Subgroups — C₃×C₇×Dic₃×C₇₁ #31822046

Order 17892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃×C₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄×C₇×C₇₁	—	3	1	no	maximal
4	C₃²×C₇×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₇₁	—	2	1	no	—
6	C₂×C₃×C₇×C₇₁	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇×C₇₁	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₃×C₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₇×C₇₁	—	3	1	no	Hall
10	C₃×C₇×C₇₁	—	2	1	no	—
11	C₃×C₇×C₇₁	Dic₃	1	1	yes	characteristic, direct product factor
12	C₃×C₇×C₇₁	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃²×C₇₁	C₂×C₇	1	1	yes	characteristic
14	C₂×C₇×C₇₁	C₃×D₃	1	1	yes	characteristic
15	C₃×C₄×C₇₁	—	3	1	no	—
16	Dic₃×C₇₁	C₃×C₇	1	1	yes	characteristic, direct product factor
17	C₃²×C₇₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
18	C₇×C₇₁	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₇₁	—	2	1	no	—
20	C₂×C₃×C₇₁	D₃×C₇	1	1	yes	characteristic
21	C₂×C₃×C₇₁	C₂×C₃×C₇	1	1	yes	characteristic
22	C₄×C₇₁	—	3	1	no	Hall
23	C₃×C₇×Dic₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₃×C₇₁	—	2	1	no	—
25	C₃×C₇₁	C₇×Dic₃	1	1	yes	characteristic, direct product factor
26	C₃×C₇₁	C₃×C₄×C₇	1	1	yes	characteristic, complemented
27	C₂×C₇₁	C₃×D₃×C₇	1	1	yes	characteristic
28	C₂×C₃²×C₇	C₂×C₇₁	1	1	yes	characteristic
29	C₃×C₄×C₇	—	3	1	no	—
30	C₇×Dic₃	C₃×C₇₁	1	1	yes	characteristic, direct product factor
31	C₇₁	C₃×C₇×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₃²×C₇	C₄×C₇₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₇	—	2	1	no	—
34	C₂×C₃×C₇	D₃×C₇₁	1	1	yes	characteristic
35	C₂×C₃×C₇	C₂×C₃×C₇₁	1	1	yes	characteristic
36	C₃×Dic₃	C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
37	C₄×C₇	—	3	1	no	Hall
38	C₃×C₇	—	2	1	no	—
39	C₃×C₇	Dic₃×C₇₁	1	1	yes	characteristic, direct product factor
40	C₃×C₇	C₃×C₄×C₇₁	1	1	yes	characteristic, complemented
41	C₂×C₃²	C₂×C₇×C₇₁	1	1	yes	characteristic
42	C₂×C₇	C₃×D₃×C₇₁	1	1	yes	characteristic
43	C₃×C₄	—	3	1	no	—
44	Dic₃	C₃×C₇×C₇₁	1	1	yes	characteristic, direct product factor
45	C₃²	C₄×C₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×Dic₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₂×C₃×C₇×C₇₁	1	1	yes	characteristic
49	C₂×C₃	D₃×C₇×C₇₁	1	1	yes	characteristic
50	C₄	—	3	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₄×C₇×C₇₁	1	1	yes	characteristic, complemented
53	C₃	C₇×Dic₃×C₇₁	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₃×C₇×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₇₁	D₃
commutator, hypocenter	C₃	C₃×C₄×C₇×C₇₁
Frattini	C₂	C₃×D₃×C₇×C₇₁
Fitting, socle, prime radical	C₂×C₃²×C₇×C₇₁	C₂
cosocle	C₂×C₃	C₂×C₃×C₇×C₇₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₇×C₇₁

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₃×C₇₁	C₃	direct (N × H)
4. C₃²×C₇×C₇₁	C₄	semidirect
8. C₃×Dic₃×C₇₁	C₇	direct (N × H)
11. C₃×C₇×C₇₁	Dic₃	direct (N × H)
12. C₃×C₇×C₇₁	C₃×C₄	semidirect
16. Dic₃×C₇₁	C₃×C₇	direct (N × H)
17. C₃²×C₇₁	C₄×C₇	semidirect
18. C₇×C₇₁	C₃×Dic₃	direct (N × H)
23. C₃×C₇×Dic₃	C₇₁	direct (N × H)
25. C₃×C₇₁	C₇×Dic₃	direct (N × H)
26. C₃×C₇₁	C₃×C₄×C₇	semidirect
30. C₇×Dic₃	C₃×C₇₁	direct (N × H)
31. C₇₁	C₃×C₇×Dic₃	direct (N × H)
32. C₃²×C₇	C₄×C₇₁	semidirect
36. C₃×Dic₃	C₇×C₇₁	direct (N × H)
39. C₃×C₇	Dic₃×C₇₁	direct (N × H)
40. C₃×C₇	C₃×C₄×C₇₁	semidirect
44. Dic₃	C₃×C₇×C₇₁	direct (N × H)
45. C₃²	C₄×C₇×C₇₁	semidirect
46. C₇	C₃×Dic₃×C₇₁	direct (N × H)
52. C₃	C₃×C₄×C₇×C₇₁	semidirect
53. C₃	C₇×Dic₃×C₇₁	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×C₃²×C₇×C₇₁	2
C₇×Dic₃×C₇₁	3
C₃×C₄×C₇×C₇₁	3
C₃×Dic₃×C₇₁	7
C₃×C₇×Dic₃	71

Subgroups — C3×C7×Dic3×C71 #31822046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×Dic₃×C₇₁ #31822046