consociata (sister company, all the companies in question are on the same level)
società affiliata (affiliated company)
filiale/succursale (it's a branch elsewhere)
società madre & società figlia (parent company and subsidiary company or subcompany, depending on the parent company)
Though I have to point out that "società figlia" is rarely used, but if we talk of filiali, we are implying that we're talking of the very same company (with the same name) with more branches/offices.
In other words, could you explain what you mean by subsidiary company? I'll try to find the right word.