Finite Group Databasebeta

← C₃⁶×C₄₃ #44531881

Subgroups — C₃⁶×C₄₃ #44531881

Order 31347.

113264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₄₃	C₃	1	364	yes	maximal, direct product factor
2	C₃⁴×C₄₃	C₃²	1	11011	yes	direct product factor
3	C₃³×C₄₃	C₃³	1	33880	yes	direct product factor
4	C₃⁶	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃²×C₄₃	C₃⁴	1	11011	yes	direct product factor
6	C₃⁵	C₃×C₄₃	1	364	yes	direct product factor
7	C₃×C₄₃	C₃⁵	1	364	yes	direct product factor
8	C₃⁴	C₃²×C₄₃	1	11011	yes	direct product factor
9	C₄₃	C₃⁶	1	1	yes	characteristic, direct product factor, Sylow
10	C₃³	C₃³×C₄₃	1	33880	yes	direct product factor
11	C₃²	C₃⁴×C₄₃	1	11011	yes	direct product factor
12	C₃	C₃⁵×C₄₃	1	364	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃⁵×C₄₃	C₃	direct (N × H)
2. C₃⁴×C₄₃	C₃²	direct (N × H)
3. C₃³×C₄₃	C₃³	direct (N × H)
4. C₃⁶	C₄₃	direct (N × H)
5. C₃²×C₄₃	C₃⁴	direct (N × H)
6. C₃⁵	C₃×C₄₃	direct (N × H)
7. C₃×C₄₃	C₃⁵	direct (N × H)
8. C₃⁴	C₃²×C₄₃	direct (N × H)
9. C₄₃	C₃⁶	direct (N × H)
10. C₃³	C₃³×C₄₃	direct (N × H)
11. C₃²	C₃⁴×C₄₃	direct (N × H)
12. C₃	C₃⁵×C₄₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃⁵×C₄₃	3
C₃⁶	43