Subgroups — C₂×C₃×C₄₉×C₁₀₇ #44538014

Order 31458.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₁₀₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₄₉×C₁₀₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₉×C₁₀₇	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₁₀₇	C₇	1	1	yes	maximal, characteristic
5	C₃×C₇×C₁₀₇	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₁₀₇	C₃×C₇	1	1	yes	characteristic
7	C₇×C₁₀₇	C₂×C₃×C₇	1	1	yes	characteristic
8	C₂×C₃×C₁₀₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₀₇	C₂×C₄₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₄₉	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₀₇	C₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₄₉	C₂×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
13	C₁₀₇	C₂×C₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₄₉	C₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄₉	C₂×C₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₇	C₇×C₁₀₇	1	1	yes	characteristic
17	C₃×C₇	C₂×C₇×C₁₀₇	1	1	yes	characteristic
18	C₂×C₇	C₃×C₇×C₁₀₇	1	1	yes	characteristic
19	C₇	C₂×C₃×C₇×C₁₀₇	1	1	yes	characteristic
20	C₂×C₃	C₄₉×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₄₉×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₄₉×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₂×C₃×C₇×C₁₀₇
socle, prime radical	C₂×C₃×C₇×C₁₀₇	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₉×C₁₀₇	C₂	direct (N × H)
2. C₂×C₄₉×C₁₀₇	C₃	direct (N × H)
3. C₄₉×C₁₀₇	C₂×C₃	direct (N × H)
8. C₂×C₃×C₁₀₇	C₄₉	direct (N × H)
9. C₃×C₁₀₇	C₂×C₄₉	direct (N × H)
10. C₂×C₃×C₄₉	C₁₀₇	direct (N × H)
11. C₂×C₁₀₇	C₃×C₄₉	direct (N × H)
12. C₃×C₄₉	C₂×C₁₀₇	direct (N × H)
13. C₁₀₇	C₂×C₃×C₄₉	direct (N × H)
14. C₂×C₄₉	C₃×C₁₀₇	direct (N × H)
15. C₄₉	C₂×C₃×C₁₀₇	direct (N × H)
20. C₂×C₃	C₄₉×C₁₀₇	direct (N × H)
21. C₃	C₂×C₄₉×C₁₀₇	direct (N × H)
22. C₂	C₃×C₄₉×C₁₀₇	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×C₄₉×C₁₀₇	2
C₂×C₄₉×C₁₀₇	3
C₂×C₃×C₇×C₁₀₇	7
C₂×C₃×C₄₉	107

Subgroups — C2×C3×C49×C107 #44538014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄₉×C₁₀₇ #44538014