Group #45691968 — subgroups

Subgroups — C₃×C₇×C₁₉×Dic₂₁ #45691968

Order 33516.

184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₉×Dic₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×C₁₉×Dic₇	—	3	1	no	maximal
4	C₃²×C₇²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇²×C₁₉	—	2	1	no	—
6	C₂×C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₉×Dic₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor
9	C₃×C₇×Dic₃×C₁₉	—	7	1	no	maximal
10	C₇×C₁₉×Dic₇	—	3	1	no	Hall
11	C₃×C₇²×C₁₉	—	2	1	no	—
12	C₃×C₇²×C₁₉	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
14	C₂×C₃²×C₇×C₁₉	—	2	3	no	—
15	C₂×C₃²×C₇×C₁₉	D₇	1	1	yes	characteristic
16	C₂×C₃²×C₇×C₁₉	C₂×C₇	1	1	yes	characteristic
17	C₂×C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic
18	C₃×C₇×Dic₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃×C₄×C₇×C₁₉	—	21	1	no	—
20	C₁₉×Dic₂₁	C₃×C₇	1	1	yes	characteristic, direct product factor
21	C₇×Dic₃×C₁₉	—	7	1	no	—
22	C₃×C₁₉×Dic₇	—	3	1	no	—
23	C₃²×C₇×C₁₉	—	2	3	no	—
24	C₃²×C₇×C₁₉	Dic₇	1	1	yes	characteristic, complemented
25	C₃²×C₇×C₁₉	C₄×C₇	1	1	yes	characteristic, complemented
26	C₇²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃²×C₇²	C₂×C₁₉	1	1	yes	characteristic
28	C₂×C₃×C₇×C₁₉	—	2	6	no	—
29	C₂×C₃×C₇×C₁₉	—	2	1	no	—
30	C₂×C₃×C₇×C₁₉	—	2	1	no	—
31	C₂×C₃×C₇×C₁₉	—	2	3	no	—
32	C₂×C₃×C₇×C₁₉	—	2	3	no	—
33	C₂×C₃×C₇×C₁₉	D₃×C₇	1	1	yes	characteristic
34	C₂×C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
35	C₂×C₃×C₇×C₁₉	D₂₁	1	1	yes	characteristic
36	C₂×C₃×C₇×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic
37	C₃×Dic₃×C₁₉	—	7	1	no	Hall
38	C₇×Dic₂₁	C₃×C₁₉	1	1	yes	characteristic, direct product factor
39	C₃×C₇×Dic₇	—	3	1	no	—
40	C₄×C₇×C₁₉	—	21	1	no	—
41	C₁₉×Dic₇	—	3	1	no	—
42	C₃²×C₇²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₃×C₇×C₁₉	—	2	6	no	—
44	C₃×C₇×C₁₉	—	2	3	no	—
45	C₃×C₇×C₁₉	—	2	3	no	—
46	C₃×C₇×C₁₉	—	2	1	no	—
47	C₃×C₇×C₁₉	—	2	1	no	—
48	C₃×C₇×C₁₉	C₇×Dic₃	1	1	yes	characteristic, complemented
49	C₃×C₇×C₁₉	C₃×Dic₇	1	1	yes	characteristic, complemented
50	C₃×C₇×C₁₉	Dic₂₁	1	1	yes	characteristic, direct product factor
51	C₃×C₇×C₁₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented
52	C₂×C₃²×C₁₉	C₇×D₇	1	1	yes	characteristic
53	C₂×C₃×C₇²	—	2	1	no	—
54	C₂×C₃×C₇²	D₃×C₁₉	1	1	yes	characteristic
55	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
56	C₂×C₇×C₁₉	—	2	3	no	—
57	C₂×C₇×C₁₉	C₃×D₃×C₇	1	1	yes	characteristic
58	C₂×C₇×C₁₉	C₃×D₂₁	1	1	yes	characteristic
59	C₃×Dic₂₁	C₇×C₁₉	1	1	yes	characteristic, direct product factor
60	C₃×C₇×Dic₃	—	7	1	no	—
61	C₃×C₄×C₁₉	—	21	1	no	—
62	Dic₃×C₁₉	—	7	1	no	—
63	C₇×Dic₇	—	3	1	no	Hall
64	C₃²×C₁₉	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
