You can use the resources below to compile lists of companies based on various criteria.  For example, NAICS or SIC codes, i.e. industries! 

Both of these databases include both public and private companies; parent companies and subsidiaries; US and international companies.

For both SIC and NAICS codes (and other classification codes), the codes may be called primary or secondary.  Here's what this means:

Primary:  this code designates the industry or line of business from which the company derives the greater part of its income.

Secondary:  these codes tell you which industries that your company is involved in.  A company that is highly diversified may have a dozen or even more industry codes assigned to it.

Here's more information about industry classification systems.