How to register child members of type and derived types from it into list?

I have a parent class to be inherited from:

public class Item {}

public class Base {
  public List<Item> Items;
  public void Register() {
     // How to get all members of type Item and its deribed into Items list?
  }
}

public class Shell : Base {
  Item A = new Item();
  Item B;
  Item C;
  public Shell(Item c) {
     C = c;
     B = new Item();
  }
}

I want to call Register from external code. When Register is called on say Shell instance its Items list shall get refrences to A, B, C, yet not require Shell author to add any code for it. How to do such thing in C#?