Capitalism and socialism are broadly opposing schools....
One of the oddest ideas I encounter on a regular basis (typically among Americans, because of the limited nature of our political discourse), is belief the the mixed economy is specifically a mixture of capitalism and socialism. It is not. The mixed economy is fundamentally capitalist in nature; "a little socialism" is not a meaningful concept in an economic structure. An economic system must incorporate public/collective control of the means of production to be legitimately socialist; anything short of that is likely a form of capitalism.
No ideology is pure, the collective control of the means of production in our so called capitalist economy is obvious in any business owned by the employees. There are lots. Even the purchasing of stock could be considered owning the means of prod.