Group #14518463 — subgroups

Subgroups — C₂²×D₉×3₋¹⁺² #14518463

Order 1944.

509 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 509 conjugacy classes of subgroups — too many to draw. Only its 182 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	C₂²×C₉×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₉×3₋¹⁺²	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₃×3₋¹⁺²	—	3	1	no	maximal
4	C₂²×C₃²×D₉	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₉×D₉	C₃	1	3	yes	maximal, complemented
6	C₂×C₉×3₋¹⁺²	C₂²	1	3	yes	complemented
7	D₉×3₋¹⁺²	C₂²	1	4	yes	direct product factor
8	C₂²×C₃×3₋¹⁺²	D₃	1	1	yes	characteristic
9	C₂²×C₃²×C₉	C₂×C₃	1	1	yes	characteristic
10	C₂×D₃×3₋¹⁺²	—	3	6	no	—
11	C₂×C₃²×D₉	C₂×C₃	1	6	yes	—
12	C₂²×C₉⋊C₉	—	2	3	no	—
13	C₂²×C₃²⋊C₉	—	2	1	no	—
14	C₂²×C₉²	C₂×C₃	1	3	yes	complemented
15	C₂×C₉×D₉	C₂×C₃	1	18	yes	complemented
16	C₉×3₋¹⁺²	C₂³	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₃²×D₃	—	3	1	no	—
18	C₂³×3₋¹⁺²	—	9	1	no	—
19	C₂²×D₃×C₉	—	3	3	no	—
20	C₂²×C₃×D₉	—	3	1	no	—
21	C₂²×C₃×D₉	C₃²	1	1	yes	characteristic
22	C₂×C₃×3₋¹⁺²	C₂×D₃	1	3	yes	—
23	C₂×C₃²×C₉	C₂²×C₃	1	3	yes	—
24	D₃×3₋¹⁺²	—	3	4	no	—
25	C₃²×D₉	C₂²×C₃	1	4	yes	—
26	C₂×C₉⋊C₉	—	2	9	no	—
27	C₂×C₃²⋊C₉	—	2	3	no	—
28	C₂×C₉²	C₂²×C₃	1	9	yes	complemented
29	C₉×D₉	C₂²×C₃	1	12	yes	complemented
30	C₂²×C₃³	C₃×D₃	1	1	yes	characteristic
31	C₂×C₃²×D₃	—	3	6	no	—
32	C₂²×3₋¹⁺²	—	2	1	no	—
33	C₂²×3₋¹⁺²	—	2	3	no	—
34	C₂²×3₋¹⁺²	—	9	6	no	—
35	C₂²×3₋¹⁺²	D₉	1	1	yes	characteristic, direct product factor
36	C₂²×C₃×C₉	—	2	3	no	—
37	C₂²×C₃×C₉	—	2	1	no	—
38	C₂²×C₃×C₉	—	3	1	no	—
39	C₂²×C₃×C₉	—	6	1	no	—
40	C₂²×C₃×C₉	C₃×D₃	1	3	yes	—
41	C₂²×C₃×C₉	C₂×C₃²	1	1	yes	characteristic
42	C₂×D₃×C₉	—	3	18	no	—
43	C₂×C₃×D₉	—	3	6	no	—
44	C₂×C₃×D₉	C₂×C₃²	1	6	yes	—
45	C₃×3₋¹⁺²	C₂²×D₃	1	1	yes	characteristic
46	C₃²×C₉	C₂³×C₃	1	1	yes	characteristic
47	C₉⋊C₉	—	2	3	no	—
48	C₃²⋊C₉	—	2	1	no	—
49	C₉²	C₂³×C₃	1	3	yes	complemented
50	C₂³×C₃²	—	9	1	no	—
51	C₂²×C₃×D₃	—	3	1	no	—
52	C₂²×C₃×D₃	—	9	1	no	—
53	C₂³×C₉	—	9	3	no	—
54	C₂²×D₉	3₋¹⁺²	1	1	yes	characteristic, direct product factor
55	C₂×C₃³	C₂×C₃×D₃	1	3	yes	—
56	C₃²×D₃	—	3	4	no	—
57	C₂×3₋¹⁺²	—	2	3	no	—
58	C₂×3₋¹⁺²	—	2	9	no	—
59	C₂×3₋¹⁺²	—	9	4	no	—
60	C₂×3₋¹⁺²	C₂×D₉	1	3	yes	direct product factor
61	C₂×C₃×C₉	—	2	9	no	—
62	C₂×C₃×C₉	—	2	3	no	—
63	C₂×C₃×C₉	—	3	3	no	—
64	C₂×C₃×C₉	—	6	3	no	—
65	C₂×C₃×C₉	C₂×C₃×D₃	1	9	yes	—
66	C₂×C₃×C₉	C₂²×C₃²	1	3	yes	—
