Family #252 in the 1834 Grimm census.
Family #280 in the 1857 Grimm census.
Georg Konrad was the illegitimate son of Elisabeth Kober. There is no mention of his father's name in the 1834 census. The 1857 census gives his proper surname as Schneider.
His father was probably one of these two Schneider brothers living in nearby household #242 in the 1834 census:
Johann Georg Schneider, born 1797
Jakob Alexander Schneider, born 1803
He can't be the son of brother Johann Tobias Schneider. Although Tobias was born in 1796 and old enough to be his father, he died two years before Georg Konrad's birth.
Georg Konrad continued to live close to the Schneider family in 1857. By that time, however, only Johann Georg Schneider remained living. Jakob Alexander Schneider passed away in 1851.
The death of Georg Konrad's step-father, Philipp Kober, made him the defacto head of the household at the time of the 1857 census. Philipp's brother Tobias had also died prior to the 1857 census, making Konrad Schneider the eldest male in the household.
Head of the Household Philipp Kober, age 49 in 1850, deceased 1851
Child #1Konrad Schneider, age 39, wife's illegitimate son
Wife of Child #1 Katharina Elisabeth [Fritzler] Schneider, age 37
Grandchild #1 Christina Margaretha Schneider, age 19
Grandchild #2 Philipp Michael Schneider, age 16
Grandchild #3 Philipp Jakob Schneider, age 13
Grandchild #4 Johann Heinrich Schneider, age 10
Grandchild #5 Anna Margaretha Schneider, age 8
Grandchild #6 Katharina Elisabeth Schneider, age 6
Grandchild #7 Georg Karl Schneider, age 2 years 6 months
Brother Tobias Kober, missing from 1834 census, deceased 1857
Nephew #1 Philipp Jakob Kober, age 28, missing from 1834 census
Wife of Nephew #1 Helena Katharina Kober, age 28
Nephew's Daughter #1 Louisa Kober, age 5
Nephew's Daughter #2 Christina Kober, age 3
Nephew #2 Johann Konrad Kober, age 25, missing from 1834 census
↑1834 Census of Grimm in the District of Saratov, Russia, Dated 2 February 1835, Revised Edition; Translated by Brent Mai, Concordia University, Portland, Oregon; Published by Dynasty Publishing, Beaverton, OR, USA; Copyright 2011; page 75, family #252.
↑1857 Census of Grimm in the District of Saratov, Russia, dated 5 November 1857; Translated by Brent Mai, Concordia University, Portland, Oregon; Published by Dynasty Publishing, Beaverton, OR, USA; Published 2005; page 102, family #280.