When the Senate Finance Committee produced its tax reduction bill last week, the Carter administration complained that it gave too much relief to the rich by cutting taxes on capital gains.

Yet it now turns out that the groups aided most by the Finance Committee bill are not the rich, but those in the middle and lower ranges of the income scale.

The Senate committee's bill is tilted a lot more toward the poor than the one passed earlier this year by the House, which did give most relief to taxpayers in high-and middle-income groups.

Estimates from the Treasury's computers show that, for 1979, the Finance Committee bill would heap a full 25.4 percent of its tax relief for individuals on persons in the $15,000-and under brackets - compared with 10 percent allotted these groups in the House version of the bill.

At the same time, the proportion going to high-income taxpayers - those in the $100,000-and-up brackets - would drop to 11.7 percent under the Finance Committee's version of the measure, compared with an outsized 21.3 percent in the House bill. Clearly, the distribution of benefits has been reversed.

The rub is that the Finance Committee, to lower capital gains taxes and at the same time cut rates for lower-income taxpayers, ended up with a bill that would burst the budget - particularly in future years, when the full impact of the measure would take effect.

According to Treasury estimates, by fiscal 1981 the Senate bill would add $10 billion more to the federal budget deficit than the measure passed by the House, and $6.8 billion more than President Carter's proposal. By fiscal 1982, it would rise to $1.6 billion.

As a result, the White House is in something of a fix. If Carter accedes to the tax bill approved by the House, it would short-change the lower-income groups he wants to help. But if he backs the Senate measure, he could wind up in a fiscal box.

The contours of the Finance Committee bill stem from the way the panel tried to meet the administration's objections to the House-passed measure - by adding new benefits to make up for the House bill's deficiencies rather than revamping the legislation.

The House bill had marked a major turnabout from traditional Democratic tax-cut proposals: Rather than benefitting mostly the $15,000-and-under groups, the bulk of the measure's tax relief had been pegged to taxpayers in the $20,000 to $50,000 brackets.

The Finance Committee moved to restore the more historic proportions by adding $3.9 billion in extra tax relief, concentrated primarily on those in the lower brackets. It adjusted the brackets more at that end. And it liberalized the earned income credit for the poor.

At the same time, however, the committee also voted to triple the already-generous reductions in capital gains taxes that the House approved in August, and it added a spate of special-interest tax breaks for specific industries and groups.

The result has been a proposal that blunts the nub of the criticism about the House measure's neglect of the poor and lower-middle-income groups, but costs far more - particularly in future years - than Carter can afford to accept.

Here is the breakdown:

Largely because of the new liberalized earned income credit, the Finance Committee bill would provide a near-windfall to families earning $11,000 or less. In all, more than 16 percent of the breaks would go to this group - far higher than in previous bills.

As a result, the total share of the tax burden borne by lower-income groups would decline substantially. If the Finance Committee's bill were enacted, the proportion of the nation's taxes paid by those earning $15,000 or less would dip to 12.5 percent compared to 13.7 percent now.

The Finance Committee's bill provides wage-earners with significantly greater protection that the House bill against the impact of next January's scheduled Social Security tax boost and the effects of this year's inflation in pushing workers into higher tax brackets.

Under the House measure, only those in the $12,000 to $16,000 brackets would escape a net tax increase next January when those two factors are counted. With the Finance Committee's proposal, however, most taxpayers in the $40,000-and-under brackets would come out ahead.

Despite all the administration's complaining about the extra cuts in capital gains taxes that the Finance Committee provided, there's enough added to the total pot that the proportion going to upper-income taxpayers would be significantly lower than in the House bill.

The Treasury's figures show that the Finance Committee measure would parcel out 11.7 percent of the cuts to taxpayers in the $100,000-and-up brackets, compared with 21.3 percent in the House bill. And it would leave high-income taxpayers paying 7.5 percent of taxes - the same as now.

However, this favoring of lower-income taxpayers is only temporary. Although figures for later ears weren't immediately available, it's clear that the impact of inflation would reduce the number of persons eligible for the earned income credit over the longer run.

The figures compiled by the Treasury take account of the total tax relief the bill provides for individuals, including the increased personal exemption, reduction in tax rates, cuts in capital gains taxes and the liberalized earned income credit.

The administration also is complaining that the Finance Committee's proposal for a new "minimum" tax on high-income investors - to replace the one in the House bill - would widen the opportunities for abuses by those who invest in tax shelters.

What really troubles administration officials about the bill, however, is the amount it would add to the budget deficit. The Finance Committee managed to stay almost within its budget limit this year. But it did so only by postponing the more costly breaks for future years.

As a result, while the Finance measure would cost $11.6 billion in the current fiscal year, compared with $9.4 billion for the House version of the bill, the cost would balloon to $25.9 billion in fiscal 1980 and $30.8 billion in 1981 - dashing any hopes of ending the deficit.

Among the most costly items is the committee's proposed reduction in capital gains taxes, which the panel wants to accomplish by exempting 70 percent of a capital gain from regular income taxes, rather than the present 50 percent. By 1983, that would cost $4.8 billion.

Another is the panel's proposal to allow businesses a faster depreciation writeoff for a new machinery and equipment. While the measure would drain $231 million in fiscal 1979, the cost would rise to $2.8 billion by 1983 - in addition to the basic corporate tax rate cuts.

What the administration hopes to do is to persuade the Senate to agree in House-Senate conference committee to trim some of the reductions for high-income investors, possibly by cutting the capital gains exclusion to 60 percent instead of 70 percent, and retaining the present minimum tax.

Sen. Russell B. Long (D-La.), the Finance Committee's chairman, already has suggested he might agree in conference to a 65 percent exclusion level. The administration also wants to cut back the extra writeoff for business depreciation.

At the same time, the Senate ultimately may retreat from some of the more than $1.9 billion in special-interest tax breaks for specific industries and groups, which the panel tacked on in the final hours of its markup session. The cost of these would rise to $4.1 billion by 1983.

Those include everything from a special tax break for chicken farmers in Maine and Arkansas to a $7 million windfall for Texas International Airlines and a new investment tax credit for horse-breeders. The House bill does not include most of these provisions.

It's still too early to tell what the Senate - and ultimately the conference committee - will do to reconcile the two rival tax measures. But it's clear that the Finance Committee has tempered the shortcomings of the House bill - at a price.