Subgroups — C₇⋊D₇×AGL(1,𝔽₁₉) #45692097

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₇×#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	#4296⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×AGL(1,𝔽₁₉)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇⋊D₇×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₇²×#4296	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉⋊C₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
7	(C₁₉⋊C₃)⋊(C₇⋊D₇)	C₂×C₃	1	1	yes	characteristic
8	C₇²×D₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
9	D₇×AGL(1,𝔽₁₉)	—	7	8	no	maximal
10	D₁₉×C₇⋊D₇	C₉	1	1	yes	characteristic, complemented, Hall
11	C₇²×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
12	D₇×#4296	—	7	8	no	—
13	#4296⋊D₇	—	7	8	no	—
14	C₇×AGL(1,𝔽₁₉)	D₇	1	8	yes	complemented
15	C₇⋊D₁₃₃	C₂×C₉	1	1	yes	characteristic, complemented
16	C₁₉×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic, complemented
17	C₇²×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₉×C₇⋊D₇	—	19	1	no	maximal, Hall
19	D₇×D₁₉⋊C₃	—	7	8	no	—
20	C₇×#4296	C₂×D₇	1	8	yes	complemented
21	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇²×C₉	—	19	1	no	—
23	C₉×C₇⋊D₇	—	19	1	no	—
24	C₉×C₇⋊D₇	—	19	1	no	—
25	(C₁₉⋊C₃)⋊D₇	—	7	8	no	—
26	D₇×C₁₉⋊C₃	—	7	8	no	—
27	C₇×D₁₉⋊C₃	C₃×D₇	1	8	yes	—
28	C₂×AGL(1,𝔽₁₉)	—	49	1	no	Hall
29	C₂×C₃×C₇⋊D₇	—	19	1	no	—
30	D₇×D₁₉	—	7	8	no	—
31	C₇²×C₉	—	19	1	no	Hall
32	C₇×C₁₉⋊C₃	C₂×C₃×D₇	1	8	yes	—
33	C₂×#4296	—	49	1	no	—
34	AGL(1,𝔽₁₉)	—	49	1	no	—
35	AGL(1,𝔽₁₉)	C₇⋊D₇	1	1	yes	characteristic, direct product factor
36	C₂×C₃×C₇²	—	19	1	no	—
37	C₃×C₇⋊D₇	—	19	1	no	—
38	C₃×C₇⋊D₇	—	19	1	no	—
39	D₁₃₃	—	7	8	no	—
40	C₇×D₁₉	C₉×D₇	1	8	yes	complemented
41	D₇×C₁₉	—	7	8	no	—
42	C₂×C₉×D₇	—	133	8	no	—
43	C₂×D₁₉⋊C₃	—	49	1	no	—
44	C₂×C₇⋊D₇	—	19	1	no	Hall
45	#4296	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
46	C₃×C₇²	—	19	1	no	—
47	C₇×C₁₉	C₂×C₉×D₇	1	8	yes	complemented
48	C₂×C₇×C₉	—	19	8	no	—
49	C₉×D₇	—	133	8	no	—
50	C₉×D₇	—	133	8	no	—
51	C₂×C₁₉⋊C₃	—	49	1	no	—
52	D₁₉⋊C₃	—	49	1	no	—
53	D₁₉⋊C₃	C₃×C₇⋊D₇	1	1	yes	characteristic
54	C₂×C₇²	—	19	1	no	—
55	C₇⋊D₇	—	19	1	no	—
56	C₇⋊D₇	AGL(1,𝔽₁₉)	1	1	yes	characteristic, direct product factor
57	C₂×C₃×D₇	—	133	8	no	—
58	C₂×D₁₉	—	49	1	no	Hall
59	C₇×C₉	—	19	8	no	—
60	C₁₉⋊C₃	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic
61	C₇²	C₂×AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₃×C₇	—	19	8	no	—
63	C₃×D₇	—	133	8	no	—
64	C₃×D₇	—	133	8	no	—
65	C₂×C₁₉	—	49	1	no	—
66	D₁₉	—	49	1	no	—
67	D₁₉	C₉×C₇⋊D₇	1	1	yes	characteristic, complemented
68	C₂²×C₉	—	931	1	no	Hall
69	C₂×D₇	—	133	8	no	—
70	C₃×C₇	—	19	8	no	—
71	C₁₉	C₂×C₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₉	—	19	1	no	—
73	C₂×C₉	—	931	1	no	—
74	C₂×C₉	—	931	1	no	—
75	C₂×C₇	—	19	8	no	—
76	D₇	—	7	8	no	—
77	D₇	—	133	8	no	—
78	C₂²×C₃	—	931	1	no	—
79	C₉	—	19	1	no	Sylow
80	C₇	D₇×AGL(1,𝔽₁₉)	1	8	yes	complemented
81	C₂×C₃	—	19	1	no	—
82	C₂×C₃	—	931	1	no	—
83	C₂×C₃	—	931	1	no	—
84	C₂²	—	931	1	no	Sylow
85	C₃	—	19	1	no	—
86	C₂	—	19	1	no	—
87	C₂	—	49	1	no	—
88	C₂	—	931	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₉	C₂²×C₉
prime radical	C₇⋊D₇×D₁₉⋊C₃	C₃
cosocle	C₇²×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇⋊D₇×#4296	C₂	semidirect
2. #4296⋊(C₇⋊D₇)	C₂	semidirect
3. C₇²×AGL(1,𝔽₁₉)	C₂	semidirect
5. C₇²×#4296	C₂²	semidirect
10. D₁₉×C₇⋊D₇	C₉	semidirect
14. C₇×AGL(1,𝔽₁₉)	D₇	semidirect
15. C₇⋊D₁₃₃	C₂×C₉	semidirect
16. C₁₉×C₇⋊D₇	C₂×C₉	semidirect
17. C₇²×D₁₉	C₂×C₉	semidirect
20. C₇×#4296	C₂×D₇	semidirect
21. C₇²×C₁₉	C₂²×C₉	semidirect
35. AGL(1,𝔽₁₉)	C₇⋊D₇	direct (N × H)
40. C₇×D₁₉	C₉×D₇	semidirect
45. #4296	C₂×C₇⋊D₇	semidirect
47. C₇×C₁₉	C₂×C₉×D₇	semidirect
56. C₇⋊D₇	AGL(1,𝔽₁₉)	direct (N × H)
61. C₇²	C₂×AGL(1,𝔽₁₉)	semidirect
67. D₁₉	C₉×C₇⋊D₇	semidirect
71. C₁₉	C₂×C₉×C₇⋊D₇	semidirect
80. C₇	D₇×AGL(1,𝔽₁₉)	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊D₇×#4296	2
#4296⋊(C₇⋊D₇)	2
C₇²×AGL(1,𝔽₁₉)	2
C₇⋊D₇×D₁₉⋊C₃	3
D₇×AGL(1,𝔽₁₉)	7
C₂×C₉×C₇⋊D₇	19

Subgroups — C7⋊D7×AGL(1,𝔽19) #45692097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊D₇×AGL(1,𝔽₁₉) #45692097