65	C₃×C₇²	—	2	1	no	—
66	C₃×C₇²	Dic₃×C₁₉	1	1	yes	characteristic, complemented
67	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
68	C₇×C₁₉	—	2	3	no	—
69	C₇×C₁₉	C₃×C₇×Dic₃	1	1	yes	characteristic, complemented
70	C₇×C₁₉	C₃×Dic₂₁	1	1	yes	characteristic, direct product factor
71	C₂×C₃²×C₇	—	2	3	no	—
72	C₂×C₃²×C₇	D₇×C₁₉	1	1	yes	characteristic
73	C₂×C₃²×C₇	C₂×C₇×C₁₉	1	1	yes	characteristic
74	C₂×C₃×C₁₉	—	2	1	no	—
75	C₂×C₃×C₁₉	C₃×C₇×D₇	1	1	yes	characteristic
76	C₂×C₃×C₁₉	C₇×D₂₁	1	1	yes	characteristic
77	C₂×C₇²	C₃×D₃×C₁₉	1	1	yes	characteristic
78	C₃×C₄×C₇	—	21	1	no	—
79	Dic₂₁	C₃×C₇×C₁₉	1	1	yes	characteristic, direct product factor
80	C₃×Dic₇	—	3	1	no	—
81	C₇×Dic₃	—	7	1	no	—
82	C₄×C₁₉	—	21	1	no	Hall
83	C₃²×C₇	—	2	3	no	—
84	C₃²×C₇	C₁₉×Dic₇	1	1	yes	characteristic, complemented
85	C₃²×C₇	C₄×C₇×C₁₉	1	1	yes	characteristic, complemented
86	C₃×C₁₉	—	2	1	no	—
87	C₃×C₁₉	C₃×C₇×Dic₇	1	1	yes	characteristic, complemented
88	C₃×C₁₉	C₇×Dic₂₁	1	1	yes	characteristic, direct product factor
89	C₇²	C₃×Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
90	C₂×C₃×C₇	—	2	6	no	—
91	C₂×C₃×C₇	—	2	1	no	—
92	C₂×C₃×C₇	—	2	1	no	—
93	C₂×C₃×C₇	—	2	3	no	—
94	C₂×C₃×C₇	—	2	3	no	—
95	C₂×C₃×C₇	C₃×D₇×C₁₉	1	1	yes	characteristic
96	C₂×C₃×C₇	D₃×C₇×C₁₉	1	1	yes	characteristic
97	C₂×C₃×C₇	C₁₉×D₂₁	1	1	yes	characteristic
98	C₂×C₃×C₇	C₂×C₃×C₇×C₁₉	1	1	yes	characteristic
99	C₂×C₁₉	C₃×C₇×D₂₁	1	1	yes	characteristic
100	C₃×Dic₃	—	7	1	no	Hall
101	C₄×C₇	—	21	1	no	—
102	Dic₇	—	3	1	no	—
103	C₃×C₇	—	2	6	no	—
104	C₃×C₇	—	2	1	no	—
105	C₃×C₇	—	2	1	no	—
106	C₃×C₇	—	2	3	no	—
107	C₃×C₇	—	2	3	no	—
108	C₃×C₇	C₃×C₁₉×Dic₇	1	1	yes	characteristic, complemented
109	C₃×C₇	C₇×Dic₃×C₁₉	1	1	yes	characteristic, complemented
110	C₃×C₇	C₁₉×Dic₂₁	1	1	yes	characteristic, direct product factor
111	C₃×C₇	C₃×C₄×C₇×C₁₉	1	1	yes	characteristic, complemented
112	C₁₉	C₃×C₇×Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
113	C₂×C₃²	C₇×D₇×C₁₉	1	1	yes	characteristic
114	C₂×C₇	—	2	3	no	—
115	C₂×C₇	C₃×D₃×C₇×C₁₉	1	1	yes	characteristic
116	C₂×C₇	C₃×C₁₉×D₂₁	1	1	yes	characteristic
117	C₃×C₄	—	21	1	no	—
118	Dic₃	—	7	1	no	—
119	C₃²	C₇×C₁₉×Dic₇	1	1	yes	characteristic, complemented, Sylow
120	C₇	—	2	3	no	—
121	C₇	C₃×C₇×Dic₃×C₁₉	1	1	yes	characteristic, complemented
122	C₇	C₃×C₁₉×Dic₂₁	1	1	yes	characteristic, direct product factor
123	C₂×C₃	—	2	1	no	—
124	C₂×C₃	C₃×C₇×D₇×C₁₉	1	1	yes	characteristic
125	C₂×C₃	C₇×C₁₉×D₂₁	1	1	yes	characteristic
126	C₄	—	21	1	no	Sylow
127	C₃	—	2	1	no	—
128	C₃	C₃×C₇×C₁₉×Dic₇	1	1	yes	characteristic, complemented
129	C₃	C₇×C₁₉×Dic₂₁	1	1	yes	characteristic, direct product factor
130	C₂	C₃×C₇×C₁₉×D₂₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃²×C₇²×C₁₉

