S835I defines "controlled foreign company" as "a company which is (a) not resident in the State, and (b) controlled by a company or companies resident in the State".
S835J outlines the meaning of control for the purposes of the CFC rules.
A person is regarded as having control of a company if the person has or is entitled to acquire, directly or indirectly: - the majority of the issued share capital or voting power, - an amount of capital that entitles the person, in circumstances where there would be a total distribution of income, to more than 50 per cent of the distribution, or, - such rights that entitle the person to more than 50% of the distributable assets on a winding up or otherwise , or, - any part of the share capital, where as a result the person would be able to control the composition of the board of directors. 
Control is deemed to also exist in other circumstances including taking future rights into account, nominee rights, and rights of associated companies (which requires the identification of a 25% relationship between two companies) along with associates.