In a Perfect Information Game a subgame is a subtree of the original game tree rooted at any node.
This definition is problematic for Imperfect Information Game since such subtree could include one part of the information set and exclude another.
Defining Subgame for Imperfect Information Game
To define a subgame for an Imperfect Information Game a generalized concept of information set is used.
Resources
Resources I referred to when making this note: