Does it fall under fiscal, monetary, or supply-side, or perhaps some other group? Also (seeing as minimum wage is a form of price control policy), where does the broader "price control policy" fall?
Looking up each of those terms you ask about would have given you your answer.
Fiscal policy is economic policy enacted through government. The minimum wage is a type of fiscal policy.
Monetary policy is economic policy enacted through central banking. The minimum wage is NOT a type of monetary policy.
Supply-side is a macroeconomic theory that growth is best achieved through capital investment and lowering barriers to production. Usually the policy suggestions to come out of this are to remove government regulation and lower marginal tax rates. The minimum wage is a type of regulation, so minimum wage would not fall under the doctrine of classical supply side economics.
I don't understand what you mean when you ask where "price control policy" falls under. There's no real categorization for it besides also being a type of fiscal policy.
Firstly a general observation. There can be more than one way correctly to classify an economic policy. One reason is that classifications can be broader or finer (more detailed). Another is that classifications may relate either to the nature of the policy instrument or to the economic objectives of its use.
A minimum wage policy typically has the objective of relieving poverty for those in work, so in terms of its objective could be classified as an example of a policy to raise economic welfare (how successful it may be in achieving that objective is a further question).
In terms of the nature of the policy instrument, a minimum wage policy could as you say be regarded as a form of price control policy. Price control policy in turn could be regarded as an example of economic regulation, implying direct controls on the operation of particular markets (other examples being import or export quotas and rationing - by the government rather than the market - of scarce goods). However, the objectives of price controls, which include price ceilings as well as price floors, and more generally of economic regulation are often very different to those of a minimum wage policy. For example, price ceilings applying to a wide range of goods have sometimes been adopted as an instrument of counter-inflation policy.