C₂

yes

maximal, characteristic

C₇×C₁₉×Dic₂₁

C₃

yes

maximal, characteristic, direct product factor

C₃×C₇×C₁₉×Dic₇

—

maximal

C₃²×C₇²×C₁₉

C₄

yes

characteristic, complemented, Hall

C₂×C₃×C₇²×C₁₉

—

C₂×C₃×C₇²×C₁₉

D₃

yes

characteristic

C₂×C₃×C₇²×C₁₉

C₂×C₃

yes

characteristic

C₃×C₁₉×Dic₂₁

C₇

yes

maximal, characteristic, direct product factor

C₃×C₇×Dic₃×C₁₉

—

maximal

C₇×C₁₉×Dic₇

—

Hall

C₃×C₇²×C₁₉

—

C₃×C₇²×C₁₉

Dic₃

yes

characteristic, complemented

C₃×C₇²×C₁₉

C₃×C₄

yes

characteristic, complemented

C₂×C₃²×C₇×C₁₉

—

C₂×C₃²×C₇×C₁₉

D₇

yes

characteristic

C₂×C₃²×C₇×C₁₉

C₂×C₇

yes

characteristic

C₂×C₇²×C₁₉

C₃×D₃

yes

characteristic

C₃×C₇×Dic₂₁

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃×C₄×C₇×C₁₉

—

C₁₉×Dic₂₁

C₃×C₇

yes

characteristic, direct product factor

C₇×Dic₃×C₁₉

—

C₃×C₁₉×Dic₇

—

C₃²×C₇×C₁₉

—

C₃²×C₇×C₁₉

Dic₇

yes

characteristic, complemented

C₃²×C₇×C₁₉

C₄×C₇

yes

characteristic, complemented

C₇²×C₁₉

C₃×Dic₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₇²

C₂×C₁₉

yes

characteristic

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

—

C₂×C₃×C₇×C₁₉

D₃×C₇

yes

characteristic

C₂×C₃×C₇×C₁₉

C₃×D₇

yes

characteristic

C₂×C₃×C₇×C₁₉

D₂₁

yes

characteristic

C₂×C₃×C₇×C₁₉

C₂×C₃×C₇

yes

characteristic

C₃×Dic₃×C₁₉

—

Hall

C₇×Dic₂₁

C₃×C₁₉

yes

characteristic, direct product factor

C₃×C₇×Dic₇

—

C₄×C₇×C₁₉

—

C₁₉×Dic₇

—

C₃²×C₇²

C₄×C₁₉

yes

characteristic, complemented, Hall

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

—

C₃×C₇×C₁₉

C₇×Dic₃

yes

characteristic, complemented

C₃×C₇×C₁₉

C₃×Dic₇

yes

characteristic, complemented

C₃×C₇×C₁₉

Dic₂₁

yes

characteristic, direct product factor

C₃×C₇×C₁₉

C₃×C₄×C₇

yes

characteristic, complemented

C₂×C₃²×C₁₉

C₇×D₇

yes

characteristic

C₂×C₃×C₇²

—

C₂×C₃×C₇²

D₃×C₁₉

yes

characteristic

C₂×C₃×C₇²

C₂×C₃×C₁₉

yes

characteristic

C₂×C₇×C₁₉

—

C₂×C₇×C₁₉

C₃×D₃×C₇

yes

characteristic

C₂×C₇×C₁₉

C₃×D₂₁

yes

characteristic

C₃×Dic₂₁

C₇×C₁₉

yes

characteristic, direct product factor

C₃×C₇×Dic₃

—

C₃×C₄×C₁₉

—

Dic₃×C₁₉

