When Immelt took over for Jack Welch in 2001, he faced a significant challenge in continuing the pace of GE’s growth. Even if earnings continued to increase, the stock price was “unlikely to climb at the clip it did under Welch — for reasons that have little to do with Immelt’s management skills and everything to do with his timing,” Fortune predicted during his first month as CEO.

Just to maintain its rate of revenue growth, wrote Jerry Useem for Fortune in 2001 as Immelt took over, GE would have had to expand by roughly $17 billion that year — the equivalent of one 3M (or one Qwest, if you prefer).

Three years later, Immelt was still chasing this central challenge: “We have to make our own growth,” he told Fortune in 2004.

He never achieved this growth, to the chagrin of investors, and Flannery will now have his turn.

One of America’s flagship corporations, GE has been on the Fortune 500 list since 1955. It’s one of only 54 companies to tout such a long Fortune 500 streak.

The company lands at 13th on this year’s list, falling from a 4th place ranking in 2010 — the highest under Immelt’s time at the helm.

Despite being heralded as exactly the type of CEO you might design, guiding the 127-year-old company through the wake of the September 11th terrorist attacks and the Great Recession, Immelt’s leadership wasn’t enough to return the GE’s stock price to what it once was.

Investors largely agree that the company’s performance was poor during his tenure, with stocks dropping nearly 30% since he became CEO.

Flannery will take over without the staggering expectations that Welch’s legacy left for Immelt, but the growth challenge remains. With the massive conglomerate operating more like a mutual fund than a business, there may be little reason to believe new leadership will improve the company’s numbers.

GE’s stock closed at $28.94 today following the news.