A company which controls another company is known as the ‘holding company’ and the company so controlled is termed as ‘subsidiary company’.
Section 4 of the companies act 1956 provides that a holding company is one if it
(1) Controls the composition of board of directors of another company; or
(2) Holds more than half of the nominal value of equity share capital of another company; or
(3) Is a subsidiary of any company which is in turn a subsidiary of another company
An example will illustrate the point. Company B is a subsidiary of company A, and company C is a subsidiary of company B. Company C will be a subsidiary of company A.
A subsidiary company cannot hold shares or be a member of its holding company except as a legal representative of a deceased member of the holding company or any trustee.