—

C₇×Dic₇

—

Hall

C₃²×C₁₉

C₇×Dic₇

yes

characteristic, complemented, Hall

C₃×C₇²

—

C₃×C₇²

Dic₃×C₁₉

yes

characteristic, complemented

C₃×C₇²

C₃×C₄×C₁₉

yes

characteristic, complemented

C₇×C₁₉

—

C₇×C₁₉

C₃×C₇×Dic₃

yes

characteristic, complemented

C₇×C₁₉

C₃×Dic₂₁

yes

characteristic, direct product factor

C₂×C₃²×C₇

—

C₂×C₃²×C₇

D₇×C₁₉

yes

characteristic

C₂×C₃²×C₇

C₂×C₇×C₁₉

yes

characteristic

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₃×C₇×D₇

yes

characteristic

C₂×C₃×C₁₉

C₇×D₂₁

yes

characteristic

C₂×C₇²

C₃×D₃×C₁₉

yes

characteristic

C₃×C₄×C₇

—

Dic₂₁

C₃×C₇×C₁₉

yes

characteristic, direct product factor

C₃×Dic₇

—

C₇×Dic₃

—

C₄×C₁₉

—

Hall

C₃²×C₇

—

C₃²×C₇

C₁₉×Dic₇

yes

characteristic, complemented

C₃²×C₇

C₄×C₇×C₁₉

yes

characteristic, complemented

C₃×C₁₉

—

C₃×C₁₉

C₃×C₇×Dic₇

yes

characteristic, complemented

C₃×C₁₉

C₇×Dic₂₁

yes

characteristic, direct product factor

C₇²

C₃×Dic₃×C₁₉

yes

characteristic, complemented, Sylow

C₂×C₃×C₇

—

C₂×C₃×C₇

—

C₂×C₃×C₇

—

C₂×C₃×C₇

—

C₂×C₃×C₇

—

C₂×C₃×C₇

C₃×D₇×C₁₉

yes

characteristic

C₂×C₃×C₇

D₃×C₇×C₁₉

yes

characteristic

C₂×C₃×C₇

C₁₉×D₂₁

yes

characteristic

C₂×C₃×C₇

C₂×C₃×C₇×C₁₉

yes

characteristic

C₂×C₁₉

C₃×C₇×D₂₁

yes

characteristic

100

C₃×Dic₃

—

Hall

101

C₄×C₇

—

102

Dic₇

—

103

C₃×C₇

—

104

C₃×C₇

—

105

C₃×C₇

—

106

C₃×C₇

—

107

C₃×C₇

—

108

C₃×C₇

C₃×C₁₉×Dic₇

yes

characteristic, complemented

109

C₃×C₇

C₇×Dic₃×C₁₉

yes

characteristic, complemented

110

C₃×C₇

C₁₉×Dic₂₁

yes

characteristic, direct product factor

111

C₃×C₇

C₃×C₄×C₇×C₁₉

yes

characteristic, complemented

112

C₁₉

C₃×C₇×Dic₂₁

yes

characteristic, direct product factor, Sylow

113

C₂×C₃²

C₇×D₇×C₁₉

yes

characteristic

114

C₂×C₇

—

115

C₂×C₇

C₃×D₃×C₇×C₁₉

yes

characteristic

116

C₂×C₇

C₃×C₁₉×D₂₁

yes

characteristic

117

C₃×C₄

—

118

Dic₃

—

119

C₃²

C₇×C₁₉×Dic₇

yes

characteristic, complemented, Sylow

120

C₇

—

121

C₇

C₃×C₇×Dic₃×C₁₉

yes

characteristic, complemented

122

C₇

C₃×C₁₉×Dic₂₁

yes

characteristic, direct product factor

