Subgroups — C₄₁×#10587717 #36375607

Order 22386.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#63271	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₃×C₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₄₁×D₁₃⋊C₃	—	7	1	no	maximal, Hall
5	C₂×ΓL(1,𝔽₈)×C₄₁	—	13	1	no	maximal, Hall
6	C₁₃⋊C₃×C₄₁	—	7	1	no	Hall
7	D₁₃×C₄₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
8	ΓL(1,𝔽₈)×C₄₁	—	13	1	no	Hall
9	C₂×C₇×C₄₁	—	13	1	no	Hall
10	#10587717	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×C₄₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
12	C₇×C₄₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
13	#63271	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₄₁	—	91	1	no	Hall
15	C₇×D₁₃	C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄₁	—	91	1	no	Hall
17	C₇×C₁₃	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₁	—	13	1	no	Hall
19	D₁₃⋊C₃	—	7	1	no	Hall
20	C₂×ΓL(1,𝔽₈)	—	13	1	no	Hall
21	C₄₁	#10587717	1	1	yes	characteristic, direct product factor, Sylow
22	C₁₃⋊C₃	—	7	1	no	Hall
23	D₁₃	ΓL(1,𝔽₈)×C₄₁	1	1	yes	characteristic, complemented, Hall
24	ΓL(1,𝔽₈)	—	13	1	no	Hall
25	C₂×C₇	—	13	1	no	Hall
26	C₁₃	C₂×ΓL(1,𝔽₈)×C₄₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₄₁×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	—	91	1	no	Sylow
30	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	#10587717
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₄₁	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×#63271	C₂	semidirect
2. C₇×D₁₃×C₄₁	C₃	semidirect
3. C₇×C₁₃×C₄₁	C₂×C₃	semidirect
7. D₁₃×C₄₁	ΓL(1,𝔽₈)	semidirect
10. #10587717	C₄₁	direct (N × H)
11. C₁₃×C₄₁	C₂×ΓL(1,𝔽₈)	semidirect
12. C₇×C₄₁	D₁₃⋊C₃	semidirect
13. #63271	C₂×C₄₁	semidirect
15. C₇×D₁₃	C₃×C₄₁	semidirect
17. C₇×C₁₃	C₂×C₃×C₄₁	semidirect
21. C₄₁	#10587717	direct (N × H)
23. D₁₃	ΓL(1,𝔽₈)×C₄₁	semidirect
26. C₁₃	C₂×ΓL(1,𝔽₈)×C₄₁	semidirect
27. C₇	C₄₁×D₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#63271	2
C₇×D₁₃×C₄₁	3
C₄₁×D₁₃⋊C₃	7
C₂×ΓL(1,𝔽₈)×C₄₁	13
#10587717	41

Subgroups — C41×#10587717 #36375607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#10587717 #36375607