The Greek adjective anypotaktos (ἀνυπότακτος) combines the alpha-privative with hypotassoo (G5293, to submit, be subject). It means insubordinate, unruly, not subject to authority, or rebellious.
Anypotaktos appears in Hebrews 2:8 to describe the 'not yet' of Christ's cosmic reign: 'In putting everything under him, God left nothing that is not subject (anypotakton) to him. Yet at present we do not see everything subject to him' — the tension between inaugurated and consummated eschatology. In Titus 1:6 and 1:10 it describes rebellious household members and false teachers. Insubordination to God's order — from rebellious children to false teachers to powers not yet subdued — is the fundamental problem that Christ's lordship progressively resolves.