Subgroups — C₆₁×#10587720 #45686609

Order 33306.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#63270	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃⋊C₃×C₆₁	—	7	1	no	maximal, Hall
5	AGL(1,𝔽₇)×C₆₁	—	13	1	no	maximal, Hall
6	C₁₃⋊C₃×C₆₁	—	7	1	no	Hall
7	C₂×C₁₃×C₆₁	—	7	1	no	Hall
8	ΓL(1,𝔽₈)×C₆₁	—	13	1	no	Hall
9	D₇×C₆₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₆₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
11	#10587720	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₆₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₆₁	—	91	1	no	Hall
14	#63270	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	—	91	1	no	Hall
16	C₁₃×D₇	C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₆₁	—	7	1	no	Hall
18	C₇×C₁₃	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₃⋊C₃	—	7	1	no	Hall
20	C₆₁	#10587720	1	1	yes	characteristic, direct product factor, Sylow
21	AGL(1,𝔽₇)	—	13	1	no	Hall
22	C₁₃⋊C₃	—	7	1	no	Hall
23	C₂×C₁₃	—	7	1	no	Hall
24	ΓL(1,𝔽₈)	—	13	1	no	Hall
25	D₇	C₁₃⋊C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
26	C₁₃	AGL(1,𝔽₇)×C₆₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₂×C₁₃⋊C₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	—	91	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₁	#10587720
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₆₁	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₆₁

Complements

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

N	H ≅ G/N	type
1. C₆₁×#63270	C₂	semidirect
2. C₁₃×D₇×C₆₁	C₃	semidirect
3. C₇×C₁₃×C₆₁	C₂×C₃	semidirect
9. D₇×C₆₁	C₁₃⋊C₃	semidirect
10. C₁₃×C₆₁	AGL(1,𝔽₇)	semidirect
11. #10587720	C₆₁	direct (N × H)
12. C₇×C₆₁	C₂×C₁₃⋊C₃	semidirect
14. #63270	C₂×C₆₁	semidirect
16. C₁₃×D₇	C₃×C₆₁	semidirect
18. C₇×C₁₃	C₂×C₃×C₆₁	semidirect
20. C₆₁	#10587720	direct (N × H)
25. D₇	C₁₃⋊C₃×C₆₁	semidirect
26. C₁₃	AGL(1,𝔽₇)×C₆₁	semidirect
27. C₇	C₂×C₁₃⋊C₃×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#63270	2
C₁₃×D₇×C₆₁	3
C₂×C₁₃⋊C₃×C₆₁	7
AGL(1,𝔽₇)×C₆₁	13
#10587720	61

Subgroups — C61×#10587720 #45686609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#10587720 #45686609