Oscar Wilde's The Picture of Dorian Gray certainly criticizes and mocks at the prudish and hypocritical Victorian social values by presenting to the audience the exaggerated preoccupations of the Victorian newly-rising upper-middle classes.
As a class, the 19th century upper middle class consisted on stuffy, classicist, hyper-emotional and overly-self-serving, so-called philanthropists who actually did their charity work in aims of demonstrating to their peers that they were well enough to give much to others. After Queen Victoria's death in 1901, British society shut its doors to the Victorian paradigm and was happy to welcome a less "busy" and more flexible Edwardian era. However, the Victorian frame of mind, and all that came with it, would remain in the British psyche until the modern era.
All of this being said, The Picture of Dorian Gray is like a stamp in which time and space are frozen to show the exact dynamics of social behavior among Victorians. For example, the social structure of England is seen immediately when Basil describes the way in which me meets Dorian. They are at a social gathering where the hostess is making much of her guests. Basil is there because, in his words
You know we poor artists have to show ourselves in society from time to time, just to remind the public that we are not savages. With an evening coat and a white tie, as you told me once, anybody, even a stock-broker, can gain a reputation for being civilized.
On a similar note, chapter 3 gives the reader an insight of the nature of Dorian's birth; one which seems to have tarnished his very destiny
Kelso's grandson! ... I knew his mother...She was an extraordinarily beautiful girl...made all the men frantic by running away with a penniless young fellow -- a mere nobody...
Perhaps, the most interesting instance on social structure is also given in the first three chapters where Wilde makes a description of Lord Fermore, Lord Henry's uncle, illustrating the emptiness of the aristocratic lifestyle, ideals, and the ironic power that they still held over others.
Lord Fermor...was considered generous by Society as he fed the people who amused him. His father had been our ambassador at Madrid [but wanted Paris, instead because] he considered that he was fully entitled by reason of his birth, his indolence, the good English of his dispatches, and his inordinate passion for pleasure.
Therefore, the social structure in The Picture of Dorian Gray is one in which money rules over dignity, respect, and acceptance. It is a very bleak society, indeed. Notice how a job labels the worth of a person, and how an asinine rank determines the privileges of some within society. This is Wilde's comment on the social structure of the England that he knew for over 40 years.