E. F. Hutton Group Inc., parent company of the brokerage firm that was shaken by a guilty plea to a million-dollar check-kiting scheme, announced today the broadest reorganization in its modern history.

Hutton said it will lump its brokerage unit's operations into two "strategic business groups," one covering services for individual investors and the other covering institutional and capital markets.

Robert Foman, Hutton's chairman and chief executive, said the company will centralize its operating and support units along customer lines, centralize the policy-making process, and decentralize administration and implementation.

Hutton, the nation's second-largest independent, full-service brokerage firm, with some $18 billion in assets, may emphasize attracting institutional customers more as a result of the new organization, said Brenda Davis McCoy, an analyst for the bond-trading firm of Mabon, Nugent & Co. who follows Hutton.

Other major elements of the reorganization include:

*An organization for individual investment services to improve liaison between the home office and regional centers.

*The formation of a management committee for policy development. The appointment of Scott Pierce, formerly president of the E. F. Hutton & Co. brokerage firm, to vice chairman of the E. F. Hutton Group.

*The appointment of Robert Rittereiser, president and chief operating officer of the E. F. Hutton Group, to the additional position of president of E. F. Hutton and Co.

Rittereiser, formerly chief financial officer of Merrill Lynch & Co., joined Hutton in June, a month after Hutton pleaded guilty to 2,000 counts of mail and wire fraud for shuffling funds between its domestic bank accounts to avoid paying interest costs.

The violations occurred at commercial banks at which Hutton had checking accounts between July 1, 1980, and Feb. 28, 1982. Hutton agreed to pay $2.75 million in penalties and established a pool of $8 million to compensate banks that may have been defrauded.

In a decision that brought heated criticism, the Justice Department decided not to prosecute the company or any individuals identified as participants.

"Our recent experience, painful as it has been, has also given us a mandate to consider far-reaching changes in our entire top management approach," Foman said at the time of Rittereiser's appointment.