How to get the name of a subtype field in a feature class in Python?

I have a geodatabase with many feature classes. Some of the feature classes have subtype fields. Their names vary feature class by feature class. I now want to find the names of those subtype fields.
What I have so far is:

for fc in arcpy.ListFeatureClasses("*","",dataset):
    subtypefields = arcpy.da.ListSubtypes(fc)
    for subtype in subtypefields:

Now, I don’t know how to continue from here. Any help will be appreciated.
Thanks!