I think they are plenty of other puppets missing on the picture, especially for countries like Italy and Denmark. Here is the Wikipedia definition of a puppet regime:

A puppet state is a country that is nominally independent, but in reality, under the control of another power.

The term has two distinct but related meanings. First, it refers to a state whose government depends on a foreign power for its existence and which closely follows the will of that foreign power in key policy issues; sometimes economic, sometimes strategic.