Subgroups — C₉×D₁₉×C₇⋊D₇ #45691662

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₇⋊D₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₉×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic
5	C₇²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇⋊D₁₃₃	C₂×C₃	1	1	yes	characteristic
7	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇²×D₁₉	C₂×C₃	1	1	yes	characteristic
9	C₉×D₇×D₁₉	—	7	8	no	maximal
10	D₁₉×C₇⋊D₇	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
12	C₉×D₁₃₃	—	7	8	no	—
13	C₉×D₇×C₁₉	—	7	8	no	—
14	C₇×C₉×D₁₉	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	C₃×D₇×D₁₉	—	7	8	no	—
20	C₇×C₉×C₁₉	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	D₁₉	1	1	yes	characteristic, direct product factor
25	C₃×D₁₃₃	—	7	8	no	—
26	C₃×D₇×C₁₉	—	7	8	no	—
27	C₃×C₇×D₁₉	C₃×D₇	1	8	yes	—
28	C₂×C₉×D₁₉	—	49	1	no	Hall
29	C₂×C₃×C₇⋊D₇	—	19	1	no	—
30	D₇×D₁₉	—	7	8	no	—
31	C₇²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₉	C₂×C₃×D₇	1	8	yes	—
33	C₂×C₉×C₁₉	—	49	1	no	—
34	C₉×D₁₉	—	49	1	no	—
35	C₉×D₁₉	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	C₃×D₁₉	1	1	yes	characteristic
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×C₃×D₁₉	—	49	1	no	—
44	C₂×C₇⋊D₇	—	19	1	no	Hall
45	C₉×C₁₉	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
46	C₃×C₇²	C₂×C₃×D₁₉	1	1	yes	characteristic
47	C₇×C₁₉	C₂×C₉×D₇	1	8	yes	complemented
48	C₂×C₇×C₉	—	19	8	no	—
49	C₉×D₇	—	7	8	no	—
50	C₉×D₇	—	133	8	no	—
51	C₂×C₃×C₁₉	—	49	1	no	—
52	C₃×D₁₉	—	49	1	no	—
53	C₃×D₁₉	C₃×C₇⋊D₇	1	1	yes	characteristic
54	C₂×C₇²	—	19	1	no	—
55	C₇⋊D₇	—	19	1	no	—
56	C₇⋊D₇	C₉×D₁₉	1	1	yes	characteristic, direct product factor
57	C₂×C₃×D₇	—	133	8	no	—
58	C₂×D₁₉	—	49	1	no	Hall
59	C₇×C₉	D₇×D₁₉	1	8	yes	complemented
60	C₃×C₁₉	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic
61	C₇²	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₃×C₇	—	19	8	no	—
63	C₃×D₇	—	7	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, direct product factor
68	C₂²×C₉	—	931	1	no	Hall
69	C₂×D₇	—	133	8	no	—
70	C₃×C₇	C₃×D₇×D₁₉	1	8	yes	—
71	C₁₉	C₂×C₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₉	—	19	1	no	—
73	C₂×C₉	—	49	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	D₁₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
80	C₇	C₉×D₇×D₁₉	1	8	yes	complemented
81	C₂×C₃	—	19	1	no	—
82	C₂×C₃	—	49	1	no	—
83	C₂×C₃	—	931	1	no	—
84	C₂²	—	931	1	no	Sylow
85	C₃	C₃×D₁₉×C₇⋊D₇	1	1	yes	characteristic
86	C₂	—	19	1	no	—
87	C₂	—	49	1	no	—
88	C₂	—	931	1	no	—

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

Complements

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

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

Maximal subgroups

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

subgroup	index
C₉×C₇⋊D₁₃₃	2
C₉×C₁₉×C₇⋊D₇	2
C₇²×C₉×D₁₉	2
C₃×D₁₉×C₇⋊D₇	3
C₉×D₇×D₁₉	7
C₂×C₉×C₇⋊D₇	19

Subgroups — C9×D19×C7⋊D7 #45691662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₁₉×C₇⋊D₇ #45691662