Here's a link that shows who makes what at Kenmore:
http://www.appliance411.com/purchase/sears.shtml
whirlpool includes: whirlpool, maytag, kitchenaid, jenn-air, amana, ikea and a few others.
I think Frigidaire also includes electrolux, gibson, tappan.
GE makes hotpoint.
I think LG and Samsung are single brand companies (for these types of appliances).