Order 2816.
1934 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D11 |
| commutator, socle, prime radical, cosocle | C24×C11 | C24 |
| Fitting | C22×C11×C4⋊Q8 | C2 |
| hypercenter | C22×C4⋊Q8 | D11 |
| hypocenter | C11 | #15143 |
| LCS | G ▷ C24×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 49. C2×C4⋊Dic11 | Q8 | semidirect |
| 57. C2×C4×Dic11 | Q8 | semidirect |
| 61. C11⋊#95 | Q8 | semidirect |
| 160. C2×Dic11 | C4⋊Q8 | semidirect |
| 199. C4×C11 | #395 | semidirect |
| 295. C11 | #15143 | semidirect |
| 363. C4 | #10622842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622842 | 2 |
| C2×#10622541 | 2 |
| C2×#10622589 | 2 |
| #13066879 | 2 |
| #13066845 | 2 |
| C4×C11⋊#95 | 2 |
| C22×C11×C4⋊Q8 | 2 |
| #15143 | 11 |