123

C₂×C₃

—

124

C₂×C₃

C₃×C₇×D₇×C₁₉

yes

characteristic

125

C₂×C₃

C₇×C₁₉×D₂₁

yes

characteristic

126

C₄

—

Sylow

127

C₃

—

128

C₃

C₃×C₇×C₁₉×Dic₇

yes

characteristic, complemented

129

C₃

C₇×C₁₉×Dic₂₁

yes

characteristic, direct product factor

130

C₂

C₃×C₇×C₁₉×D₂₁

yes

characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₉	D₂₁
commutator, hypocenter	C₃×C₇	C₃×C₄×C₇×C₁₉
Frattini	C₂	C₃×C₇×C₁₉×D₂₁
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₃×C₇	C₂×C₃×C₇×C₁₉
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃×C₇×C₁₉

subgroup

G/H

center, hypercenter

C₂×C₃×C₇×C₁₉

D₂₁

commutator, hypocenter

C₃×C₇

C₃×C₄×C₇×C₁₉

Frattini

C₂

C₃×C₇×C₁₉×D₂₁

Fitting, socle, prime radical

C₂×C₃²×C₇²×C₁₉

C₂

cosocle

C₂×C₃×C₇

C₂×C₃×C₇×C₁₉

LCS

G ▷ C₃×C₇

UCS

C₁ ◁ C₂×C₃×C₇×C₁₉

N	H ≅ G/N	type
2. C₇×C₁₉×Dic₂₁	C₃	direct (N × H)
4. C₃²×C₇²×C₁₉	C₄	semidirect
8. C₃×C₁₉×Dic₂₁	C₇	direct (N × H)
12. C₃×C₇²×C₁₉	Dic₃	semidirect
13. C₃×C₇²×C₁₉	C₃×C₄	semidirect
18. C₃×C₇×Dic₂₁	C₁₉	direct (N × H)
20. C₁₉×Dic₂₁	C₃×C₇	direct (N × H)
24. C₃²×C₇×C₁₉	Dic₇	semidirect
25. C₃²×C₇×C₁₉	C₄×C₇	semidirect
26. C₇²×C₁₉	C₃×Dic₃	semidirect
38. C₇×Dic₂₁	C₃×C₁₉	direct (N × H)
42. C₃²×C₇²	C₄×C₁₉	semidirect
48. C₃×C₇×C₁₉	C₇×Dic₃	semidirect
49. C₃×C₇×C₁₉	C₃×Dic₇	semidirect
50. C₃×C₇×C₁₉	Dic₂₁	direct (N × H)
51. C₃×C₇×C₁₉	C₃×C₄×C₇	semidirect
59. C₃×Dic₂₁	C₇×C₁₉	direct (N × H)
64. C₃²×C₁₉	C₇×Dic₇	semidirect
66. C₃×C₇²	Dic₃×C₁₉	semidirect
67. C₃×C₇²	C₃×C₄×C₁₉	semidirect
69. C₇×C₁₉	C₃×C₇×Dic₃	semidirect
70. C₇×C₁₉	C₃×Dic₂₁	direct (N × H)
79. Dic₂₁	C₃×C₇×C₁₉	direct (N × H)
84. C₃²×C₇	C₁₉×Dic₇	semidirect
85. C₃²×C₇	C₄×C₇×C₁₉	semidirect
87. C₃×C₁₉	C₃×C₇×Dic₇	semidirect
88. C₃×C₁₉	C₇×Dic₂₁	direct (N × H)
89. C₇²	C₃×Dic₃×C₁₉	semidirect
108. C₃×C₇	C₃×C₁₉×Dic₇	semidirect
109. C₃×C₇	C₇×Dic₃×C₁₉	semidirect
110. C₃×C₇	C₁₉×Dic₂₁	direct (N × H)
111. C₃×C₇	C₃×C₄×C₇×C₁₉	semidirect
112. C₁₉	C₃×C₇×Dic₂₁	direct (N × H)
119. C₃²	C₇×C₁₉×Dic₇	semidirect
121. C₇	C₃×C₇×Dic₃×C₁₉	semidirect
122. C₇	C₃×C₁₉×Dic₂₁	direct (N × H)
128. C₃	C₃×C₇×C₁₉×Dic₇	semidirect
129. C₃	C₇×C₁₉×Dic₂₁	direct (N × H)

