Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1766 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1766 conjugacy classes of subgroups — too many to draw. Only its 158 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 | C22×D4 | C23×C41 |
| prime radical | C22×#127×C41 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C24×C41 ◁ C23×D4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C41×#353 | C2 | semidirect |
| 3. C41×#1781 | C2 | semidirect |
| 5. C23×D4×C41 | C4 | semidirect |
| 9. C2×#127×C41 | C4 | semidirect |
| 11. C22×C42×C41 | C4 | semidirect |
| 13. C2×#99×C41 | C22 | semidirect |
| 80. C2×D4×C41 | C22⋊C4 | semidirect |
| 96. C42×C41 | C22⋊C4 | semidirect |
| 144. #12693 | C41 | direct (N × H) |
| 164. C22×C41 | #353 | semidirect |
| 173. C2×#353 | C2×C41 | semidirect |
| 174. #1781 | C2×C41 | semidirect |
| 184. C23×D4 | C4×C41 | semidirect |
| 188. C2×#127 | C4×C41 | semidirect |
| 190. C22×C42 | C4×C41 | semidirect |
| 192. C2×#99 | C22×C41 | semidirect |
| 195. C41 | #12693 | direct (N × H) |
| 260. C2×D4 | C22⋊C4×C41 | semidirect |
| 276. C42 | C22⋊C4×C41 | semidirect |
| 343. C22 | C41×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#127×C41 | 2 |
| C2×C41×#353 | 2 |
| C41×#1781 | 2 |
| #12693 | 41 |