Subgroups — #44527726

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29509854	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×(C₁₉⋊C₃)⋊D₁₃	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#17984638	—	7	1	no	maximal, Hall
5	C₇×D₂₄₇	C₉	1	1	yes	characteristic, complemented, Hall
6	#14558807	—	13	1	no	maximal, Hall
7	#14555739	—	7	1	no	Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	#13109896	—	19	1	no	maximal, Hall
10	(C₁₉⋊C₃)⋊D₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	#11924780	—	13	1	no	Hall
12	#11717941	—	19	1	no	Hall
13	C₇×D₁₉⋊C₃	—	13	1	no	—
14	C₁₃×C₁₉⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃×C₇×D₁₃	—	19	1	no	—
16	D₂₄₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₉⋊C₃	D₁₃⋊C₃	1	1	yes	characteristic
18	AGL(1,𝔽₁₉)	—	91	1	no	Hall
19	C₃×C₇×C₁₃	—	19	1	no	—
20	C₇×D₁₉	—	13	1	no	Hall
21	C₁₃×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
22	D₁₃⋊C₉	—	133	1	no	Hall
23	C₇×D₁₃	—	19	1	no	Hall
24	#4296	—	91	1	no	Hall
25	C₇×C₁₉	D₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇⋊C₉	—	247	1	no	Hall
27	C₁₃⋊C₉	—	133	1	no	Hall
28	D₁₉⋊C₃	—	13	1	no	—
29	C₇×C₁₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃	—	19	1	no	—
31	C₇⋊C₉	—	247	1	no	Hall
32	C₁₉⋊C₃	#10587716	1	1	yes	characteristic
33	C₂×C₃×C₇	—	247	1	no	—
34	C₃×C₁₃	—	19	1	no	—
35	D₁₉	—	13	1	no	Hall
36	D₁₃	—	19	1	no	Hall
37	C₃×C₇	—	19	1	no	—
38	C₁₉	#13109896	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₉	—	1729	1	no	Hall
40	C₂×C₇	—	247	1	no	Hall
41	C₁₃	#14558807	1	1	yes	characteristic, complemented, Sylow
42	C₉	—	1729	1	no	Sylow
43	C₇	#17984638	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	247	1	no	—
45	C₃	—	19	1	no	—
46	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₉
prime radical	C₇×(C₁₉⋊C₃)⋊D₁₃	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. #29509854	C₂	semidirect
5. C₇×D₂₄₇	C₉	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
16. D₂₄₇	C₇⋊C₉	semidirect
21. C₁₃×C₁₉	C₂×C₇⋊C₉	semidirect
25. C₇×C₁₉	D₁₃⋊C₉	semidirect
29. C₇×C₁₃	AGL(1,𝔽₁₉)	semidirect
38. C₁₉	#13109896	semidirect
41. C₁₃	#14558807	semidirect
43. C₇	#17984638	semidirect

Maximal subgroups

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

subgroup	index
#29509854	2
C₇×(C₁₉⋊C₃)⋊D₁₃	3
#17984638	7
#14558807	13
#13109896	19