Steve, thanks for the add'l input. I have checked the immigrants from Germany from 1830-1860 coming to USA through Castle Garden. There were 73 Rademachers. That info is available on the Internet. The ages and first names are given along with the ship's name and date of arrival. you should be able to access it.
The Wisconsin Historical Society (on the Internet) lists that there is an article regarding Henry G.(sic) Rademacher in the Milwaukee Sentinel of 26 April 1920 with reference "Year": 1857-1920. You may wish to check this further, the dates seem to coincide.
The WHS lists a death record in Milwaukee County for a Henry Rademacher on 31 May 1906: Ref - Reel 097, Vlume 33, Page 0466, Image 0012, Index Vol. 10, Sequence #311175.
Also, available on the Internet is the Immigrant Ships Transcribers Guild. These are some of the 34 Rademacher names -
Johann (16) to Wisconsin from Bremen departure to NYC aboard Ship Magdalene, arrived 29 June 1868.
C. L. Rademacher, (39) 'gentleman' U. S. resident, aboard Steamer Washington from Bremerhaven to NYC arrived 30 August 1854. He probably was returning from a visit to Germany.
Henry (44) watchmaker, sailed from Liverpool aboard City of Washington to NYC, arrived 19 August 1858, passenger #230.
This information was copied from the passenger list of the Ship Elise, from Bremen to NYC, arriving 19 May 1836 - - -
135 John Georg Rademacher (28) male mason
136 Carol. Redemacher, his wife (28) female
137 Charles Rademacher, his child (4mo) male
138 John Henry Rademacher (34) male mason
139 Fried^k Rademacher, his wife (32) female
140 John Henry Rademacher, his child (7) male
141 F??? Chr? Rademaker, his child (4) male
142 John Charles Rademacher child (2) male
I spent considerable time on this today, so I hope you find a clue or two to assist your further research. Good luck.