Finite Group Databasebeta

← C₇×C₁₁²×C₃₇ #44531353

Subgroups — C₇×C₁₁²×C₃₇ #44531353

Order 31339.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₇×C₁₁×C₃₇	C₁₁	1	12	yes	maximal, direct product factor
3	C₇×C₁₁²	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×C₃₇	C₇×C₁₁	1	12	yes	direct product factor
5	C₇×C₃₇	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
6	C₁₁²	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
7	C₇×C₁₁	C₁₁×C₃₇	1	12	yes	direct product factor
8	C₃₇	C₇×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
9	C₁₁	C₇×C₁₁×C₃₇	1	12	yes	direct product factor
10	C₇	C₁₁²×C₃₇	1	1	yes	characteristic, direct product factor, Sylow

	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. C₁₁²×C₃₇	C₇	direct (N × H)
2. C₇×C₁₁×C₃₇	C₁₁	direct (N × H)
3. C₇×C₁₁²	C₃₇	direct (N × H)
4. C₁₁×C₃₇	C₇×C₁₁	direct (N × H)
5. C₇×C₃₇	C₁₁²	direct (N × H)
6. C₁₁²	C₇×C₃₇	direct (N × H)
7. C₇×C₁₁	C₁₁×C₃₇	direct (N × H)
8. C₃₇	C₇×C₁₁²	direct (N × H)
9. C₁₁	C₇×C₁₁×C₃₇	direct (N × H)
10. C₇	C₁₁²×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁²×C₃₇	7
C₇×C₁₁×C₃₇	11
C₇×C₁₁²	37