Subgroups — C₃×C₇×#11716326 #30660752

Order 16758.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#87705	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#11716326	C₃	1	3	yes	maximal, direct product factor
4	C₇×#87705	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₃×C₇×C₁₉⋊C₃	—	7	1	no	maximal
7	C₃×#11716326	C₇	1	1	yes	maximal, characteristic, direct product factor
8	C₇×D₇×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×#87705	C₂×C₇	1	1	yes	characteristic, complemented
10	C₃×C₇×C₁₉⋊C₃	—	7	1	no	—
11	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
13	C₂×C₃×C₇×C₁₉	—	21	1	no	—
14	C₃×D₇×C₁₉	C₃×C₇	1	1	yes	characteristic, complemented
15	C₂×C₇×C₁₉⋊C₃	—	7	3	no	—
16	#11716326	C₃×C₇	1	3	yes	direct product factor
17	C₃×C₇×ΓL(1,𝔽₈)	—	19	1	no	Hall
18	C₃×C₇×C₁₉	—	6	1	no	—
19	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	C₃×C₇×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
21	#87705	C₂×C₃×C₇	1	3	yes	complemented
22	C₇×C₁₉⋊C₃	—	7	3	no	—
23	C₂×C₃×C₁₉⋊C₃	—	7	1	no	Hall
24	C₃×C₇×D₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
25	C₇×AGL(1,𝔽₇)	—	19	3	no	—
26	C₂×C₇×C₁₉	—	21	1	no	—
27	D₇×C₁₉	C₃²×C₇	1	1	yes	characteristic, complemented
28	C₃×C₁₉⋊C₃	—	7	1	no	Hall
29	C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
30	C₇×ΓL(1,𝔽₈)	—	19	3	no	—
31	C₇×C₁₉	—	6	1	no	—
32	C₇×C₁₉	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
33	C₇×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
34	C₂×C₃²×C₇	—	133	1	no	—
35	C₃×AGL(1,𝔽₇)	—	19	1	no	—
36	C₂×C₃×C₁₉	—	21	1	no	—
37	C₂×C₁₉⋊C₃	—	7	3	no	—
38	C₇×D₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₃²×C₇	—	133	1	no	—
40	C₃×ΓL(1,𝔽₈)	—	19	1	no	—
41	C₃×C₁₉	C₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
42	C₁₉⋊C₃	—	7	3	no	—
43	C₇²	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃×C₇	—	21	1	no	—
45	C₂×C₃×C₇	—	133	3	no	—
46	C₃×D₇	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
47	AGL(1,𝔽₇)	—	19	3	no	—
48	C₂×C₁₉	—	21	1	no	Hall
49	C₃×C₇	—	6	1	no	—
50	C₃×C₇	—	133	3	no	—
51	C₃×C₇	#11716326	1	1	yes	characteristic, direct product factor
52	C₃×C₇	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
53	ΓL(1,𝔽₈)	—	19	3	no	—
54	C₁₉	C₃×C₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃²	—	133	1	no	Hall
56	C₂×C₇	—	21	1	no	—
57	D₇	C₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
58	C₃²	—	133	1	no	Sylow
59	C₇	—	6	1	no	—
60	C₇	C₃×#11716326	1	1	yes	characteristic, direct product factor
61	C₇	C₂×C₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
62	C₂×C₃	—	21	1	no	—
63	C₂×C₃	—	133	3	no	—
64	C₃	—	133	3	no	—
65	C₃	C₇×#11716326	1	1	yes	characteristic, direct product factor
66	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	#11716326
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#87705	C₂	semidirect
2. C₃×C₇×D₇×C₁₉	C₃	semidirect
3. C₇×#11716326	C₃	direct (N × H)
4. C₇×#87705	C₂×C₃	semidirect
5. C₃×C₇²×C₁₉	C₂×C₃	semidirect
7. C₃×#11716326	C₇	direct (N × H)
8. C₇×D₇×C₁₉	C₃²	semidirect
9. C₃×#87705	C₂×C₇	semidirect
11. C₇²×C₁₉	C₂×C₃²	semidirect
14. C₃×D₇×C₁₉	C₃×C₇	semidirect
16. #11716326	C₃×C₇	direct (N × H)
19. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
20. C₃×C₇×C₁₉	C₂×C₃×C₇	semidirect
21. #87705	C₂×C₃×C₇	semidirect
24. C₃×C₇×D₇	C₁₉⋊C₃	semidirect
27. D₇×C₁₉	C₃²×C₇	semidirect
29. C₃×C₇²	C₂×C₁₉⋊C₃	semidirect
32. C₇×C₁₉	C₃×AGL(1,𝔽₇)	semidirect
33. C₇×C₁₉	C₂×C₃²×C₇	semidirect
38. C₇×D₇	C₃×C₁₉⋊C₃	semidirect
41. C₃×C₁₉	C₇×AGL(1,𝔽₇)	semidirect
43. C₇²	C₂×C₃×C₁₉⋊C₃	semidirect
46. C₃×D₇	C₇×C₁₉⋊C₃	semidirect
51. C₃×C₇	#11716326	direct (N × H)
52. C₃×C₇	C₂×C₇×C₁₉⋊C₃	semidirect
54. C₁₉	C₃×C₇×AGL(1,𝔽₇)	semidirect
57. D₇	C₃×C₇×C₁₉⋊C₃	semidirect
60. C₇	C₃×#11716326	direct (N × H)
61. C₇	C₂×C₃×C₇×C₁₉⋊C₃	semidirect
65. C₃	C₇×#11716326	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×#87705	2
C₃×C₇×D₇×C₁₉	3
C₇×#11716326	3
C₂×C₃×C₇×C₁₉⋊C₃	7
C₃×#11716326	7
C₃×C₇×AGL(1,𝔽₇)	19

Subgroups — C3×C7×#11716326 #30660752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×#11716326 #30660752