Subgroups — C₂×#19150317 #26013994

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	#19150317	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₁₃₃	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×D₁₃₃	C₂×C₃	1	2	yes	complemented
7	C₂×#11716321	—	7	1	no	maximal
8	C₂×(C₁₉⋊C₃)⋊D₇	—	7	1	no	maximal
9	C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×#87704	D₇	1	1	yes	characteristic, complemented
11	C₂×C₇×C₁₉⋊C₃	—	7	1	no	—
12	#11716321	—	7	2	no	—
13	(C₁₉⋊C₃)⋊D₇	—	7	2	no	—
14	C₂×D₇×ΓL(1,𝔽₈)	—	19	1	no	maximal, Hall
15	C₂×D₁₃₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	C₂×C₇×D₁₉	—	7	1	no	—
17	#87704	C₂×D₇	1	1	yes	characteristic, complemented
18	C₇×C₁₉⋊C₃	—	7	1	no	—
19	C₂×C₇×ΓL(1,𝔽₈)	—	19	1	no	—
20	D₇×ΓL(1,𝔽₈)	—	19	2	no	—
21	C₂×C₇×C₁₉	—	6	1	no	—
22	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₂×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
24	D₁₃₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
25	C₇×D₁₉	—	7	2	no	—
26	C₂×D₁₉⋊C₃	—	49	1	no	Hall
27	C₂×C₇×D₇	—	19	1	no	Hall
28	C₇×ΓL(1,𝔽₈)	—	19	1	no	Hall
29	C₇×C₁₉	—	6	1	no	—
30	C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
31	C₇×C₁₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented
32	C₂×C₁₉⋊C₃	—	7	1	no	—
33	D₁₉⋊C₃	—	49	2	no	—
34	C₂×C₇²	D₁₉⋊C₃	1	1	yes	characteristic, complemented
35	C₇×D₇	—	19	2	no	—
36	C₂×C₃×D₇	—	133	1	no	—
37	C₂²×ΓL(1,𝔽₈)	—	133	1	no	—
38	C₂×D₁₉	—	7	1	no	Hall
39	C₁₉⋊C₃	—	7	1	no	Hall
40	C₇²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃×C₇	—	133	1	no	—
42	C₃×D₇	—	133	2	no	—
43	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
44	C₂×ΓL(1,𝔽₈)	—	133	2	no	—
45	C₂×C₁₉	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
46	D₁₉	—	7	2	no	—
47	C₂²×C₇	—	133	1	no	—
48	C₂×D₇	—	19	1	no	—
49	C₃×C₇	—	133	1	no	—
50	ΓL(1,𝔽₈)	—	19	1	no	—
51	C₁₉	C₂×D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₇	—	6	1	no	—
53	C₂×C₇	—	133	2	no	—
54	C₂×C₇	(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
55	C₂×C₇	#11716321	1	1	yes	characteristic, complemented
56	D₇	—	19	2	no	—
57	C₂²×C₃	—	931	1	no	Hall
58	C₇	—	6	1	no	—
59	C₇	C₂×(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
60	C₇	C₂×#11716321	1	1	yes	characteristic, complemented
61	C₂×C₃	—	133	1	no	—
62	C₂×C₃	—	931	2	no	—
63	C₂²	—	133	1	no	Sylow
64	C₃	—	133	1	no	Sylow
65	C₂	—	133	2	no	—
66	C₂	#19150317	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#19150317
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#87704	C₂	semidirect
2. #19150317	C₂	direct (N × H)
3. C₂×C₇×D₁₃₃	C₃	semidirect
4. C₇×#87704	C₂²	semidirect
5. C₂×C₇²×C₁₉	C₂×C₃	semidirect
6. C₇×D₁₃₃	C₂×C₃	semidirect
9. C₇²×C₁₉	C₂²×C₃	semidirect
10. C₂×#87704	D₇	semidirect
15. C₂×D₁₃₃	ΓL(1,𝔽₈)	semidirect
17. #87704	C₂×D₇	semidirect
22. C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
23. C₂×C₇×C₁₉	C₃×D₇	semidirect
24. D₁₃₃	C₂×ΓL(1,𝔽₈)	semidirect
30. C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	semidirect
31. C₇×C₁₉	C₂×C₃×D₇	semidirect
34. C₂×C₇²	D₁₉⋊C₃	semidirect
40. C₇²	C₂×D₁₉⋊C₃	semidirect
45. C₂×C₁₉	D₇×ΓL(1,𝔽₈)	semidirect
51. C₁₉	C₂×D₇×ΓL(1,𝔽₈)	semidirect
54. C₂×C₇	(C₁₉⋊C₃)⋊D₇	semidirect
55. C₂×C₇	#11716321	semidirect
59. C₇	C₂×(C₁₉⋊C₃)⋊D₇	semidirect
60. C₇	C₂×#11716321	semidirect
66. C₂	#19150317	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
#19150317	2
C₂×C₇×D₁₃₃	3
C₂×#11716321	7
C₂×(C₁₉⋊C₃)⋊D₇	7
C₂×D₇×ΓL(1,𝔽₈)	19

Subgroups — C2×#19150317 #26013994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19150317 #26013994