Subgroups — C₃×C₇×Dic₄₀₇ #46803136

Order 34188.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₁×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₄₀₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₁×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₄₀₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇×Dic₃₇	—	11	1	no	maximal, Hall
7	C₇×C₁₁×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₁₁×C₃₇	C₂×C₇	1	1	yes	characteristic
9	Dic₄₀₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₇×C₃₇	D₁₁	1	1	yes	characteristic
11	C₃×C₁₁×C₃₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×Dic₃₇	—	11	1	no	Hall
13	C₃×C₇×Dic₁₁	—	37	1	no	maximal, Hall
14	C₂×C₁₁×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₇×C₃₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×C₃₇	C₃×D₁₁	1	1	yes	characteristic
17	C₂×C₃×C₇×C₁₁	D₃₇	1	1	yes	characteristic
18	C₃×Dic₃₇	—	11	1	no	Hall
19	C₁₁×C₃₇	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
20	C₇×Dic₁₁	—	37	1	no	Hall
21	C₇×C₃₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇×C₁₁	Dic₃₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₃₇	C₇×D₁₁	1	1	yes	characteristic
24	C₂×C₇×C₁₁	C₃×D₃₇	1	1	yes	characteristic
25	Dic₃₇	—	11	1	no	Hall
26	C₃×Dic₁₁	—	37	1	no	Hall
27	C₃×C₃₇	C₇×Dic₁₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₄×C₇	—	407	1	no	Hall
29	C₇×C₁₁	C₃×Dic₃₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₇	C₃×C₇×D₁₁	1	1	yes	characteristic
31	C₂×C₃×C₁₁	C₇×D₃₇	1	1	yes	characteristic
32	Dic₁₁	—	37	1	no	Hall
33	C₂×C₃×C₇	D₄₀₇	1	1	yes	characteristic
34	C₃₇	C₃×C₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₁₁	C₇×Dic₃₇	1	1	yes	characteristic, complemented, Hall
36	C₄×C₇	—	407	1	no	Hall
37	C₂×C₁₁	C₃×C₇×D₃₇	1	1	yes	characteristic
38	C₃×C₇	Dic₄₀₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇	C₃×D₄₀₇	1	1	yes	characteristic
40	C₃×C₄	—	407	1	no	Hall
41	C₁₁	C₃×C₇×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₃×Dic₄₀₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₇×D₄₀₇	1	1	yes	characteristic
44	C₄	—	407	1	no	Sylow
45	C₃	C₇×Dic₄₀₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₇×D₄₀₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₄₀₇
commutator, hypocenter	C₁₁×C₃₇	C₃×C₄×C₇
Frattini	C₂	C₃×C₇×D₄₀₇
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₁×C₃₇	C₂
cosocle	C₂×C₁₁×C₃₇	C₂×C₃×C₇
LCS	G ▷ C₁₁×C₃₇
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₄₀₇	C₃	direct (N × H)
3. C₃×C₇×C₁₁×C₃₇	C₄	semidirect
5. C₃×Dic₄₀₇	C₇	direct (N × H)
7. C₇×C₁₁×C₃₇	C₃×C₄	semidirect
9. Dic₄₀₇	C₃×C₇	direct (N × H)
11. C₃×C₁₁×C₃₇	C₄×C₇	semidirect
15. C₃×C₇×C₃₇	Dic₁₁	semidirect
19. C₁₁×C₃₇	C₃×C₄×C₇	semidirect
21. C₇×C₃₇	C₃×Dic₁₁	semidirect
22. C₃×C₇×C₁₁	Dic₃₇	semidirect
27. C₃×C₃₇	C₇×Dic₁₁	semidirect
29. C₇×C₁₁	C₃×Dic₃₇	semidirect
34. C₃₇	C₃×C₇×Dic₁₁	semidirect
35. C₃×C₁₁	C₇×Dic₃₇	semidirect
38. C₃×C₇	Dic₄₀₇	direct (N × H)
41. C₁₁	C₃×C₇×Dic₃₇	semidirect
42. C₇	C₃×Dic₄₀₇	direct (N × H)
45. C₃	C₇×Dic₄₀₇	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×C₃×C₇×C₁₁×C₃₇	2
C₇×Dic₄₀₇	3
C₃×Dic₄₀₇	7
C₃×C₇×Dic₃₇	11
C₃×C₇×Dic₁₁	37

Subgroups — C3×C7×Dic407 #46803136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×Dic₄₀₇ #46803136