In A Preface to Paradise Lost, C. S. Lewis destroys the notion that Milton was an egalitarian, explaining that Milton held what Lewis calls the "Hierarchical conception" of not only society but also the very cosmos itself:

According to this conception degrees of value are objectively present in the universe. Everything except God has some natural superior; everything except unformed matter has some natural inferior. The goodness, happiness, and dignity of every being consists in obeying its natural superior and ruling its natural inferiors. When it fails in either part of this twofold task we have disease or monstrosity in the scheme of things until the [guilty] being is either destroyed or corrected. One or the other it will certainly be; for by stepping out of its place in the system (whether it step up like a rebellious angel or down like an uxorious husband) it has made the very nature of things its enemy. It cannot succeed.

Lewis explains that in Milton's Hierarchical conception, one's happiness consists in joyfully submitting to one's place. In this view, once we submit to the God-designed natural order of authority, we are free to become what we were fully created to become. To illustrate this concept, Lewis uses the metaphors of taking part in a dance or playing an instrument in an orchestra. Yes, you must submit to the rules of the dance or the notes on the music--but once you do submit to the created order, you become what you were created to be:

[Milton] pictures the life of beatitude as one of order--an intricate dance, so intricate that it seems irregular precisely when its regularity is most elaborate. He pictures his whole universe as a universe of degrees, from root to stalk, from stalk to flower, from flower to breath, from fruit to human reason (V, 480). He delights in the ceremonious interchange of unequal courtesies, with condescension (a beautiful word which we have spoiled) on the one side and reverence on the other. He shows us the Father 'with rayes direct' shining full on the Son, and the Son 'o'er his scepter bowing' as He rose (VI, 719, 746). ...

Discipline . . . exists for the sake of what seems its very opposite--for freedom, almost for extravagance. The pattern deep hidden in the dance, hidden so deep that shallow spectators cannot see it, alone gives beauty to the wild, free gestures that fill it. . . The happy soul is, like a planet, a wandering star; yet in that very wandering (as astronomy teaches) invariable; she is eccentric beyond all predicting, yet equable in her eccentricity. The heavenly frolic arises from an orchestra which is in tune; the rules of courtesy make perfect ease and freedom possible between those who obey them. Without sin, the universe is a Solemn Game: and there is no good game without rules.  

Lewis also discusses how the Hierarchical conception sees civil society, private life, and other areas:

When Donne says 'thy love shall be my love's sphere,' he has for his background the cosmic hierarchy of the Platonic theologians. . . . Every being is a conductor of superior love . . . to the being below it, and of inferior love . . . to the being above. Such is the loving inequality between the intelligence who guides a sphere and the sphere which is guided. This is not metaphor. For the Renaissance thinker, not less but more than for the schoolman, the universe was packed and tingling with anthropomorphic life; its true picture is to be found in the elaborate title pages of old folios where winds blow at the corners and at the bottom dolphins spout, and the eye passes upward through cities and kings and angels to four Hebrew letters with rays darting from them at the top, which represent the ineffable Name. Hence we are only on the borderline of metaphor Spenser's Artegall reproves the leveling giant by telling him that all things were created 'in goodly measure' and 'doe know their certaine bound,' so that hills do not 'disdaine' vallies nor valies 'envy hills; in virtue of the same grand Authority who causes kings to command and subjects to obey.

According to Lewis, the Hierarchical conception was held from Aristotle to the eighteenth century. He argues that it is difficult for modern readers to understand older literature because the concept is so foreign to us. For example, Shakespeare fully accepted this Hierarchical view as well. Lewis argues,

Hierarchy is a favourite theme with Shakespeare. A failure to accept his notion of natural authority makes nonsense, for example, of The Taming of the Shrew. . . . If the poet had not meant us to rejoice in the correction of Katharina he would have made her a more amiable character.

Lewis cites other examples from Shakespeare as well, including A Comedy of Errors, The Tempest, King Lear, and Macbeth. Along the way, he shows how this natural order of things can be violated:

Now if once the conception of Hierarchy is fully grasped, we see that order can be destroyed in two ways: (1) By ruling or obeying natural equals, that is by Tyranny or Servility. (2) By failing to obey a natural superior or to rule a natural inferior--that is, by Rebellion or Remisness. And these . . . are equally monstrosities.

Examples of such violation include Macbeth (who let his wife tell him what to do) and Lear (who failed to take responsibility for his kingdom).

Finally, Lewis critiques modern Milton critics who see Satan as some sort of ironic hero:

It would not be surprising if we, who were mostly brought up on egalitarian or even antinomian ideas, should come to the poem with minds prepossessed in favour of Satan against God and of Eve against Adam, and then read into the poet a sympathy with those prepossessions which is not really there.