ButtonGroup is not a component, so it cannot be added to the panel. You need to add the individual components.
Your question is not very clear so I am not exactly sure what you are trying to achieve.
JPanel buttonPanel = new JPanel();
buttonPanel.setLayout(new BoxLayout(buttonPanel, BoxLayout.LINE_AXIS));
buttonPanel.add(radio1);
buttonPanel.add(radio2);
eastpanel.add(buttonPanel, BorderLayout.EAST)