Subgroups — C₃×C₇×Dic₃×C₃₁ #21462956

Order 7812.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄×C₇×C₃₁	—	3	1	no	maximal
4	C₃²×C₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₃₁	—	2	1	no	—
6	C₂×C₃×C₇×C₃₁	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇×C₃₁	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₃×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₇×C₃₁	—	3	1	no	Hall
10	C₃×C₇×C₃₁	—	2	1	no	—
11	C₃×C₇×C₃₁	Dic₃	1	1	yes	characteristic, direct product factor
12	C₃×C₇×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃²×C₃₁	C₂×C₇	1	1	yes	characteristic
14	C₂×C₇×C₃₁	C₃×D₃	1	1	yes	characteristic
15	C₃×C₄×C₃₁	—	3	1	no	—
16	Dic₃×C₃₁	C₃×C₇	1	1	yes	characteristic, direct product factor
17	C₃²×C₃₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
18	C₃×C₇×Dic₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₇×C₃₁	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₃₁	—	2	1	no	—
21	C₂×C₃×C₃₁	D₃×C₇	1	1	yes	characteristic
22	C₂×C₃×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic
23	C₂×C₃²×C₇	C₂×C₃₁	1	1	yes	characteristic
24	C₄×C₃₁	—	3	1	no	Hall
25	C₃×C₃₁	—	2	1	no	—
26	C₃×C₃₁	C₇×Dic₃	1	1	yes	characteristic, direct product factor
27	C₃×C₃₁	C₃×C₄×C₇	1	1	yes	characteristic, complemented
28	C₃×C₄×C₇	—	3	1	no	—
29	C₇×Dic₃	C₃×C₃₁	1	1	yes	characteristic, direct product factor
30	C₃²×C₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃₁	C₃×D₃×C₇	1	1	yes	characteristic
32	C₂×C₃×C₇	—	2	1	no	—
33	C₂×C₃×C₇	D₃×C₃₁	1	1	yes	characteristic
34	C₂×C₃×C₇	C₂×C₃×C₃₁	1	1	yes	characteristic
35	C₃×Dic₃	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
36	C₃₁	C₃×C₇×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₄×C₇	—	3	1	no	Hall
38	C₃×C₇	—	2	1	no	—
39	C₃×C₇	Dic₃×C₃₁	1	1	yes	characteristic, direct product factor
40	C₃×C₇	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented
41	C₂×C₃²	C₂×C₇×C₃₁	1	1	yes	characteristic
42	C₂×C₇	C₃×D₃×C₃₁	1	1	yes	characteristic
43	C₃×C₄	—	3	1	no	—
44	Dic₃	C₃×C₇×C₃₁	1	1	yes	characteristic, direct product factor
45	C₃²	C₄×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×Dic₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	D₃×C₇×C₃₁	1	1	yes	characteristic
49	C₂×C₃	C₂×C₃×C₇×C₃₁	1	1	yes	characteristic
50	C₄	—	3	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₄×C₇×C₃₁	1	1	yes	characteristic, complemented
53	C₃	C₇×Dic₃×C₃₁	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₃×C₇×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₃₁	D₃
commutator, hypocenter	C₃	C₃×C₄×C₇×C₃₁
Frattini	C₂	C₃×D₃×C₇×C₃₁
Fitting, socle	C₂×C₃²×C₇×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₃×C₃₁	C₃	direct (N × H)
4. C₃²×C₇×C₃₁	C₄	semidirect
8. C₃×Dic₃×C₃₁	C₇	direct (N × H)
11. C₃×C₇×C₃₁	Dic₃	direct (N × H)
12. C₃×C₇×C₃₁	C₃×C₄	semidirect
16. Dic₃×C₃₁	C₃×C₇	direct (N × H)
17. C₃²×C₃₁	C₄×C₇	semidirect
18. C₃×C₇×Dic₃	C₃₁	direct (N × H)
19. C₇×C₃₁	C₃×Dic₃	direct (N × H)
26. C₃×C₃₁	C₇×Dic₃	direct (N × H)
27. C₃×C₃₁	C₃×C₄×C₇	semidirect
29. C₇×Dic₃	C₃×C₃₁	direct (N × H)
30. C₃²×C₇	C₄×C₃₁	semidirect
35. C₃×Dic₃	C₇×C₃₁	direct (N × H)
36. C₃₁	C₃×C₇×Dic₃	direct (N × H)
39. C₃×C₇	Dic₃×C₃₁	direct (N × H)
40. C₃×C₇	C₃×C₄×C₃₁	semidirect
44. Dic₃	C₃×C₇×C₃₁	direct (N × H)
45. C₃²	C₄×C₇×C₃₁	semidirect
46. C₇	C₃×Dic₃×C₃₁	direct (N × H)
52. C₃	C₃×C₄×C₇×C₃₁	semidirect
53. C₃	C₇×Dic₃×C₃₁	direct (N × H)

Subgroups — C3×C7×Dic3×C31 #21462956

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×Dic₃×C₃₁ #21462956