Subgroups — C₁₁×#14579424 #43245331

Order 28182.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#13046197	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₆₁⋊C₃	—	7	1	no	maximal, Hall
5	#14579424	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₆₁⋊C₃	—	7	1	no	Hall
7	C₂×C₁₁×C₆₁	—	7	1	no	Hall
8	#13046197	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	D₇×C₆₁	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×C₆₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
11	C₁₁×AGL(1,𝔽₇)	—	61	1	no	maximal, Hall
12	C₇×C₆₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₆₁⋊C₃	—	7	1	no	Hall
14	C₁₁×ΓL(1,𝔽₈)	—	61	1	no	Hall
15	C₆₁⋊C₃	—	7	1	no	Hall
16	C₁₁×D₇	C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₆₁	—	7	1	no	Hall
18	C₇×C₁₁	C₂×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₁	—	427	1	no	Hall
20	C₆₁	C₁₁×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
21	AGL(1,𝔽₇)	—	61	1	no	Hall
22	C₃×C₁₁	—	427	1	no	Hall
23	C₂×C₁₁	—	7	1	no	Hall
24	ΓL(1,𝔽₈)	—	61	1	no	Hall
25	D₇	C₁₁×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₁₁	#14579424	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₁₁×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	427	1	no	Hall
29	C₃	—	427	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	#14579424
commutator, cosocle, hypocenter	C₇×C₆₁	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₆₁	C₂×C₃
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×#13046197	C₂	semidirect
2. C₁₁×D₇×C₆₁	C₃	semidirect
3. C₇×C₁₁×C₆₁	C₂×C₃	semidirect
5. #14579424	C₁₁	direct (N × H)
8. #13046197	C₂×C₁₁	semidirect
9. D₇×C₆₁	C₃×C₁₁	semidirect
10. C₁₁×C₆₁	AGL(1,𝔽₇)	semidirect
12. C₇×C₆₁	C₂×C₃×C₁₁	semidirect
16. C₁₁×D₇	C₆₁⋊C₃	semidirect
18. C₇×C₁₁	C₂×C₆₁⋊C₃	semidirect
20. C₆₁	C₁₁×AGL(1,𝔽₇)	semidirect
25. D₇	C₁₁×C₆₁⋊C₃	semidirect
26. C₁₁	#14579424	direct (N × H)
27. C₇	C₂×C₁₁×C₆₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#13046197	2
C₁₁×D₇×C₆₁	3
C₂×C₁₁×C₆₁⋊C₃	7
#14579424	11
C₁₁×AGL(1,𝔽₇)	61

Subgroups — C11×#14579424 #43245331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#14579424 #43245331