It appears that God the Father is subjecting all things to the Son:
Hebrews 2:5-9 (DRB)
For God hath not subjected unto angels the world to come, whereof we speak. 6 But one in a certain place hath testified, saying: What is man, that thou art mindful of him: or the son of man, that thou visitest him? 7 Thou hast made him a little lower than the angels: thou hast crowned him with glory and honour, and hast set him over the works of thy hands: 8 Thou hast subjected all things under his feet. For in that he hath subjected all things to him, he left nothing not subject to him. But now we see not as yet all things subject to him. 9 But we see Jesus, who was made a little lower than the angels, for the suffering of death, crowned with glory and honour: that, through the grace of God, he might taste death for all.
Matthew 22:41-46 (DRB)
And the Pharisees being gathered together, Jesus asked them, 42 Saying: What think you of Christ? whose son is he? They say to him: David's. 43 He saith to them: How then doth David in spirit call him Lord, saying: 44 The Lord said to my Lord, Sit on my right hand, until I make thy enemies thy footstool? 45 If David then call him Lord, how is he his son? 46 And no man was able to answer him a word; neither durst any man from that day forth ask him any more questions.
And yet, like the raising to life of Jesus, the unity of operation is so great that the action can rightly and equally be attributed to the Father (Acts 13:30; Gal 1:1), the Son (Jn 2:19, 21; 10:17-18), and the Holy Ghost (Rom 8:11; 1:4):
Philippians 3:20 (DRB)
But our conversation is in heaven; from whence also we look for the Saviour, our Lord Jesus Christ, who will reform the body of our lowness, made like to the body of his glory, according to the operation whereby also he is able to [subject] all things unto himself.
But for this instance, it seems that the humanity of Christ is particularly in view, since the author presents Him as crowned with glory He never had in His human nature, but which He of course did in His divine (Jn 1:1-3, 14; 17:5; 8:58; Phil 2:5-11; cf. Mic 5:2).
One would think, therefore, that the active subjection is by the Father under the feet of the Son, and so the passage should be read in that light all throughout; except there is a very clear instance in the beginning where Christ is said to subject His enemies Himself:
1 Corinthians 15:20-27 (DRB)
But now Christ is risen from the dead, the firstfruits of them that sleep: 21 For by a man came death, and by a man the resurrection of the dead. 22 And as in Adam all die, so also in Christ all shall be made alive. 23 But every one in his own order: the firstfruits Christ, then they that are of Christ, who have believed in his coming. 24 Afterwards the end, when he shall have delivered up the kingdom to God and the Father, when he shall have brought to nought all principality, and power, and virtue. 25 For he must reign, until he hath put all his enemies under his feet. 26 And the enemy death shall be destroyed last: For he hath put all things under his feet. And whereas he saith, 27 All things are put under him; undoubtedly, he is excepted, who put all things under him.
Then we begin to be introduced to a clear unidentified person who is indubitably God the Father who is said to be responsible for the subjection of all things to Christ. This merely adds information to the fact that Christ is subjecting His enemies under His feet: namely, that God the Father is the One accomplishing or provisioning this prerogative and right of conquest of the King, Jesus.
1 Corinthians 15:28 (DRB)
And when all things shall be subdued unto him [notice the passive on the part of Christ], then the Son also himself shall be subject unto him that put all things under him, that God may be all in all.
("That God may be all and in all" seems to me to imply that God is ultimately made the summit, center and focus of all creation, and the servanthood of Jesus is subsumed into what was before His incarnation. Another way to look at it is that Jesus holds His rightful possession, the saints and their obedience, in His hand and what is being described is a divinely humble, loving, sharing of His 'spoils,' the saints, in an ultimate sense, with the Father.)