Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
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×C61 | C2×#99 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C61 |
| prime radical | C61×#2635 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×C4×D4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#99×C61 | C2 | semidirect |
| 3. C61×#1460 | C2 | semidirect |
| 4. C61×#1352 | C2 | semidirect |
| 5. C61×#1343 | C2 | semidirect |
| 6. C2×#121×C61 | C4 | semidirect |
| 10. C61×#400 | C4 | semidirect |
| 13. C61×#394 | C4 | semidirect |
| 18. C61×#381 | C4 | semidirect |
| 155. #11729 | C61 | direct (N × H) |
| 189. C4×#99 | C2×C61 | semidirect |
| 190. #1460 | C2×C61 | semidirect |
| 191. #1352 | C2×C61 | semidirect |
| 192. #1343 | C2×C61 | semidirect |
| 201. C2×#121 | C4×C61 | semidirect |
| 205. #400 | C4×C61 | semidirect |
| 208. #394 | C4×C61 | semidirect |
| 213. #381 | C4×C61 | semidirect |
| 218. C61 | #11729 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2635 | 2 |
| C4×#99×C61 | 2 |
| C61×#1460 | 2 |
| C61×#1352 | 2 |
| C61×#1343 | 2 |
| #11729 | 61 |