C41×#1789 | 2 |
| C41×#1462 | 2 |
| C41×#1284 | 2 |
| #9475 | 41 |