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We consider a multigroup multicast cell-free multiple-input multiple-output (MIMO) downlink system with short-term power constraints. In particular, the normalized conjugate beamforming scheme is adopted at each access point (AP) to keep the downlink power strictly under the power budget regardless of small scale fading. In the considered scenario, APs multicast signals to multiple groups of users whereby users in the same group receive the same message. Under this setup, we are interested in maximizing the minimum achievable rate of all groups, commonly known as the max-min fairness problem, which has not been studied before in this context. To solve the considered problem, we first present a bisection method which in fact has been widely used in previous studies for cell-free massive MIMO, and then propose an accelerated projected gradient (APG) method. We show that the proposed APG method outperforms the bisection method requiring lesser run time while still achieving the same objective value. Moreover, the considered power control scheme provides significantly improved performance and more fairness among the users compared to the equal power allocation scheme.