Objection 1. It seems that God is contained in a genus. For a substance is a being that subsists of itself. But this is especially true of God. Therefore God is in a genus of substance.
Objection 2. Further, nothing can be measured save by something of its own genus; as length is measured by length and numbers by number. But God is the measure of all substances, as the Commentator shows (Metaph. x). Therefore God is in the genus of substance.
On the contrary, In the mind, genus is prior to what it contains. But nothing is prior to God either really or mentally. Therefore God is not in any genus.
I answer that, A thing can be in a genus in two ways; either absolutely and properly, as a species contained under a genus; or as being reducible to it, as principles and privations. For example, a point and unity are reduced to the genus of quantity, as its principles; while blindness and all other privations are reduced to the genus of habit. But in neither way is God in a genus. That He cannot be a species of any genus may be shown in three ways.
First, because a species is constituted of genus and difference. Now that from which the difference constituting the species is derived, is always related to that from which the genus is derived, as actuality is related to potentiality. For animal is derived from sensitive nature, by concretion as it were, for that is animal, which has a sensitive nature. Rational being, on the other hand, is derived from intellectual nature, because that is rational, which has an intellectual nature, and intelligence is compared to sense, as actuality is to potentiality. The same argument holds good in other things. Hence since in God actuality is not added to potentiality, it is impossible that He should be in any genus as a species.
Secondly, since the existence of God is His essence, if God were in any genus, He would be the genus "being", because, since genus is predicated as an essential it refers to the essence of a thing. But the Philosopher has shown (Metaph. iii) that being cannot be a genus, for every genus has differences distinct from its generic essence. Now no difference can exist distinct from being; for non-being cannot be a difference. It follows then that God is not in a genus.
Thirdly, because all in one genus agree in the quiddity or essence of the genus which is predicated of them as an essential, but they differ in their existence. For the existence of man and of horse is not the same; as also of this man and that man: thus in every member of a genus, existence and quiddity--i.e. essence--must differ. But in God they do not differ, as shown in the preceding article. Therefore it is plain that God is not in a genus as if He were a species. From this it is also plain that He has no genus nor difference, nor can there be any definition of Him; nor, save through His effects, a demonstration of Him: for a definition is from genus and difference; and the mean of a demonstration is a definition. That God is not in a genus, as reducible to it as its principle, is clear from this, that a principle reducible to any genus does not extend beyond that genus; as, a point is the principle of continuous quantity alone; and unity, of discontinuous quantity. But God is the principle of all being. Therefore He is not contained in any genus as its principle.
Reply to Objection 1. The word substance signifies not only what exists of itself--for existence cannot of itself be a genus, as shown in the body of the article; but, it also signifies an essence that has the property of existing in this way--namely, of existing of itself; this existence, however, is not its essence. Thus it is clear that God is not in the genus of substance.
Reply to Objection 2. This objection turns upon proportionate measure which must be homogeneous with what is measured. Now, God is not a measure proportionate to anything. Still, He is called the measure of all things, in the sense that everything has being only according as it resembles Him.
Source: Summa Theologica (New Advent)