Is 192.168.122.1 a valid IP?

Yes it is a valid private IP address.
Classful IP addressing is outdated and can be confusing at times. A class C address is an address with a 255.255.255.0 subnet mask. The 192.168.0.0 block of addresses was originally supposed to be 256 separate Class C addresses. The range would be 192.168.0.0-192.168.255.255. Valid subnets were 192.168.0.0, 192.168.1.0, 192.168.2.0, etc.

Nowadays, Classful IP addressing has gone away. We now have something called CIDR. With CIDR, all you really need to know is that these addresses are valid private IP addresses:

10.0.0.0-10.255.255.255
172.16.0.0-172.31.255.255
192.168.0.0-192.168.255.255

How you divide those up into subnets is up to you.

Classful networking is no longer used, instead you need to look into classless inter-domain routing. Also that is a valid IP that is in one of the ranged reserved for private use (See RFC 1918). You might also want to read this post about sub netting.

As Kyle mentioned, there are no classes anymore, and haven't been for almost 15 years.

The private network IP ranges are:
10.0.0.0 to 10.255.255.255
172.16.0.0 to 172.31.255.255
192.168.0.0 to 192.168.255.255

RFC1918 as has been posted, and should be read. Excerpt:

"3. Private Address Space

The Internet Assigned Numbers Authority (IANA) has reserved the following three blocks of the IP address space for private internets:

 10.0.0.0        -   10.255.255.255  (10/8 prefix)
 172.16.0.0      -   172.31.255.255  (172.16/12 prefix)
 192.168.0.0     -   192.168.255.255 (192.168/16 prefix)

We will refer to the first block as "24-bit block", the second as "20-bit block", and to the third as "16-bit" block. Note that (in pre-CIDR notation) the first block is nothing but a single class A network number, while the second block is a set of 16 contiguous class B network numbers, and third block is a set of 256 contiguous class C network numbers."

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