Subgroups — #44527786

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14555740	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×(C₁₉⋊C₃)⋊D₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#17984645	—	7	1	no	maximal, Hall
5	C₁₃×D₁₃₃	C₉	1	1	yes	characteristic, complemented, Hall
6	#4296⋊D₇	—	13	1	no	maximal, Hall
7	#14555740	D₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	D₇×C₁₃⋊C₉	—	19	1	no	maximal, Hall
10	C₁₃×D₁₉⋊C₃	—	7	1	no	—
11	C₇×#4296	—	13	1	no	Hall
12	C₇×C₁₃⋊C₉	—	19	1	no	Hall
13	(C₁₉⋊C₃)⋊D₇	C₁₃⋊C₃	1	1	yes	characteristic
14	C₁₃×C₁₉⋊C₃	C₃×D₇	1	1	yes	characteristic
15	C₃×C₁₃×D₇	—	19	1	no	—
16	C₁₃×D₁₉	—	7	1	no	Hall
17	C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	AGL(1,𝔽₁₉)	—	91	1	no	Hall
19	C₃×C₇×C₁₃	—	19	1	no	—
20	D₁₃₃	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₁₉	C₉×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃⋊C₉	—	133	1	no	Hall
23	C₁₃×D₇	—	19	1	no	Hall
24	#4296	—	13	1	no	Hall
25	C₇×C₁₉	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
26	C₉×D₇	—	247	1	no	Hall
27	C₁₃⋊C₉	—	19	1	no	Hall
28	D₁₉⋊C₃	—	7	1	no	—
29	C₇×C₁₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	—	133	1	no	—
31	C₇×C₉	—	247	1	no	Hall
32	C₁₉⋊C₃	D₇×C₁₃⋊C₃	1	1	yes	characteristic
33	C₃×D₇	—	19	1	no	—
34	C₃×C₁₃	—	19	1	no	—
35	D₁₉	—	7	1	no	Hall
36	C₂×C₁₃	—	133	1	no	Hall
37	C₃×C₇	—	19	1	no	—
38	C₁₉	D₇×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₉	—	1729	1	no	Hall
40	D₇	—	19	1	no	Hall
41	C₁₃	#4296⋊D₇	1	1	yes	characteristic, complemented, Sylow
42	C₉	—	247	1	no	Sylow
43	C₇	#17984645	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	133	1	no	—
45	C₃	—	19	1	no	—
46	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₉
prime radical	C₁₃×(C₁₉⋊C₃)⋊D₇	C₃
cosocle	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×#14555740	C₂	semidirect
5. C₁₃×D₁₃₃	C₉	semidirect
7. #14555740	D₇	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
20. D₁₃₃	C₁₃⋊C₉	semidirect
21. C₁₃×C₁₉	C₉×D₇	semidirect
25. C₇×C₁₉	C₂×C₁₃⋊C₉	semidirect
29. C₇×C₁₃	AGL(1,𝔽₁₉)	semidirect
38. C₁₉	D₇×C₁₃⋊C₉	semidirect
41. C₁₃	#4296⋊D₇	semidirect
43. C₇	#17984645	semidirect

Maximal subgroups

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

subgroup	index
C₇×#14555740	2
C₁₃×(C₁₉⋊C₃)⋊D₇	3
#17984645	7
#4296⋊D₇	13
D₇×C₁₃⋊C₉	19