The Senate Appropriations subcommittee yesterday approved 8 to 4, the $13.3 million requested by President Carter to register 19 and 20-year-old males for a possible military draft.

The government could not draft young men into military service without an act of Congress, and Carter told congressional leaders yesterday that he forsees no need to ask Congress for power to resume the draft, which was ended in 1973.

But one of the arguments used by opponents is that resumption of registration only would produce dissension and noncompliance by young people which either would require prosecution of large numbers or expose registration as a "hollow sham" if no attempt was made to police it.

The arugment for registration is that it would give the defense establishment a head start on mobilizing an army in time of crisis, but opponents contend that registration alone is meaningless without classification and some training, that America's adversaries realize this but that the United States will be lulled into a false sense of security when the Pentagon has compiled a list of names. The House approved the money last week.

Sen. Charles McC. Mathias (R-Md.), who cast one of the "no" votes yesterday, said the defense establishment's most pressing problem is manpower, but that the most serious part of the problem is retaining the trained, experienced men who are leaving because pay and fringe benefits have failed to keep up with inflation.

"We can't sit around and nibble at the edge of the probelm," said Mathias. "We need a comprehensive approach. Maybe we don't need 19 and 20-year-olds. Maybe we need 50-year-olds."

Sen. William Proxmire ((d-Wis.), subcommittee chairman, who also voted against registration, said he understood registration in advance of mobilization would save only seven days. But Sen. Sam Nunn (D-Ga.), chairman of the Armed Services subcomittee on manpower, said it would save three months, Nunn said the military's manpower problem is so serious it cannot meet its needs and in a crisis would be short of men needed "after we call up all we've got."

Other votes against were cast by Sens. Henry Bellmon (R-Okla.) and Patrick Leahy (D-Vt.).