Cooperation is a ubiquitous behavior in many biological systems and is well-known for promoting Allee effects. However, few studies have paid attention to mechanisms inducing Allee effects in predators. Here, we focus on hunting cooperation and use a classical predator prey system for identifying the impact of this mechanism. We add a cooperation term to the attack rate of the predator population, and investigate the equilibrium stability in phase plane and bifurcation diagrams. We show that hunting cooperation can be beneficial to the predator population by increasing the attack rate. We identify a scenario in which hunting cooperation produces Allee effects in predators and allows the latter to persist when the prey population does not sustain them in the absence of hunting cooperation. However, hunting cooperation can turn detrimental to predators when prey density drastically decreases because of increased predation pressure, which in turn decreases the predator intake. Hunting cooperation can also destabilize the system and promote a sudden collapse of the predator population. We generalize the model and prove that demographic Allee effects always occur when (1) the attack rate increases with the predator density, and (2) the functional response increases with the attack rate. We conclude that Allee effects in predators might be more widespread than expected. Mechanisms inducing such effects may strongly influence not only predators, but also the fate of ecosystems involving predators as in biological control programs.