Subgroups — C₂×C₇×#11716325 #26013951

Order 11172.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#87704	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#11716325	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×#87704	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₇×C₁₉	C₂×C₃	1	2	yes	complemented
7	C₂²×C₇×C₁₉⋊C₃	—	7	1	no	maximal
8	C₂×#11716325	C₇	1	1	yes	maximal, characteristic, direct product factor
9	C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×#87704	C₂×C₇	1	1	yes	characteristic, complemented
11	C₂×C₇×C₁₉⋊C₃	—	7	2	no	—
12	C₂×C₇×C₁₉⋊C₃	—	7	1	no	—
13	#11716325	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₇×AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
15	C₂²×C₇×C₁₉	—	7	1	no	—
16	C₂×D₇×C₁₉	C₃×C₇	1	1	yes	characteristic, complemented
17	#87704	C₂²×C₇	1	1	yes	characteristic, complemented
18	C₇×C₁₉⋊C₃	—	7	1	no	—
19	C₂×C₇×ΓL(1,𝔽₈)	—	19	1	no	—
20	C₇×AGL(1,𝔽₇)	—	19	2	no	—
21	C₂×C₇×C₁₉	—	6	1	no	—
22	C₂×C₇×C₁₉	—	7	2	no	—
23	C₂×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
24	C₂×C₇×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
25	D₇×C₁₉	C₂×C₃×C₇	1	2	yes	complemented
26	C₂²×C₁₉⋊C₃	—	7	1	no	Hall
27	C₂×C₇×D₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₇×ΓL(1,𝔽₈)	—	19	1	no	Hall
29	C₇×C₁₉	—	6	1	no	—
30	C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
31	C₇×C₁₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
32	C₂×C₁₉⋊C₃	—	7	2	no	—
33	C₂×C₁₉⋊C₃	—	7	1	no	—
34	C₂×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
35	C₇×D₇	C₂×C₁₉⋊C₃	1	2	yes	complemented
36	C₂²×C₃×C₇	—	133	1	no	—
37	C₂×AGL(1,𝔽₇)	—	19	1	no	—
38	C₂²×C₁₉	—	7	1	no	Hall
39	C₁₉⋊C₃	—	7	1	no	Hall
40	C₇²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃×C₇	—	133	2	no	—
42	C₂×C₃×C₇	—	133	1	no	—
43	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
44	AGL(1,𝔽₇)	—	19	2	no	—
45	C₂×C₁₉	—	7	2	no	—
46	C₂×C₁₉	C₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
47	C₂²×C₇	—	7	1	no	—
48	C₂×D₇	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
49	C₃×C₇	—	133	1	no	—
50	ΓL(1,𝔽₈)	—	19	1	no	—
51	C₁₉	C₂×C₇×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₇	—	6	1	no	—
53	C₂×C₇	—	7	2	no	—
54	C₂×C₇	#11716325	1	1	yes	characteristic, direct product factor
55	C₂×C₇	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
56	D₇	C₂×C₇×C₁₉⋊C₃	1	2	yes	complemented
57	C₂²×C₃	—	133	1	no	Hall
58	C₇	—	6	1	no	—
59	C₇	C₂×#11716325	1	1	yes	characteristic, direct product factor
60	C₇	C₂²×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
61	C₂×C₃	—	133	2	no	—
62	C₂×C₃	—	133	1	no	—
63	C₂²	—	7	1	no	Sylow
64	C₃	—	133	1	no	Sylow
65	C₂	—	7	2	no	—
66	C₂	C₇×#11716325	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	#11716325
commutator, cosocle, hypocenter	C₇×C₁₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#87704	C₂	semidirect
2. C₇×#11716325	C₂	direct (N × H)
3. C₂×C₇×D₇×C₁₉	C₃	semidirect
4. C₇×#87704	C₂²	semidirect
5. C₂×C₇²×C₁₉	C₂×C₃	semidirect
6. C₇×D₇×C₁₉	C₂×C₃	semidirect
8. C₂×#11716325	C₇	direct (N × H)
9. C₇²×C₁₉	C₂²×C₃	semidirect
10. C₂×#87704	C₂×C₇	semidirect
13. #11716325	C₂×C₇	direct (N × H)
16. C₂×D₇×C₁₉	C₃×C₇	semidirect
17. #87704	C₂²×C₇	semidirect
23. C₂×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
24. C₂×C₇×C₁₉	C₂×C₃×C₇	semidirect
25. D₇×C₁₉	C₂×C₃×C₇	semidirect
27. C₂×C₇×D₇	C₁₉⋊C₃	semidirect
30. C₇×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
31. C₇×C₁₉	C₂²×C₃×C₇	semidirect
34. C₂×C₇²	C₂×C₁₉⋊C₃	semidirect
35. C₇×D₇	C₂×C₁₉⋊C₃	semidirect
40. C₇²	C₂²×C₁₉⋊C₃	semidirect
46. C₂×C₁₉	C₇×AGL(1,𝔽₇)	semidirect
48. C₂×D₇	C₇×C₁₉⋊C₃	semidirect
51. C₁₉	C₂×C₇×AGL(1,𝔽₇)	semidirect
54. C₂×C₇	#11716325	direct (N × H)
55. C₂×C₇	C₂×C₇×C₁₉⋊C₃	semidirect
56. D₇	C₂×C₇×C₁₉⋊C₃	semidirect
59. C₇	C₂×#11716325	direct (N × H)
60. C₇	C₂²×C₇×C₁₉⋊C₃	semidirect
66. C₂	C₇×#11716325	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×C₇×#87704	2
C₇×#11716325	2
C₂×C₇×D₇×C₁₉	3
C₂²×C₇×C₁₉⋊C₃	7
C₂×#11716325	7
C₂×C₇×AGL(1,𝔽₇)	19

Subgroups — C2×C7×#11716325 #26013951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#11716325 #26013951