It is possible to compare a variable, for example age, between an entire group of patients and a subgroup of patients (a part of the entire group)?
Yes you can.
However, I would think its only appropriate if you remove your subgroup from the "entire group" data such that they are independent measures.
Next I would also worry about the interpretation of the result. Is this leftover "entire group" really representative of something now that you've remove some subgroup of interest?
But to repeat, just in terms of "can you compare to groups' ages to one another"… Yes of course.
Under parametric assumptions a t-test will do just fine.
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