Chopard ranked last on the list, with 183,000 fans.
Of course, a big Facebook fan base doesn’t necessarily equate to success, especially in luxury. Hermes ranks second to last on the list with about a half million fans. Yet within the luxury industry, and judging from its profits, Hermes is well regarded as a model of success.
What’s more, some luxury purists might not consider Burberry or Coach true luxury brands, since they are such mass retail companies.
As BCG states in the report, going digital raises fundamental questions for luxury brands like, “How can a luxury brand be selective when it has more than eight million fans on Facebook?” and “How can a luxury provider control its brand on the Web when context is so important to that brand?”
All important questions. Still, BCG says that even the most exclusive luxury companies will ignore the web and social media at their own peril.
Luxury companies, it says, should “put digital at the heart of the company and rethink, in depth, the marketing and commercial approach accordingly.”
-By CNBC's Robert Frank
Follow Robert Frank on Twitter: @robtfrank