How did Chicago's organized crime infiltrate every aspect of society?

The arrival of Alphonse Capone from New York in 1920 when he inherited Giovanni Torrio's gang, along with the passage of the 18th Amendment, marked the beginning of the infiltration of organized crime in Chicago, Illinois. 

Criminal activity began with gambling and prostitution in the 1900's; then gangsters made political connections in order to secure the continued operation of their concerns. Having such rackets in place prepared gangsters for the exploitation of Prohibition. In fact, people's desire for liquor or beer in Chicago seemed to increase when sales became illegal. 

Regarding the sale of liquor, Al Capone contended,

"All I do is to supply a public demand … somebody had to throw some liquor on that thirst. Why not me?" [ http://www.umich.edu/~eng217/student_projects/nkazmers/organizedcrime2.html ]  

With the sales of illegal liquor, Giovanni (John) Torrio, who led the Chicago Outfit, along with the help of Al Capone, turned this Outfit into a criminal machine that brought in $100 million a year. But, conflicts began between the Irish gang on the North Side, who controlled liquor sales in their part of the city, and the Italian gang on the South Side. Of course, these gangs were able to corrupt police and politicians with their added incomes thanks to Prohibition. Consequently, the courts became corrupt, as well, and many of the gangsters did not get convicted and serve prison sentences. With the massive fortune that he was making during Prohibition, Capone was able to bribe most of the law enforcement agents from the highest ranks to lower ones, as well as politicians in districts where he operated his illegal businesses. 

During Prohibition, Capone took over the operation of more distilleries and breweries. With his profits, he then constructed even more gambling houses, speakeasies, and houses of prostitution, as well as distilleries and breweries in the suburbs. Also, with his profits Capone began racketeering, which is the involvement of gangsters into legitimate businesses. Many of the labor unions were extorted by the mob, and, not surprisingly, some businesses willingly used labor racketeers to help control their competition, thus by-passing the Sherman Anti-trust Act that prohibited price fixing and collective bargaining.

It is well documented that Al Capone's mob was notorious for coercion. Whenever businesses and employees did not contribute a percentage of their income from enterprises, they ran the risk of their place being blown up or their being "taken for a ride." Living under such fear from this powerful mobster, many businesses acquiesced to extortion.
As his empire increased, Capone extended his "strong-arming." He became able to bribe very high officials. One such official was Mayor William Hale Thompson, who was a personal friend of "Big Jim" Colosimo. When the city was extremely short of funds during the Depression, some of the city leaders looked to the mob for financial aid, in turn providing "favors." The corrupt Thompson was later named the "worst mayor in history" and, after his death a safe was found that contained $1.84 million in cash and securities.