In a class C subnet there are a total of 256 address , but only 254 are usable. Let's look at the subnet the you are using.
192.1.1.0 is used for network identification.
192.1.1.1 - 192.1.1.254 can be assigned to clients (nodes)
192.1.1.255 is used for network broadcasts
Since you are using a public range of IP addresses you have two choices.
1.Try to lease an additional range of public IP addresses then create two routed subnets. This could be costly.
2. Switch to one of the private IP address ranges and use SNAT for access to the internet. The private ranges are as follows.
Class C 192.168.0.0 - 192.168.255.255
Class B 172.16.0.0 - 172.31.255.255
Class A 10.0.0.0 - 10.255.255.255
If you switched to the Class B private range of 172.16.0.0 - 172.16.255.255 it would give you a total of 65,536 IP addresses with 65,534 usable. 172.16.0.0 would be used for network ID and 172.16.255.255 would be used for broadcasts.
If you went with the Class A private you would have a total of 16,777,216 IP address's.
If you are using DHCP you could transistion to either class with relative ease. Your would have to either statically assign IP addresses to all of your servers or use DHCP resevations to accomplish the same thing. For your workstations you could create a group policy startup script that would run a simple batch job to release the old IP address's and then renew them with the new range. Then just have the users reboot there systems and they should all be assigned addresses from the new range.
All the batch job would have to contain would be the following lines.
ipconfig /release
ipconfig /renew