Does the iPhone 4s support 4g

Depends on who you ask.

A google search would find the answer :

Why Does MyiPhone 4S Now Say 4G, Not 3G? Because It Is ...

AT&T iPhone 4S goes "4G" after iOS 5.1 update

AT&T iPhone 4S Now Has 4G…Kinda-Sorta - ABC News

iOS 5.1 shows '4G' indicator in iPhone 4S status bar for AT&T | The ...

IsAT&T Misleading iPhone 4S Users About 4G Access? - The ...

iOS 5.1 update brings 4G service to AT&T iPhone 4S devices... kind of

iPhone4G: iOS 5.1 update shows AT&T iPhone 4S is 4G...

No, AT&T has redefined 4G for marketing purposes to mean HSPA+, which the 4S does support. But it is not true 4G as in LTE. The only Apple device that supports LTE is the new iPad. Some will argue that even LTE is not "true" 4G, but the industry accepts that it is even though international standards don't agree.

Since HSPA+ is, by definition, now considered 4G, I would say yes, the iPhone supports 4G. It's nowhere near as quick as 4G LTE though.

HSPA+ is only 4G by AT&T's definition. At around 5 Mbps it's faster than HSPA, but not by an order of magnitude. By contract my LTE hotspot get 15-25 Mbps when it can find an LTE signal. But the technical definition of 4G is 100 Mbps. That clearly differs from the marketing definition.