67	D₃×C₉	—	3	12	no	—
68	C₃×D₉	—	3	4	no	—
69	C₃×D₉	C₂²×C₃²	1	4	yes	—
70	C₂²×C₃²	—	2	1	no	—
71	C₂²×C₃²	—	3	1	no	—
72	C₂²×C₃²	—	6	1	no	—
73	C₂²×C₃²	—	9	6	no	—
74	C₂²×C₃²	C₃×D₉	1	1	yes	characteristic
75	C₂²×C₃²	C₃²×D₃	1	1	yes	characteristic
76	C₂×C₃×D₃	—	3	6	no	—
77	C₂×C₃×D₃	—	9	6	no	—
78	C₂²×C₉	—	2	3	no	—
79	C₂²×C₉	—	2	1	no	—
80	C₂²×C₉	—	6	3	no	—
81	C₂²×C₉	—	6	1	no	—
82	C₂²×C₉	—	9	18	no	—
83	C₂²×C₉	C₃×D₉	1	3	yes	complemented
84	C₂²×C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
85	C₂×D₉	C₂×3₋¹⁺²	1	6	yes	direct product factor
86	C₃³	C₂²×C₃×D₃	1	1	yes	characteristic
87	3₋¹⁺²	—	2	1	no	—
88	3₋¹⁺²	—	2	3	no	—
89	3₋¹⁺²	C₂²×D₉	1	1	yes	characteristic, direct product factor
90	C₃×C₉	—	2	3	no	—
91	C₃×C₉	—	2	1	no	—
92	C₃×C₉	—	3	1	no	—
93	C₃×C₉	—	6	1	no	—
94	C₃×C₉	C₂²×C₃×D₃	1	3	yes	—
95	C₃×C₉	C₂³×C₃²	1	1	yes	characteristic
96	C₂³×C₃	—	9	1	no	—
97	C₂³×C₃	—	27	1	no	—
98	C₂²×D₃	—	3	1	no	—
99	C₂×C₃²	—	2	3	no	—
100	C₂×C₃²	—	3	3	no	—
101	C₂×C₃²	—	6	3	no	—
102	C₂×C₃²	—	9	4	no	—
103	C₂×C₃²	C₂×C₃×D₉	1	3	yes	—
104	C₂×C₃²	C₂×C₃²×D₃	1	3	yes	—
105	C₃×D₃	—	3	4	no	—
106	C₃×D₃	—	9	4	no	—
107	C₂×C₉	—	2	9	no	—
108	C₂×C₉	—	2	3	no	—
109	C₂×C₉	—	6	9	no	—
110	C₂×C₉	—	6	3	no	—
111	C₂×C₉	—	9	12	no	—
112	C₂×C₉	C₂×C₃×D₉	1	9	yes	complemented
113	C₂×C₉	C₂²×3₋¹⁺²	1	3	yes	complemented
114	D₉	C₂²×3₋¹⁺²	1	4	yes	direct product factor
115	C₂²×C₃	—	2	1	no	—
116	C₂²×C₃	—	3	1	no	—
117	C₂²×C₃	—	6	1	no	—
118	C₂²×C₃	—	9	6	no	—
119	C₂²×C₃	—	27	6	no	—
120	C₂²×C₃	C₃²×D₉	1	1	yes	characteristic
121	C₂²×C₃	D₃×3₋¹⁺²	1	1	yes	characteristic
122	C₂×D₃	—	3	6	no	—
123	C₃²	—	2	1	no	—
124	C₃²	—	3	1	no	—
125	C₃²	—	6	1	no	—
126	C₃²	C₂²×C₃×D₉	1	1	yes	characteristic
127	C₃²	C₂²×C₃²×D₃	1	1	yes	characteristic
128	C₉	—	2	3	no	—
129	C₉	—	2	1	no	—
130	C₉	—	6	3	no	—
131	C₉	—	6	1	no	—
132	C₉	C₂²×C₃×D₉	1	3	yes	complemented
133	C₉	C₂³×3₋¹⁺²	1	1	yes	characteristic, complemented
134	C₂³	—	9	1	no	Sylow
135	C₂×C₃	—	2	3	no	—
136	C₂×C₃	—	3	3	no	—
137	C₂×C₃	—	6	3	no	—
138	C₂×C₃	—	9	4	no	—
139	C₂×C₃	—	27	4	no	—
140	C₂×C₃	C₂×C₃²×D₉	1	3	yes	—
141	C₂×C₃	C₂×D₃×3₋¹⁺²	1	3	yes	—
142	D₃	—	3	4	no	—
143	C₂²	—	9	6	no	—
144	C₂²	D₉×3₋¹⁺²	1	1	yes	characteristic, direct product factor
145	C₃	—	2	1	no	—
146	C₃	—	3	1	no	—
147	C₃	—	6	1	no	—
148	C₃	C₂²×C₃²×D₉	1	1	yes	characteristic
149	C₃	C₂²×D₃×3₋¹⁺²	1	1	yes	characteristic
150	C₂	—	9	4	no	—
151	C₂	C₂×D₉×3₋¹⁺²	1	3	yes	direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₉×3₋¹⁺²

