Finite Group Databasebeta

← C₂×C₃×C₃₇×C₁₀₉ #37564083

Subgroups — C₂×C₃×C₃₇×C₁₀₉ #37564083

Order 24198.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₁₀₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃₇×C₁₀₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₇×C₁₀₉	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₀₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₀₉	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃×C₃₇	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₀₉	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₃₇	C₂×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
9	C₁₀₉	C₂×C₃×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃₇	C₃×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃₇	C₂×C₃×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	C₃₇×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₃₇×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₃₇×C₁₀₉	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. C₃×C₃₇×C₁₀₉	C₂	direct (N × H)
2. C₂×C₃₇×C₁₀₉	C₃	direct (N × H)
3. C₃₇×C₁₀₉	C₂×C₃	direct (N × H)
4. C₂×C₃×C₁₀₉	C₃₇	direct (N × H)
5. C₃×C₁₀₉	C₂×C₃₇	direct (N × H)
6. C₂×C₃×C₃₇	C₁₀₉	direct (N × H)
7. C₂×C₁₀₉	C₃×C₃₇	direct (N × H)
8. C₃×C₃₇	C₂×C₁₀₉	direct (N × H)
9. C₁₀₉	C₂×C₃×C₃₇	direct (N × H)
10. C₂×C₃₇	C₃×C₁₀₉	direct (N × H)
11. C₃₇	C₂×C₃×C₁₀₉	direct (N × H)
12. C₂×C₃	C₃₇×C₁₀₉	direct (N × H)
13. C₃	C₂×C₃₇×C₁₀₉	direct (N × H)
14. C₂	C₃×C₃₇×C₁₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₇×C₁₀₉	2
C₂×C₃₇×C₁₀₉	3
C₂×C₃×C₁₀₉	37
C₂×C₃×C₃₇	109