Subgroups — C₃×C₇×A₄×C₁₀₇ #41004149

Order 26964.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×A₄×C₁₀₇	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇×C₁₀₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇×C₁₀₇	—	4	1	no	maximal, Hall
4	C₂×C₃×C₇×C₁₀₇	—	3	1	no	—
5	C₃×A₄×C₁₀₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₇×C₁₀₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₁₀₇	—	4	3	no	—
8	C₃×C₇×C₁₀₇	A₄	1	1	yes	characteristic, direct product factor
9	C₂×C₇×C₁₀₇	—	3	1	no	—
10	C₂²×C₃×C₁₀₇	C₃×C₇	1	1	yes	characteristic, complemented
11	A₄×C₁₀₇	C₃×C₇	1	3	yes	direct product factor
12	C₃²×C₁₀₇	—	4	1	no	Hall
13	C₇×C₁₀₇	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₁₀₇	—	3	1	no	—
15	C₂²×C₁₀₇	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₀₇	—	4	3	no	—
17	C₃×C₁₀₇	C₇×A₄	1	1	yes	characteristic, direct product factor
18	C₃×C₇×A₄	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₁₀₇	—	3	1	no	—
20	C₁₀₇	C₃×C₇×A₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₃×C₇	C₃×C₁₀₇	1	1	yes	characteristic, complemented
22	C₇×A₄	C₃×C₁₀₇	1	3	yes	direct product factor
23	C₃²×C₇	—	4	1	no	Hall
24	C₂×C₃×C₇	—	3	1	no	—
25	C₃×A₄	C₇×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₇	C₃²×C₁₀₇	1	1	yes	characteristic, complemented, Hall
27	C₃×C₇	—	4	3	no	—
28	C₃×C₇	A₄×C₁₀₇	1	1	yes	characteristic, direct product factor
29	C₂×C₇	—	3	1	no	—
30	C₂²×C₃	C₃×C₇×C₁₀₇	1	1	yes	characteristic, complemented
31	A₄	C₃×C₇×C₁₀₇	1	3	yes	direct product factor
32	C₃²	—	4	1	no	Sylow
33	C₇	C₃×A₄×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃²×C₇×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	4	3	no	—
37	C₃	C₇×A₄×C₁₀₇	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₀₇	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₇×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇×C₁₀₇	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₇×C₁₀₇

Complements

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

N	H ≅ G/N	type
1. C₇×A₄×C₁₀₇	C₃	direct (N × H)
2. C₂²×C₃×C₇×C₁₀₇	C₃	semidirect
5. C₃×A₄×C₁₀₇	C₇	direct (N × H)
6. C₂²×C₇×C₁₀₇	C₃²	semidirect
8. C₃×C₇×C₁₀₇	A₄	direct (N × H)
10. C₂²×C₃×C₁₀₇	C₃×C₇	semidirect
11. A₄×C₁₀₇	C₃×C₇	direct (N × H)
13. C₇×C₁₀₇	C₃×A₄	direct (N × H)
15. C₂²×C₁₀₇	C₃²×C₇	semidirect
17. C₃×C₁₀₇	C₇×A₄	direct (N × H)
18. C₃×C₇×A₄	C₁₀₇	direct (N × H)
20. C₁₀₇	C₃×C₇×A₄	direct (N × H)
21. C₂²×C₃×C₇	C₃×C₁₀₇	semidirect
22. C₇×A₄	C₃×C₁₀₇	direct (N × H)
25. C₃×A₄	C₇×C₁₀₇	direct (N × H)
26. C₂²×C₇	C₃²×C₁₀₇	semidirect
28. C₃×C₇	A₄×C₁₀₇	direct (N × H)
30. C₂²×C₃	C₃×C₇×C₁₀₇	semidirect
31. A₄	C₃×C₇×C₁₀₇	direct (N × H)
33. C₇	C₃×A₄×C₁₀₇	direct (N × H)
35. C₂²	C₃²×C₇×C₁₀₇	semidirect
37. C₃	C₇×A₄×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
C₇×A₄×C₁₀₇	3
C₂²×C₃×C₇×C₁₀₇	3
C₃²×C₇×C₁₀₇	4
C₃×A₄×C₁₀₇	7
C₃×C₇×A₄	107

Subgroups — C3×C7×A4×C107 #41004149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×A₄×C₁₀₇ #41004149