diff --git a/dbms/src/Interpreters/ExpressionAnalyzer.cpp b/dbms/src/Interpreters/ExpressionAnalyzer.cpp
index b825225e4a02a93586a15fbce68375c7d15f28ec..3c347d62a2804581d0438e9381e296ba07c771c2 100644
--- a/dbms/src/Interpreters/ExpressionAnalyzer.cpp
+++ b/dbms/src/Interpreters/ExpressionAnalyzer.cpp
@@ -211,13 +211,17 @@ void ExpressionAnalyzer::analyzeAggregation()
 				/// constant expressions have non-null column pointer at this stage
 				if (const auto is_constexpr = col.column)
 				{
-					if (i < group_asts.size() - 1)
-						group_asts[i] = std::move(group_asts.back());
+					/// but don't remove last key column if no aggregate functions, otherwise aggregation will not work
+					if (!aggregate_descriptions.empty() || group_asts.size() > 1)
+					{
+						if (i < group_asts.size() - 1)
+							group_asts[i] = std::move(group_asts.back());
 
-					group_asts.pop_back();
-					i -= 1;
+						group_asts.pop_back();
+						i -= 1;
 
-					continue;
+						continue;
+					}
 				}
 
 				NameAndTypePair key{column_name, col.type};
@@ -781,7 +785,26 @@ void ExpressionAnalyzer::optimizeGroupBy()
 	}
 
 	if (group_exprs.empty())
-		select_query->group_expression_list = nullptr;
+	{
+		/** Нельзя полностью убирать GROUP BY. Потому что если при этом даже агрегатных функций не было, то получится, что не будет агрегации.
+		  * Вместо этого оставим GROUP BY const.
+		  * Далее см. удаление констант в методе analyzeAggregation.
+		  */
+
+		/// Нужно вставить константу, которая не является именем столбца таблицы. Такой случай редкий, но бывает.
+		UInt64 unused_column = 0;
+		String unused_column_name = toString(unused_column);
+
+		while (columns.end() != std::find_if(columns.begin(), columns.end(),
+			[&unused_column_name](const NameAndTypePair & name_type) { return name_type.name == unused_column_name; }))
+		{
+			++unused_column;
+			unused_column_name = toString(unused_column);
+		}
+
+		select_query->group_expression_list = new ASTExpressionList;
+		select_query->group_expression_list->children.push_back(new ASTLiteral(StringRange(), UInt64(unused_column)));
+	}
 }
 
 
diff --git a/dbms/tests/queries/0_stateless/00257_no_aggregates_and_constant_keys.reference b/dbms/tests/queries/0_stateless/00257_no_aggregates_and_constant_keys.reference
new file mode 100644
index 0000000000000000000000000000000000000000..fc77ed8a2412b230cef31013fef7a7f375ea9a5c
--- /dev/null
+++ b/dbms/tests/queries/0_stateless/00257_no_aggregates_and_constant_keys.reference
@@ -0,0 +1,29 @@
+40
+41
+2	42
+43
+11
+40
+
+40
+41
+
+41
+2	42
+
+2	42
+43
+
+43
+11
+
+11
+11
+
+11
+1
+
+1
+2
+
+2
diff --git a/dbms/tests/queries/0_stateless/00257_no_aggregates_and_constant_keys.sql b/dbms/tests/queries/0_stateless/00257_no_aggregates_and_constant_keys.sql
new file mode 100644
index 0000000000000000000000000000000000000000..15f4536e18f70aa1615486c895180950504e8844
--- /dev/null
+++ b/dbms/tests/queries/0_stateless/00257_no_aggregates_and_constant_keys.sql
@@ -0,0 +1,15 @@
+select 40 as z from (select * from system.numbers limit 3) group by z;
+select 41 as z from remote('127.0.0.{1,2}', system.one) group by z;
+select count(), 42 AS z from remote('127.0.0.{1,2}', system.one) group by z;
+select 43 AS z from remote('127.0.0.{1,2}', system.one) group by 42, 43, 44;
+select 11 AS z from (SELECT 2 UNION ALL SELECT 3) group by 42, 43, 44;
+
+select 40 as z from (select * from system.numbers limit 3) group by z WITH TOTALS;
+select 41 as z from remote('127.0.0.{1,2}', system.one) group by z WITH TOTALS;
+select count(), 42 AS z from remote('127.0.0.{1,2}', system.one) group by z WITH TOTALS;
+select 43 AS z from remote('127.0.0.{1,2}', system.one) group by 42, 43, 44 WITH TOTALS;
+select 11 AS z from (SELECT 1 UNION ALL SELECT 2) group by 42, 43, 44 WITH TOTALS;
+select 11 AS z from (SELECT 2 UNION ALL SELECT 3) group by 42, 43, 44 WITH TOTALS;
+
+SELECT count() WITH TOTALS;
+SELECT count() FROM remote('127.0.0.{1,2}', system.one) WITH TOTALS;