Organizing contacts into groups can help to locate specific contacts faster with iOS. Unfortunately, the stock iOS Contacts app does not have built-in support for creating new contact groups. While existing groups can be accessed directly from iOS, new groups must be created and populated with contacts by using iCloud.
This process will only work if iCloud is enabled to sync with the iPhone under Settings -> iCloud -> Contacts. To begin, access the iCloud website at iCloud.com and sign in using the same Apple ID and password that is connected to your iOS device. Once logged in follow these steps: