Pentagon's alphabet now has three C's.

The military hardware most important in deterring - or, should deterrence fail, in fighting - a nuclear war may not be an MX missile, a B-1 bomber, a Trident submarine, or even all of them in concert.

It's more likely to be a complex maze of black boxes, antennas, computers, radars, and satellites designed to make all of this strategic weaponry work as advertised.

Tucked within Pentagon documents and, most recently, this week's report of the special commission on MX basing is the assertion that America's primary military concern must be this command, control, and communications system, dubbed C3 for short.

''Our first defense priority should be to ensure that there is continuing, constitutionally legitimate, and full control of our strategic forces under conditions of stress or actual attack,'' states the report of the Commission on Strategic Forces, which presented its recommendations to President Reagan Monday.

In a related development, the Pentagon Tuesday announced new proposals to improve superpower communications during times of crisis. These include addition of a high-speed facsimile capability to the Direct Communications Link (''hot line''), permitting transmission of full pages of text as well as maps and graphs; the establishment of high-speed communications between the US National Military Command Center and its Soviet counterpart; and faster data transmission on existing diplomatic communications channels.

The President is expected to act on these recommendations within the next few weeks.

Despite the strengthening of such peaceful means of communication, however, US officials want to upgrade weapons communications links as well. This means preventing an attacker from blacking out command and control systems in a first strike and ensuring that the systems work if a nuclear war begins. Continuing actions of the Carter administration, Reagan officials are stressing C3 modernization. Annual Pentagon spending for strategic communications jumped nearly 60 percent this year over 1982, and will nearly triple (to more than $1 billion) by 1985. Procurement of new systems alone will jump more than 10-fold during the same period.

C3 systems are important for any military power, but especially so for the US. This country has three-quarters of its strategic forces in submarines and airplanes, which have longer and more vulnerable C3 links. The Soviet Union has three-fourths of its strategic warheads on land-based missiles, making direct control simpler to maintain.

There is an important political part of this equation, too. If the White House is to get the strategic modernization it wants, it must be able to show nuclear freeze advocates that the US is not moving toward a ''launch on warning'' doctrine. Many defense experts argue that such a doctrine lowers the nuclear threshold. To reassure freeze supporters, the President must give them some guarantee that the Pentagon can control its nuclear weapons during times of stress, not launch missiles except in retaliation for an actual attack, and be able to recall bombers.

This political aspect is important as well in theater nuclear forces, where any appearance of a hair-trigger or inadvertent launch must be avoided to convince European allies that they should accept placement of new cruise and Pershing II missiles on their soil.

Improved command, control, and communications facilities also are important for NATO's new emphasis on conventional deterrence. This envisions an ''electronic battlefield'' in which the allies take advantage of their technological advantage to offset the Soviet edge in tanks, aircraft, and other weapons by counterattacking enemy forces behind the line of engagement with very accurate long-range conventional munitions. This strategy relies on ''real time'' (immediate) intelligence data and weapons control.

Improving command and control facilities is featured in the Pentagon's classified five-year Defense Guidance as well as in public budget documents and congressional testimony. This directs the military services to integrate plans for using strategic, theater, and battlefield nuclear weapons, which will require modernized C3 systems. It also calls for plans to disable the Soviet command and control structure if necessary.

There is little argument in Congress or among strategic experts that upgraded systems of this kind are needed.

''Obviously, you ought to try to protect your command, control, and communications,'' said Paul Warnke, chief SALT II negotiator and former director of the Arms Control and Disarmament Agency. At the same time, he cautions, with a clearly superior C3 system ''you might eventually convince yourself that you can fight a limited or protracted nuclear war.''