Kingdom of Satan
Satan is represented as having a kingdom (Matthew 12) and power (Acts 26), whose rule is exercised in the souls of those who disobey God.
More definitely the kingdom of Satan means the organized forces of the evil spirits under the leadership of Satan, the "Adversary," the devil.
By God's permission this kingdom extends over all that is not of heaven, until the struggle between the powers of hell and the kingdom of God on earth, as foretold in the Apocalypse (cf. 12, 7-9; cf. 20) shall end with the Last Judgment in the final triumph of Christ and His Saints.
New Catholic Dictionary