Much of The Picture of Dorian Gray is a coded story of things that could not be expressed openly in the mainstream literature of the Victorian period.
Wilde was hardly a socialist or a revolutionary, at least in his public persona. Yet he indirectly criticizes England's class structure in the doomed relationship of Dorian and Sibyl Vane. One wonders how much of the dismissive attitude toward her by Dorian's friends, Lord Henry and Basil, is rooted in their class snobbishness. Lord Henry is cynical about everything, so he would be against her no matter what her background happened to be. But Sibyl's powerlessness in front of Dorian when he coldly rejects her is at least partly due to her not being a titled lady or a member of the upper-class in general. It is only a "common" person, a girl of working-class background, whom he would dare treat in so reprehensible a way.
Dorian becomes an outcast, yet until he murders Basil we are really not shown directly the specifics of what his rebellion consists of. He is still "of society" while he flouts the values of the community. Most readers today, especially when taking into account Wilde's own biography, tend to think Dorian has adopted a gay lifestyle. This is the terrible, unmentionable "crime." From the veiled (and not always completely so) references and the fact that his actions are merely hinted at, we know they must be something "worse" than the usual things like seducing women, forgery, or engaging in some other criminal enterprise that would be evils a Victorian writer could mention directly. Dorian thus retains his outwardly aristocratic appearance and role, but his actions are subversive to the values of the Victorian community.
Even apart from his flouting the societal strictures of that time (and later) against the gay lifestyle, Dorian's "decadence" has already begun when he destroys Sibyl. This is arguably the most important factor in the decay of Dorian's soul, and it is what he observes in the picture's change even before he learns of her suicide. But paradoxically, the humanity and decency he retains at that moment are what set him on his downward course. He is genuinely shocked by the news that she has killed herself and knows that he's to blame. It's as if he now views himself as hopelessly sinful, irredeemable, and that he may as well just go ahead with all the "crimes" he knows he has the potential to commit.