The submit button is located outside and after the function that generates the fields on the contact form. This is intended to make it easy for users to implement a graphical submit button, perhaps using a script like Chris Poole's DOM image rollover.
Open contact.php
Inside the form you will find the submit button:
<input type="submit" name="sendme" id="sendme" value="Send" title="Send your message" />
Copy this line of code then remove it. In sc_admin add an HTML snippet to your form and paste this into it. Place the snippet anywhere in the field order you want.