In this paper, multi-group multicast beamforming is considered for the full digital and hybrid beamforming. The wireless system comprises of a multiple-antenna base station and single-antenna users. Quality-of-service (QoS)-aware design is investigated where the optimization objective is to minimize the total transmitted power subject to the signal-to-interference-plus-noise ratio (SINR) constraint at each user. In addition to the SINR constraints, per-antenna power constraint is included for each antenna of the base station. The original optimization problem for full digital beamforming is transformed into an equivalent form such that the alternating direction method of multipliers (ADMM) can be applied in an effective and computationally inexpensive manner for the large-scale antenna systems. In this new formulation, the beamformer weight vectors are decomposed into two subspaces in order to decrease the number of dual variables and multiplications. The optimum update equations are obtained for the proposed ADMM algorithm. This new reformulation is used for two different hybrid beamforming structures employing phase shifters and vector modulators. Optimum updates are derived for each system. The proposed algorithms decrease computational complexity of the existing ADMM algorithms due to the effective reformulation as well as the direct solution of the nonconvex problem. In the simulation results, it is shown that the proposed methods have better convergence behavior and less computational time than the benchmark algorithms. Furthermore, the proposed method for hybrid beamforming with vector modulators performs better than its counterpart in the literature in terms of transmitted power. (C) 2019 Elsevier Inc. All rights reserved.