Subgroups of Linear Groups

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You should tell us how B is constructed, otherwise we will not be able to understand where is your problem coming from. As for me, it works as expected:

sage: G = SL(2,GF(3)) ; G
Special Linear Group of degree 2 over Finite Field of size 3
sage: a = G.gens()[0] ; a
[1 1]
[0 1]
sage: H = G.subgroup([a]) ; H
Matrix group over Finite Field of size 3 with 1 generators (
[1 1]
[0 1]
)
sage: a^2 in H
True
sage: G.gens()[1]
[0 1]
[2 0]
sage: G.gens()[1] in H
False

put all code a line,it can run normal,your code only choose the first and second gens of 24.better use like :if G.subgroup().gens()==2

G = SL(2,GF(3));D = G.subgroup([G[1],G[2]]);D

Matrix group over Finite Field of size 3 with 2 generators ( [0 1] [0 1] [2 1], [2 2] ) G = SL(2,GF(3)).list();G;len(G)

( [0 1] [0 1] [0 1] [0 2] [0 2] [0 2] [1 0] [1 0] [1 0] [1 1] [2 0], [2 1], [2 2], [1 0], [1 1], [1 2], [0 1], [1 1], [2 1], [0 1],

[1 1] [1 1] [1 2] [1 2] [1 2] [2 0] [2 0] [2 0] [2 1] [2 1] [1 2], [2 0], [0 1], [1 0], [2 2], [0 2], [1 2], [2 2], [0 2], [1 1],

[2 1] [2 2] [2 2] [2 2] [2 0], [0 2], [1 0], [2 1] ) 24