Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1224 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 150 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 | #120 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C23×C4 | C23×C41 |
| prime radical | C2×C41×#392 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2312 | C2 | semidirect |
| 3. C41×#1786 | C2 | semidirect |
| 4. C2×C41×#323 | C2 | semidirect |
| 5. C41×#1294 | C2 | semidirect |
| 13. C41×#392 | C4 | semidirect |
| 35. C2×C4⋊C4×C41 | D4 | semidirect |
| 165. #9020 | C41 | direct (N × H) |
| 201. #2312 | C2×C41 | semidirect |
| 202. #1786 | C2×C41 | semidirect |
| 203. C2×#323 | C2×C41 | semidirect |
| 204. #1294 | C2×C41 | semidirect |
| 221. #392 | C4×C41 | semidirect |
| 228. C41 | #9020 | direct (N × H) |
| 244. C2×C4⋊C4 | D4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#392 | 2 |
| C41×#2312 | 2 |
| C41×#1786 | 2 |
| C2×C41×#323 | 2 |
| C41×#1294 | 2 |
| #9020 | 41 |