Order 15616.
1022 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 98 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C23×C61 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C61 ◁ C22×D4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C61×B(4,𝔽2) | C2 | semidirect |
| 2. C2×C61×#453 | C2 | semidirect |
| 3. C61×#2669 | C2 | semidirect |
| 4. C2×C61×#353 | C2 | semidirect |
| 5. C2×C61×AΣL(1,𝔽16) | C2 | semidirect |
| 6. C61×#1790 | C2 | semidirect |
| 7. C61×#1390 | C2 | semidirect |
| 38. H(5,𝔽2)×C61 | D4 | semidirect |
| 50. C22×D4×C61 | D4 | semidirect |
| 52. C23×C4×C61 | D4 | semidirect |
| 82. C2×C22⋊C4×C61 | D4 | semidirect |
| 83. C2×C42×C61 | D4 | semidirect |
| 86. #100×C61 | D4 | semidirect |
| 92. #99×C61 | D4 | semidirect |
| 302. #13346 | C61 | direct (N × H) |
| 356. C2×B(4,𝔽2) | C2×C61 | semidirect |
| 357. C2×#453 | C2×C61 | semidirect |
| 358. #2669 | C2×C61 | semidirect |
| 359. C2×#353 | C2×C61 | semidirect |
| 360. C2×AΣL(1,𝔽16) | C2×C61 | semidirect |
| 361. #1790 | C2×C61 | semidirect |
| 362. #1390 | C2×C61 | semidirect |
| 400. C61 | #13346 | direct (N × H) |
| 406. H(5,𝔽2) | D4×C61 | semidirect |
| 418. C22×D4 | D4×C61 | semidirect |
| 420. C23×C4 | D4×C61 | semidirect |
| 450. C2×C22⋊C4 | D4×C61 | semidirect |
| 451. C2×C42 | D4×C61 | semidirect |
| 454. #100 | D4×C61 | semidirect |
| 460. #99 | D4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C61×B(4,𝔽2) | 2 |
| C2×C61×#453 | 2 |
| C61×#2669 | 2 |
| C2×C61×#353 | 2 |
| C2×C61×AΣL(1,𝔽16) | 2 |
| C61×#1790 | 2 |
| C61×#1390 | 2 |
| #13346 | 61 |