The word 旗下 is formed by combining the character 旗, meaning "flag", with 下, meaning "under", creating the literal phrase "under the flag". This originates from historical contexts where flags represented military or organizational units, so being "under the flag" indicated affiliation with or subordination to that unit's leader. Over time, this concrete spatial relationship evolved to denote modern concepts of being under the authority or within the structure of a larger organization, such as a subsidiary company.