Of the 10.8 million Americans who were out of work last month, more than 2 million, or about one-fifth, were teen-agers. Including teen-agers, nearly three-fifths lived in households where there was another worker, and for half the unemployed, the other worker was employed full time.

These figures from among the many published by the Labor Department yesterday suggest that unemployment may not always mean destitution in these complicated times.

But the new statistical portrait of the unemployed also contains some figures pointing in the opposite direction: toward misery. For all the talk of a social safety net, only about two-fifths of the 10.8 million people who were out of work were receiving unemployment benefits in mid-July.

More than half the unemployed were adult men. Most of them--as well as some portion of the adult women--presumably were the main breadwinners in their households.

The figures also show that the pain of unemployment is disproportionately bunched in certain sectors of the population, the economy and the country, not spread evenly across all strata.

About 2.1 million of the unemployed were black, or close to 20 percent, but blacks make up a little over 11 percent of the U.S. population. Similarly, about 832,000 or 8 percent of the out-of-work were Hispanic, but those of Hispanic origin make up 6 percent of the population.

About half the unemployed were what the Labor Department's Bureau of Labor Statistics calls blue-collar workers, and only about a quarter were white-collar types. The others fell into other categories.

Looked at another way, some 2.7 million of these workers were from the manufacturing sector, where the unemployment rate last month was 12 percent. And, 1.1 million were from the hard-hit construction industry, where 20 percent were out of work.

On the other hand, only 746,000 were from government at all levels, and the government unemployment rate was only 4.6 percent.

More than half the unemployed--5.9 million--were concentrated in just 10 large and heavily industrial states, led by California, the most-populous state, with 1.2 million unemployed, and Illinois, with 696,000.

The remaining eight states are New York, Texas, Pennsylvania, Ohio, Florida, Michigan, New Jersey, and Massachusetts. Together these states also have a little over half the nation's population.

The highest July unemployment rate among the states was in Michigan, the auto state, which had 14.4 percent. Illinois had 12.3 percent, Ohio 11.8, Pennsylvania 10.8, and California 10.5.

The May unemployment figures, the most recent to be broken down to such a level, show the Flint, Mich., metropolitan area with the highest jobless rate among localities, with 19.8 percent, and the Rockford, Ill., area second at 19.3 percent.

Other Michigan areas--Battle Creek, Bay City, Detroit, Jackson, Muskegon, Saginaw--were in the 14 to 16 percent range.

The Decatur, Ill., area was at 18.4 percent; Youngstown, Ohio, at 17.1 percent; Kankakee, Ill., at 15.4 percent; and Modesto, Calif., an area with chronic unemployment especially in agriculture, at 18.9 percent. The New York City area had a rate of 8.1 percent.