Subgroups — C₃×C₇×#13095532 #45657498

Order 32634.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#11715912	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#13095532	C₃	1	3	yes	maximal, direct product factor
4	C₇×#11715912	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×#13095532	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₇×D₃₇⋊C₃	—	7	1	no	maximal
8	C₇²×D₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₃₇⋊C₃	—	7	1	no	—
10	C₃×#11715912	C₂×C₇	1	1	yes	characteristic, complemented
11	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×D₃₇	—	3	2	no	—
13	C₃×C₇×D₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₃×C₇×D₃₇	C₃×C₇	1	1	yes	characteristic, complemented
15	#13095532	C₃×C₇	1	3	yes	direct product factor
16	C₇×D₃₇⋊C₃	—	7	3	no	—
17	C₂×C₃×C₇×ΓL(1,𝔽₈)	—	37	1	no	maximal, Hall
18	C₃×C₇×C₃₇	—	3	2	no	—
19	C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
20	C₃×C₇×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
21	#11715912	C₂×C₃×C₇	1	3	yes	complemented
22	C₇×C₃₇⋊C₃	—	7	3	no	—
23	C₃×D₃₇⋊C₃	—	7	1	no	Hall
24	C₇×D₃₇	—	3	2	no	—
25	C₇×D₃₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
26	C₇×D₃₇	C₃²×C₇	1	1	yes	characteristic, complemented
27	C₃×C₇×ΓL(1,𝔽₈)	—	37	1	no	Hall
28	C₃×C₃₇⋊C₃	—	7	1	no	Hall
29	C₂×C₃×C₇²	—	37	1	no	—
30	C₂×C₇×ΓL(1,𝔽₈)	—	37	3	no	—
31	C₇×C₃₇	—	3	2	no	—
32	C₇×C₃₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
33	C₇×C₃₇	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
34	C₃×D₃₇	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
35	D₃₇⋊C₃	—	7	3	no	—
36	C₃×C₇²	D₃₇⋊C₃	1	1	yes	characteristic, complemented
37	C₇×ΓL(1,𝔽₈)	—	37	3	no	—
38	C₂×C₃²×C₇	—	259	1	no	—
39	C₂×C₃×ΓL(1,𝔽₈)	—	37	1	no	—
40	C₃×C₃₇	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
41	C₃₇⋊C₃	—	7	3	no	—
42	C₂×C₇²	—	37	1	no	Hall
43	D₃₇	C₃×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
44	C₃²×C₇	—	259	1	no	—
45	C₃×ΓL(1,𝔽₈)	—	37	1	no	—
46	C₇²	C₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃×C₇	—	259	3	no	—
48	C₂×C₃×C₇	—	37	1	no	—
49	C₂×C₃×C₇	—	37	1	no	—
50	C₂×C₃×C₇	—	111	2	no	—
51	C₂×ΓL(1,𝔽₈)	—	37	3	no	—
52	C₃₇	C₂×C₃×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₇	—	3	2	no	—
54	C₃×C₇	—	259	3	no	—
55	C₃×C₇	C₇×D₃₇⋊C₃	1	1	yes	characteristic, complemented
56	C₃×C₇	#13095532	1	1	yes	characteristic, direct product factor
57	ΓL(1,𝔽₈)	—	37	3	no	—
58	C₂×C₃²	—	259	1	no	Hall
59	C₂×C₇	—	37	1	no	—
60	C₂×C₇	—	37	1	no	—
61	C₂×C₇	—	111	2	no	—
62	C₃²	—	259	1	no	Sylow
63	C₇	—	3	2	no	—
64	C₇	C₃×C₇×D₃₇⋊C₃	1	1	yes	characteristic, complemented
65	C₇	C₃×#13095532	1	1	yes	characteristic, direct product factor
66	C₂×C₃	—	259	3	no	—
67	C₂×C₃	—	37	1	no	—
68	C₃	—	259	3	no	—
69	C₃	C₇×#13095532	1	1	yes	characteristic, direct product factor
70	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	#13095532
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#11715912	C₂	semidirect
2. C₃×C₇²×D₃₇	C₃	semidirect
3. C₇×#13095532	C₃	direct (N × H)
4. C₇×#11715912	C₂×C₃	semidirect
5. C₃×C₇²×C₃₇	C₂×C₃	semidirect
6. C₃×#13095532	C₇	direct (N × H)
8. C₇²×D₃₇	C₃²	semidirect
10. C₃×#11715912	C₂×C₇	semidirect
11. C₇²×C₃₇	C₂×C₃²	semidirect
13. C₃×C₇×D₃₇	ΓL(1,𝔽₈)	semidirect
14. C₃×C₇×D₃₇	C₃×C₇	semidirect
15. #13095532	C₃×C₇	direct (N × H)
19. C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	semidirect
20. C₃×C₇×C₃₇	C₂×C₃×C₇	semidirect
21. #11715912	C₂×C₃×C₇	semidirect
25. C₇×D₃₇	C₃×ΓL(1,𝔽₈)	semidirect
26. C₇×D₃₇	C₃²×C₇	semidirect
32. C₇×C₃₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
33. C₇×C₃₇	C₂×C₃²×C₇	semidirect
34. C₃×D₃₇	C₇×ΓL(1,𝔽₈)	semidirect
36. C₃×C₇²	D₃₇⋊C₃	semidirect
40. C₃×C₃₇	C₂×C₇×ΓL(1,𝔽₈)	semidirect
43. D₃₇	C₃×C₇×ΓL(1,𝔽₈)	semidirect
46. C₇²	C₃×D₃₇⋊C₃	semidirect
52. C₃₇	C₂×C₃×C₇×ΓL(1,𝔽₈)	semidirect
55. C₃×C₇	C₇×D₃₇⋊C₃	semidirect
56. C₃×C₇	#13095532	direct (N × H)
64. C₇	C₃×C₇×D₃₇⋊C₃	semidirect
65. C₇	C₃×#13095532	direct (N × H)
69. C₃	C₇×#13095532	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×C₇×#11715912	2
C₃×C₇²×D₃₇	3
C₇×#13095532	3
C₃×#13095532	7
C₃×C₇×D₃₇⋊C₃	7
C₂×C₃×C₇×ΓL(1,𝔽₈)	37

Subgroups — C3×C7×#13095532 #45657498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×#13095532 #45657498