How to get the only row with MAX values for multiple columns on a SELECT query?

For SQL Server 2014.

I'm trying to build a select query to get ID, Child1 and Child2, where Child2 is the maxiumum value for @Parent = 'A'.

Child2 = (Child1 * 2) or ((Child1 * 2) - 1)

 ID |   Parent |  Child1 |  Child2
----|----------|---------|---------
258 |        A |       4 |       7
262 |        A |       4 |       8
277 |        C |      15 |      29
263 |        C |      15 |      30
202 |        A |       7 |      13
219 |        A |       7 |      14
  4 |        A |       8 |      15
220 |        A |       8 |      16
278 |        B |       4 |       7
  9 |        B |       4 |       8

For example:

Results for parameter @Parent = 'A': 220, 8, 16

Results for parameter @Parent = 'B': 9, 4, 8

Results for parameter @Parent = 'C': 263, 15, 30

I'm using this:

select ID, max(Child1) as CH1, max(Child2) as CH2 from Table1 where Parent = A group by ID

but the result is multiple:

 ID |     CH1 |     CH2
----|---------|---------
258 |       4 |       7
262 |       4 |       8
202 |       7 |      13
219 |       7 |      14
  4 |       8 |      15
220 |       8 |      16

How to get only the row with max values for Child1 and Child2?