Large-eddy simulations of the flow around a circular cylinder at a Reynolds number, based on cylinder diameter and free-stream velocity, $Re_D=2{ imes}10^4$ are presented. Three different dynamic subgrid-scale models are used, viz. the dynamic eddy-viscosity model and two different mixed two-parameter models. The sensitivity to grid refinement in the spanwise and radial directions is systematically investigated. For the highest resolution considered, the effects of subgrid-scale modeling are also discussed in detail. In particular, it is shown that SGS modeling has a significant influence on the low-frequency modulations of the aerodynamics loads, which are related to significant changes in the near wake structure.