Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1184 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C61 |
| socle | C2×C61 | C2×B(4,𝔽2) |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C2×C4×C61 ◁ C2×#41×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3483 | C2 | semidirect |
| 2. C61×#3018 | C2 | semidirect |
| 3. C61×#2205 | C2 | semidirect |
| 4. C61×#2204 | C2 | semidirect |
| 5. C61×#2132 | C2 | semidirect |
| 8. Q82×C61 | C22 | semidirect |
| 10. C61×#555 | C22 | semidirect |
| 21. C61×#356 | C22 | semidirect |
| 22. C61×#355 | C22 | semidirect |
| 149. #33567 | C61 | direct (N × H) |
| 164. #3483 | C2×C61 | semidirect |
| 165. #3018 | C2×C61 | semidirect |
| 166. #2205 | C2×C61 | semidirect |
| 167. #2204 | C2×C61 | semidirect |
| 168. #2132 | C2×C61 | semidirect |
| 176. Q82 | C22×C61 | semidirect |
| 178. #555 | C22×C61 | semidirect |
| 189. #356 | C22×C61 | semidirect |
| 190. #355 | C22×C61 | semidirect |
| 191. C61 | #33567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3483 | 2 |
| C61×#3018 | 2 |
| C61×#2205 | 2 |
| C61×#2204 | 2 |
| C61×#2132 | 2 |
| #33567 | 61 |