A widening investigation into a notorious prison based gang known here as the Mexican Mafia threatens to become a potential political embarrassment to Gov. Edmund G. (Jerry) Brown.

State Attorney General Evelle J. Younger announced last week that the state Department of Justice which he heads has expanded its investigation of the gang in an attempt to find possible illegal activities by public officials. Brown formally backed the inquiry, but he stands to be harmed by it if the Department of Justice finds Mexican Mafia likns within his health and welface agency.

State legislators have been demanding a thorough investigation of the Mexican Mafia ever since the Reader's Digest in its November issue said that Health and Welface Secretary Mario G. Obledo, the most prominent Mexican-American public official in California was a "supporter" of Raphael (Chispas) Sandoval, who headed a crime-ridden rehabilitation program known as Community Concern.

After Ellen Delia, the bookkeeper for another program known as Get Going, Inc., was murdered last February, Obledo ordered an investigation into its crime connections. The Department of Justice found significant involvement by the Mexican Mafia in Get Going, which was funded by the state and federal governments. Automobiles provided employees of this organization purportedly were used to transport Mexican Mafia killers to seven contract murders.

But Obledo sharply denied the contention that he was in any way a supporter of Sandoval and asked Reader's Digest for a retraction.

Instead, Obledo received a detailed letter from the magazine's editor, Roland Strand. The Digest, which rarely engages in investigative reporting, came back strongly making only one concession to Obledo which is that it used the wrong middle initial of his name in the original article.

Otherwise, says Strand the evidence justifies the statement that Obledo was a supporter of Sandoval, who the magazine said has close friends in organized crime, including mobster Jimmy Coppola an Italian Mafia associate with whom he served time in prison.

The Digest's outspoken defense of its article came hours after Brown broke a long silence and decided to defend Obledo publicly.

He showed up unexpectedly last week at a dinner of 1,400 persons in Sacramento sponsored by Mexican-American supporters of Obledo. Amidst cires of "Viva Obledo" and "Viva el gobernador." Brown proclaimed Obledo a "great man" and said, "you're there with him - we're all with him."

In the days before the dinner Brown had been bluntly warned by Mexican-American supporters that they would withdraw their backing of him if he did not come to Obledo's defense. Mexican-Americans in California traditionally have been shortchanged in political appointments and they are generally supportive of Obledo, who was highly popular as the attorney for the Mexican-American Legal Defense Fund before his appointment.

The political support of Mexican-Americans can be significant in state elections, as Brown's father, Edmund G. (Pat) Brown, found out in 1963 when many of them deserted the Democrats to vote for Ronald Reagan.

Gov. Brown faces re-election 1978. Attorney General Younger, who is running the investigation, is one of several potential Republican challengers.