Subgroups — C₂×C₁₁×#13095531 #46803237

Order 34188.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#13095531	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×#11715913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₁×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×#11715913	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁×D₃₇	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₁₁×D₃₇⋊C₃	—	7	1	no	maximal, Hall
8	C₂×#13095531	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₁₁×D₃₇⋊C₃	—	7	2	no	—
11	C₂×C₁₁×C₃₇⋊C₃	—	7	1	no	—
12	C₂×C₁₁×D₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₂×#11715913	C₂×C₁₁	1	1	yes	characteristic, complemented
14	#13095531	C₂×C₁₁	1	2	yes	direct product factor
15	C₁₁×C₃₇⋊C₃	—	7	1	no	Hall
16	C₂×C₇×D₃₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₁₁×ΓL(1,𝔽₈)	—	37	1	no	maximal, Hall
18	C₂×C₁₁×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₁₁×D₃₇	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
20	#11715913	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
22	C₇×D₃₇	C₂×C₃×C₁₁	1	2	yes	complemented
23	C₂×C₁₁×ΓL(1,𝔽₈)	—	37	2	no	—
24	C₂×C₁₁×ΓL(1,𝔽₈)	—	37	1	no	—
25	C₂×D₃₇⋊C₃	—	7	1	no	Hall
26	C₁₁×C₃₇	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₇×C₁₁	—	37	1	no	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	1	no	—
31	D₃₇⋊C₃	—	7	2	no	—
32	C₂×C₇×C₁₁	—	37	2	no	—
33	C₂×C₇×C₁₁	D₃₇⋊C₃	1	1	yes	characteristic, complemented
34	C₂×D₃₇	C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃×C₁₁	—	259	1	no	Hall
36	C₃₇⋊C₃	—	7	1	no	Hall
37	C₂²×ΓL(1,𝔽₈)	—	37	1	no	Hall
38	C₇×C₁₁	C₂×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃₇	C₂×C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
40	D₃₇	C₂×C₁₁×ΓL(1,𝔽₈)	1	2	yes	complemented
41	C₂×C₃×C₁₁	—	259	2	no	—
42	C₂×C₃×C₁₁	—	259	1	no	—
43	C₂²×C₁₁	—	37	1	no	Hall
44	C₂×ΓL(1,𝔽₈)	—	37	2	no	—
45	C₂×ΓL(1,𝔽₈)	—	37	1	no	—
46	C₃₇	C₂²×C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
47	C₃×C₁₁	—	259	1	no	Hall
48	C₂²×C₇	—	37	1	no	Hall
49	C₂×C₁₁	—	37	2	no	—
50	C₂×C₁₁	#13095531	1	1	yes	characteristic, direct product factor
51	ΓL(1,𝔽₈)	—	37	1	no	Hall
52	C₂×C₇	—	37	2	no	—
53	C₂×C₇	C₁₁×D₃₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	259	1	no	Hall
55	C₁₁	C₂×#13095531	1	1	yes	characteristic, direct product factor, Sylow
56	C₇	C₂×C₁₁×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	259	2	no	—
58	C₂×C₃	—	259	1	no	—
59	C₂²	—	37	1	no	Sylow
60	C₃	—	259	1	no	Sylow
61	C₂	—	37	2	no	—
62	C₂	C₁₁×#13095531	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	#13095531
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×#13095531	C₂	direct (N × H)
2. C₂×C₁₁×#11715913	C₂	semidirect
3. C₂×C₇×C₁₁×D₃₇	C₃	semidirect
4. C₁₁×#11715913	C₂²	semidirect
5. C₇×C₁₁×D₃₇	C₂×C₃	semidirect
6. C₂×C₇×C₁₁×C₃₇	C₂×C₃	semidirect
8. C₂×#13095531	C₁₁	direct (N × H)
9. C₇×C₁₁×C₃₇	C₂²×C₃	semidirect
12. C₂×C₁₁×D₃₇	ΓL(1,𝔽₈)	semidirect
13. C₂×#11715913	C₂×C₁₁	semidirect
14. #13095531	C₂×C₁₁	direct (N × H)
16. C₂×C₇×D₃₇	C₃×C₁₁	semidirect
18. C₂×C₁₁×C₃₇	C₂×ΓL(1,𝔽₈)	semidirect
19. C₁₁×D₃₇	C₂×ΓL(1,𝔽₈)	semidirect
20. #11715913	C₂²×C₁₁	semidirect
21. C₂×C₇×C₃₇	C₂×C₃×C₁₁	semidirect
22. C₇×D₃₇	C₂×C₃×C₁₁	semidirect
26. C₁₁×C₃₇	C₂²×ΓL(1,𝔽₈)	semidirect
28. C₇×C₃₇	C₂²×C₃×C₁₁	semidirect
33. C₂×C₇×C₁₁	D₃₇⋊C₃	semidirect
34. C₂×D₃₇	C₁₁×ΓL(1,𝔽₈)	semidirect
38. C₇×C₁₁	C₂×D₃₇⋊C₃	semidirect
39. C₂×C₃₇	C₂×C₁₁×ΓL(1,𝔽₈)	semidirect
40. D₃₇	C₂×C₁₁×ΓL(1,𝔽₈)	semidirect
46. C₃₇	C₂²×C₁₁×ΓL(1,𝔽₈)	semidirect
50. C₂×C₁₁	#13095531	direct (N × H)
53. C₂×C₇	C₁₁×D₃₇⋊C₃	semidirect
55. C₁₁	C₂×#13095531	direct (N × H)
56. C₇	C₂×C₁₁×D₃₇⋊C₃	semidirect
62. C₂	C₁₁×#13095531	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×#13095531	2
C₂×C₁₁×#11715913	2
C₂×C₇×C₁₁×D₃₇	3
C₂×C₁₁×D₃₇⋊C₃	7
C₂×#13095531	11
C₂²×C₁₁×ΓL(1,𝔽₈)	37

Subgroups — C2×C11×#13095531 #46803237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#13095531 #46803237