TOCs involved:
c2c, Chiltern Railways, East Midlands Trains, First Capital Connect, First Great Western, Greater Anglia, London Midland, London Overground, ScotRail, South West Trains, Southeastern, Southern, Stansted Express
So you can't do Chester to Nottingham on a through ticket with Groupsave. It should also be noted that each company set Groupsave how they want to. For example FCC use a discount whilst EMT use a specific ticket type, because of this FCC's Groupsave is not valid on EMT services and EMT Groupsave is routed 'EMT Only'.
Liverpool-Nottingham should have Groupsave tickets (EMT Only).