Subgroups — C₂×C₁₁×#13095536 #46803228

Order 34188.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#13095536	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×#11715912	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×D₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×#11715912	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×D₇×C₃₇	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×C₁₁×C₃₇⋊C₃	—	7	1	no	maximal, Hall
8	C₂×#13095536	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₃₇⋊C₃	—	7	2	no	—
11	C₂×C₁₁×C₃₇⋊C₃	—	7	1	no	—
12	C₂²×C₁₁×C₃₇	—	7	1	no	Hall
13	C₂×#11715912	C₂×C₁₁	1	1	yes	characteristic, complemented
14	#13095536	C₂×C₁₁	1	2	yes	direct product factor
15	C₁₁×C₃₇⋊C₃	—	7	1	no	Hall
16	C₂×D₇×C₃₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×AGL(1,𝔽₇)	—	37	1	no	maximal, Hall
18	C₂×C₁₁×C₃₇	—	7	2	no	—
19	C₂×C₁₁×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	#11715912	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
22	D₇×C₃₇	C₂×C₃×C₁₁	1	2	yes	complemented
23	C₂×C₁₁×ΓL(1,𝔽₈)	—	37	1	no	—
24	C₁₁×AGL(1,𝔽₇)	—	37	2	no	—
25	C₂²×C₃₇⋊C₃	—	7	1	no	Hall
26	C₁₁×C₃₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₁×D₇	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₇×C₃₇	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
29	C₁₁×ΓL(1,𝔽₈)	—	37	1	no	Hall
30	C₂×C₃₇⋊C₃	—	7	2	no	—
31	C₂×C₃₇⋊C₃	—	7	1	no	—
32	C₂×C₇×C₁₁	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
33	C₁₁×D₇	C₂×C₃₇⋊C₃	1	2	yes	complemented
34	C₂²×C₃₇	—	7	1	no	Hall
35	C₂²×C₃×C₁₁	—	259	1	no	Hall
36	C₃₇⋊C₃	—	7	1	no	Hall
37	C₂×AGL(1,𝔽₇)	—	37	1	no	Hall
38	C₇×C₁₁	C₂²×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃₇	—	7	2	no	—
40	C₂×C₃₇	C₁₁×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
41	C₂×C₃×C₁₁	—	259	2	no	—
42	C₂×C₃×C₁₁	—	259	1	no	—
43	C₂²×C₁₁	—	7	1	no	Hall
44	C₂×ΓL(1,𝔽₈)	—	37	1	no	—
45	AGL(1,𝔽₇)	—	37	2	no	—
46	C₃₇	C₂×C₁₁×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
47	C₃×C₁₁	—	259	1	no	Hall
48	C₂×D₇	C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
49	C₂×C₁₁	—	7	2	no	—
50	C₂×C₁₁	#13095536	1	1	yes	characteristic, direct product factor
51	ΓL(1,𝔽₈)	—	37	1	no	Hall
52	C₂×C₇	C₂×C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, complemented
53	D₇	C₂×C₁₁×C₃₇⋊C₃	1	2	yes	complemented
54	C₂²×C₃	—	259	1	no	Hall
55	C₁₁	C₂×#13095536	1	1	yes	characteristic, direct product factor, Sylow
56	C₇	C₂²×C₁₁×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	259	2	no	—
58	C₂×C₃	—	259	1	no	—
59	C₂²	—	7	1	no	Sylow
60	C₃	—	259	1	no	Sylow
61	C₂	—	7	2	no	—
62	C₂	C₁₁×#13095536	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	#13095536
commutator, cosocle, hypocenter	C₇×C₃₇	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×#13095536	C₂	direct (N × H)
2. C₂×C₁₁×#11715912	C₂	semidirect
3. C₂×C₁₁×D₇×C₃₇	C₃	semidirect
4. C₁₁×#11715912	C₂²	semidirect
5. C₁₁×D₇×C₃₇	C₂×C₃	semidirect
6. C₂×C₇×C₁₁×C₃₇	C₂×C₃	semidirect
8. C₂×#13095536	C₁₁	direct (N × H)
9. C₇×C₁₁×C₃₇	C₂²×C₃	semidirect
13. C₂×#11715912	C₂×C₁₁	semidirect
14. #13095536	C₂×C₁₁	direct (N × H)
16. C₂×D₇×C₃₇	C₃×C₁₁	semidirect
19. C₂×C₁₁×C₃₇	AGL(1,𝔽₇)	semidirect
20. #11715912	C₂²×C₁₁	semidirect
21. C₂×C₇×C₃₇	C₂×C₃×C₁₁	semidirect
22. D₇×C₃₇	C₂×C₃×C₁₁	semidirect
26. C₁₁×C₃₇	C₂×AGL(1,𝔽₇)	semidirect
27. C₂×C₁₁×D₇	C₃₇⋊C₃	semidirect
28. C₇×C₃₇	C₂²×C₃×C₁₁	semidirect
32. C₂×C₇×C₁₁	C₂×C₃₇⋊C₃	semidirect
33. C₁₁×D₇	C₂×C₃₇⋊C₃	semidirect
38. C₇×C₁₁	C₂²×C₃₇⋊C₃	semidirect
40. C₂×C₃₇	C₁₁×AGL(1,𝔽₇)	semidirect
46. C₃₇	C₂×C₁₁×AGL(1,𝔽₇)	semidirect
48. C₂×D₇	C₁₁×C₃₇⋊C₃	semidirect
50. C₂×C₁₁	#13095536	direct (N × H)
52. C₂×C₇	C₂×C₁₁×C₃₇⋊C₃	semidirect
53. D₇	C₂×C₁₁×C₃₇⋊C₃	semidirect
55. C₁₁	C₂×#13095536	direct (N × H)
56. C₇	C₂²×C₁₁×C₃₇⋊C₃	semidirect
62. C₂	C₁₁×#13095536	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#13095536	2
C₂×C₁₁×#11715912	2
C₂×C₁₁×D₇×C₃₇	3
C₂²×C₁₁×C₃₇⋊C₃	7
C₂×#13095536	11
C₂×C₁₁×AGL(1,𝔽₇)	37

Subgroups — C2×C11×#13095536 #46803228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#13095536 #46803228