What is the social class in Brave New World?

In Brave New World social class is based on a rigid hierarchy created by genetic engineering. The state planners have designed levels of intelligence in the population which are a futuristic counterpart to the class-structure of the past world. Each level is named by a letter of the Greek alphabet—alpha through epsilon. Within each stratum there are sub-categories, such as minus, plus, and double-plus. In the story, for instance, Bernard is an Alpha (more specifically an Alpha-plus), a member of the most intelligent class, and Lenina is a Beta, the second highest main level. There are references through the story to the "lowest" level of the hierarchy, the Epsilons, who are evidently mentally-challenged people.
As is typical of dystopian novels, in Brave New World there are individuals or segments of the population who represent "the past" and have remained outside the state-controlled modernized world. Such people are encountered on the "Savage Reservation" visited by Bernard and Lenina. John, a young man whose mother had been a member of the regular society before ending up with the "savages" and giving birth to him, becomes a kind of spokesman for the "old" way of life, though at first he expects to find a kind of paradise in the modern world when he's about to enter it for the first time. John has read Shakespeare and constantly quotes him, uttering the words "brave new world" from The Tempest as a description of what he thinks this new society is going to be like, before he actually is exposed to it. One might say that the "primitive" outsiders like John represent an "underclass." These are people not conceived through in vitro fertilization like everyone in the dominant society. In some sense they are similar to the proles in Orwell's 1984.
A basic theme of the novel is the dichotomy between this new genetically-planned society and the old, messy but human world of the past. But again, as in other dystopian works, the "inhuman" futuristic world is intended to be an exaggerated form, or a projection, of what is already taking place in the author's own time. Unlike Orwell, who saw the totalitarian governments of the 1930's and 1940's as becoming universal in a nightmare dystopia, Huxley saw the increasing technological advancement of the twentieth century as the basis for a scientifically-planned pleasure-world of the future, in which each class of people instinctively "knows its place," there is complete sexual freedom, and any discontent is dealt with by government-dispensed drugs. This social structure, one in which all are presumably "happy," is a parody of the UK's (previous) class society, and, though it represents a kind of socialism, it's an inverted kind in which the opposite of the classless society envisioned by Marxian thinkers has been produced.