What is difference between QA, QC and Software Testing?

QA is the big field related to QC .QC is the process or the team which control the quality of product and if any fault detects they report it .But the QA define the procedures to test the product like TEST CASES  to run on product .Refer the product to concern department for correctness and after correctness test it again .All of this process includes QA and QC is called Software testing in which you test software for possible bugs and report it to the developing team