Finite Group Databasebeta

← C₂²×C₇×C₁₁₀₃ #44525291

Subgroups — C₂²×C₇×C₁₁₀₃ #44525291

Order 30884.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁₀₃	C₂	1	3	yes	maximal, direct product factor
2	C₇×C₁₁₀₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₁₀₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₁₀₃	C₂×C₇	1	3	yes	direct product factor
5	C₁₁₀₃	C₂²×C₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₂²×C₇	C₁₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇	C₂×C₁₁₀₃	1	3	yes	direct product factor
8	C₇	C₂²×C₁₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²	C₇×C₁₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₂×C₇×C₁₁₀₃	1	3	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. C₂×C₇×C₁₁₀₃	C₂	direct (N × H)
2. C₇×C₁₁₀₃	C₂²	direct (N × H)
3. C₂²×C₁₁₀₃	C₇	direct (N × H)
4. C₂×C₁₁₀₃	C₂×C₇	direct (N × H)
5. C₁₁₀₃	C₂²×C₇	direct (N × H)
6. C₂²×C₇	C₁₁₀₃	direct (N × H)
7. C₂×C₇	C₂×C₁₁₀₃	direct (N × H)
8. C₇	C₂²×C₁₁₀₃	direct (N × H)
9. C₂²	C₇×C₁₁₀₃	direct (N × H)
10. C₂	C₂×C₇×C₁₁₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₁₁₀₃	2
C₂²×C₁₁₀₃	7
C₂²×C₇	1103