What social classes do characters in Austen's Pride and Prejudice represent, and do any rise in class?

Charlotte, daughter of Sir Lucas, represents the upper
class of knights, who have the lowest rank of nobility as the title is not hereditary:
it does not pass on to a son. Sir Lucas demonstrates upward class mobility since he was
beknighted by the Queen and thus entered the the knighthood. Mr. Collins, whom Charlotte
marries, represents the working class comprised of lesser clergymen, doctors, teachers,
merchants, and such. Charlotte is in a higher class than Collins due to her father's
knighthood. When Collins marries Charlotte, he rises in social class by virtue of his
connection to her family.

Wickham represents the same class
as Collins’ because his father was employed as an estate steward. While he is in the
regiment, he is in the army and navy officer class of men (restricted to men then).
Members of his lower class, who had neither social position nor income to buy themselves
a commission but who had a benefactor who would buy a commission for them (as Darcy
bought Wickham's commission), could rise in social class because of the connections he
would make with the sons of nobility and independently wealthy gentlemen; these almost
exclusively made up the membership of the army and navy officer class. Wickham thus rose
in social class while in the regiment. He rose further, after being forced to marry
Lydia, through the connection of marriage to her father, because Mr. Bennet is an
independently wealthy (though running out of money) country gentleman. Wickham’s
character illustrates two ways to rise in social class. Had he accepted Darcy Sr.'s
provision for the clergy, he would have illustrated a third way the lower class might
rise through a financial benefactor.

The Bingley's
represent another way to rise in social class. Their father is a manufacturer. He
started out as a tradesman in the same class as Collins and Wickham. He made a great
success in his trade. He accumulated wealth and through wealth alone rose to the level
of independently wealthy gentleman. However, he was not a country gentleman as Mr.
Bennet was. He, Bingley's and Caroline's father, was a gentleman tradesman. The
Bingley's rose in social class through success and the acquisition of great sums of
money. The family rose so high through money, in fact, that Bingley was seen as a fit
companion for the independently wealthy and aristocratic Mr.
Darcy.

Jane and Bingley didn't really change their classes
when they married because they were both of the high class of independently wealthy
individuals. However, Jane did secure her position in their class through Bingley's
wealth, and Bingley did enhance his stature in their class because of his connection to
the country gentleman, a connection which overshadowed and improved the tradesman root
of his wealth.

Though Elizabeth and Darcy are in the same
class--Bennet and Darcy are both independently wealthy country gentlemen. Darcy however
has connections to the highest class through his connections to Lady Catherine de Bourgh
and his cousin Colonel Fitzwilliam, the son of an earl. Elizabeth, like Jane, secures
her position through Darcy’s wealth but also rises to the highest class because of her
connections through marriage to Darcy’s hereditary nobility. (This class distinction
indicates why Colonel Fitzwilliam chooses to be highly selective about whom he marries:
if he wants to retain his status in the highest class of nobility, he must marry a woman
in that class.)