Subgroups — C₇×#13094088⋊C₃ #44539808

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₇×#13094088	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₂₉×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₃₇₇	C₂×C₃	1	1	yes	characteristic
5	#13094088⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×#1181	—	13	1	no	maximal, Hall
8	C₂₉⋊(D₁₃⋊C₃)	C₂×C₇	1	1	yes	characteristic
9	#13094088	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×D₂₉	—	13	1	no	—
11	C₂₉×C₁₃⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×AGL(1,𝔽₁₃)	—	29	1	no	maximal, Hall
13	C₇×#1181	—	13	1	no	Hall
14	D₃₇₇	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₇×C₂₉	—	13	1	no	Hall
16	C₇×D₁₃⋊C₃	—	29	1	no	—
17	C₇×D₂₉	—	13	1	no	—
18	C₁₃×C₂₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
19	C₇×#261	—	29	1	no	Hall
20	C₃×#1181	—	13	1	no	Hall
21	C₇×C₁₃⋊C₃	#1181	1	1	yes	characteristic, complemented, Hall
22	C₇×C₂₉	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	—	29	1	no	—
24	C₃×D₂₉	—	13	1	no	—
25	AGL(1,𝔽₁₃)	—	29	1	no	Hall
26	#1181	—	13	1	no	Hall
27	C₇×C₁₃	C₃×#1181	1	1	yes	characteristic, complemented, Hall
28	C₃×C₂₉	—	13	1	no	Hall
29	C₃×C₄×C₇	—	377	1	no	Hall
30	D₁₃⋊C₃	—	29	1	no	—
31	D₂₉	—	13	1	no	—
32	#261	—	29	1	no	Hall
33	C₂×C₃×C₇	—	377	1	no	—
34	C₁₃⋊C₃	C₇×#1181	1	1	yes	characteristic, complemented, Hall
35	C₂₉	C₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	377	1	no	Hall
37	D₁₃	—	29	1	no	—
38	C₃×C₇	—	13	1	no	Hall
39	C₂×C₇	—	377	1	no	—
40	C₁₃	C₃×C₇×#1181	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	377	1	no	Hall
42	C₇	#13094088⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	377	1	no	—
44	C₄	—	377	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	377	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#13094088⋊C₃
commutator, hypocenter	C₁₃×C₂₉	C₃×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₉	C₃×C₄
prime radical	C₇×C₂₉⋊(D₁₃⋊C₃)	C₂
cosocle	D₃₇₇	C₂×C₃×C₇
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₇×#13094088	C₃	semidirect
3. C₇×C₂₉×C₁₃⋊C₃	C₄	semidirect
5. #13094088⋊C₃	C₇	direct (N × H)
6. C₇×C₁₃×C₂₉	C₃×C₄	semidirect
9. #13094088	C₃×C₇	semidirect
11. C₂₉×C₁₃⋊C₃	C₄×C₇	semidirect
18. C₁₃×C₂₉	C₃×C₄×C₇	semidirect
21. C₇×C₁₃⋊C₃	#1181	semidirect
22. C₇×C₂₉	AGL(1,𝔽₁₃)	semidirect
27. C₇×C₁₃	C₃×#1181	semidirect
34. C₁₃⋊C₃	C₇×#1181	semidirect
35. C₂₉	C₇×AGL(1,𝔽₁₃)	semidirect
40. C₁₃	C₃×C₇×#1181	semidirect
42. C₇	#13094088⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₉⋊(D₁₃⋊C₃)	2
C₇×#13094088	3
#13094088⋊C₃	7
C₃×C₇×#1181	13
C₇×AGL(1,𝔽₁₃)	29

Subgroups — C7×#13094088⋊C3 #44539808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#13094088⋊C₃ #44539808