H ≅ G/N

type

2. C₇×C₁₉×Dic₂₁

C₃

direct (N × H)

4. C₃²×C₇²×C₁₉

C₄

semidirect

8. C₃×C₁₉×Dic₂₁

C₇

direct (N × H)

12. C₃×C₇²×C₁₉

Dic₃

semidirect

13. C₃×C₇²×C₁₉

C₃×C₄

semidirect

18. C₃×C₇×Dic₂₁

C₁₉

direct (N × H)

20. C₁₉×Dic₂₁

C₃×C₇

direct (N × H)

24. C₃²×C₇×C₁₉

Dic₇

semidirect

25. C₃²×C₇×C₁₉

C₄×C₇

semidirect

26. C₇²×C₁₉

C₃×Dic₃

semidirect

38. C₇×Dic₂₁

C₃×C₁₉

direct (N × H)

42. C₃²×C₇²

C₄×C₁₉

semidirect

48. C₃×C₇×C₁₉

C₇×Dic₃

semidirect

49. C₃×C₇×C₁₉

C₃×Dic₇

semidirect

50. C₃×C₇×C₁₉

Dic₂₁

direct (N × H)

51. C₃×C₇×C₁₉

C₃×C₄×C₇

semidirect

59. C₃×Dic₂₁

C₇×C₁₉

direct (N × H)

64. C₃²×C₁₉

C₇×Dic₇

semidirect

66. C₃×C₇²

Dic₃×C₁₉

semidirect

67. C₃×C₇²

C₃×C₄×C₁₉

semidirect

69. C₇×C₁₉

C₃×C₇×Dic₃

semidirect

70. C₇×C₁₉

C₃×Dic₂₁

direct (N × H)

79. Dic₂₁

C₃×C₇×C₁₉

direct (N × H)

84. C₃²×C₇

C₁₉×Dic₇

semidirect

85. C₃²×C₇

C₄×C₇×C₁₉

semidirect

87. C₃×C₁₉

C₃×C₇×Dic₇

semidirect

88. C₃×C₁₉

C₇×Dic₂₁

direct (N × H)

89. C₇²

C₃×Dic₃×C₁₉

semidirect

108. C₃×C₇

C₃×C₁₉×Dic₇

semidirect

109. C₃×C₇

C₇×Dic₃×C₁₉

semidirect

110. C₃×C₇

C₁₉×Dic₂₁

direct (N × H)

111. C₃×C₇

C₃×C₄×C₇×C₁₉

semidirect

112. C₁₉

C₃×C₇×Dic₂₁

direct (N × H)

119. C₃²

C₇×C₁₉×Dic₇

semidirect

121. C₇

C₃×C₇×Dic₃×C₁₉

semidirect

122. C₇

C₃×C₁₉×Dic₂₁

direct (N × H)

128. C₃

C₃×C₇×C₁₉×Dic₇

semidirect

129. C₃

C₇×C₁₉×Dic₂₁

direct (N × H)

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

subgroup	index
C₂×C₃²×C₇²×C₁₉	2
C₇×C₁₉×Dic₂₁	3
C₃×C₇×C₁₉×Dic₇	3
C₃×C₁₉×Dic₂₁	7
C₃×C₇×Dic₃×C₁₉	7
C₃×C₇×Dic₂₁	19

subgroup

index

C₂×C₃²×C₇²×C₁₉

C₇×C₁₉×Dic₂₁

C₃×C₇×C₁₉×Dic₇

C₃×C₁₉×Dic₂₁

C₃×C₇×Dic₃×C₁₉

C₃×C₇×Dic₂₁

Subgroups — C₃×C₇×C₁₉×Dic₂₁ #45691968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×C7×C19×Dic21 #45691968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₉×Dic₂₁ #45691968