C₂

yes

maximal, characteristic, complemented

C₂×D₉×3₋¹⁺²

C₂

yes

maximal, direct product factor

C₂²×D₃×3₋¹⁺²

—

maximal

C₂²×C₃²×D₉

C₃

yes

maximal, characteristic

C₂²×C₉×D₉

C₃

yes

maximal, complemented

C₂×C₉×3₋¹⁺²

C₂²

yes

complemented

D₉×3₋¹⁺²

C₂²

yes

direct product factor

C₂²×C₃×3₋¹⁺²

D₃

yes

characteristic

C₂²×C₃²×C₉

C₂×C₃

yes

characteristic

C₂×D₃×3₋¹⁺²

—

C₂×C₃²×D₉

C₂×C₃

yes

—

C₂²×C₉⋊C₉

—

C₂²×C₃²⋊C₉

—

C₂²×C₉²

C₂×C₃

yes

complemented

C₂×C₉×D₉

C₂×C₃

yes

complemented

C₉×3₋¹⁺²

C₂³

yes

characteristic, complemented, Sylow

C₂²×C₃²×D₃

—

C₂³×3₋¹⁺²

—

C₂²×D₃×C₉

—

C₂²×C₃×D₉

—

C₂²×C₃×D₉

C₃²

yes

characteristic

C₂×C₃×3₋¹⁺²

C₂×D₃

yes

—

C₂×C₃²×C₉

C₂²×C₃

yes

—

D₃×3₋¹⁺²

—

C₃²×D₉

C₂²×C₃

yes

—

C₂×C₉⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₉²

C₂²×C₃

yes

complemented

C₉×D₉

C₂²×C₃

yes

complemented

C₂²×C₃³

C₃×D₃

yes

characteristic

C₂×C₃²×D₃

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

D₉

yes

characteristic, direct product factor

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

C₃×D₃

yes

—

C₂²×C₃×C₉

C₂×C₃²

yes

characteristic

C₂×D₃×C₉

—

C₂×C₃×D₉

—

C₂×C₃×D₉

C₂×C₃²

yes

—

C₃×3₋¹⁺²

C₂²×D₃

yes

characteristic

C₃²×C₉

C₂³×C₃

yes

characteristic

C₉⋊C₉

—

C₃²⋊C₉

—

C₉²

C₂³×C₃

yes

complemented

C₂³×C₃²

—

C₂²×C₃×D₃

—

C₂²×C₃×D₃

—

C₂³×C₉

—

C₂²×D₉

3₋¹⁺²

yes

characteristic, direct product factor

C₂×C₃³

C₂×C₃×D₃

yes

—

C₃²×D₃

—

C₂×3₋¹⁺²

—

C₂×3₋¹⁺²

—

C₂×3₋¹⁺²

—

C₂×3₋¹⁺²

C₂×D₉

yes

direct product factor

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

C₂×C₃×D₃

yes

—

C₂×C₃×C₉

C₂²×C₃²

yes

—

D₃×C₉

—

C₃×D₉

—

C₃×D₉

C₂²×C₃²

yes

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

C₃×D₉

yes

characteristic

C₂²×C₃²

C₃²×D₃

yes

characteristic

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₃×D₉

yes

complemented

C₂²×C₉

C₂×3₋¹⁺²

yes

characteristic, complemented

C₂×D₉

C₂×3₋¹⁺²

yes

direct product factor

C₃³

C₂²×C₃×D₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

C₂²×D₉

yes

characteristic, direct product factor

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₂²×C₃×D₃

yes

—

C₃×C₉

C₂³×C₃²

yes

characteristic

C₂³×C₃

—

C₂³×C₃

—

C₂²×D₃

—

C₂×C₃²

—

100

C₂×C₃²

—

101

C₂×C₃²

—

102

C₂×C₃²

—

103

C₂×C₃²

C₂×C₃×D₉

yes

—

104

C₂×C₃²

C₂×C₃²×D₃

yes

—

105

C₃×D₃

—

106

C₃×D₃

—

107

C₂×C₉

—

108

C₂×C₉

—

109

C₂×C₉

—

110

C₂×C₉

—

111

C₂×C₉

—

112

C₂×C₉

C₂×C₃×D₉

yes

complemented

113

C₂×C₉

C₂²×3₋¹⁺²

yes

complemented

114

D₉

C₂²×3₋¹⁺²

yes

direct product factor

115

C₂²×C₃

—

116

C₂²×C₃

—

117

C₂²×C₃

—

118

C₂²×C₃

—

119

C₂²×C₃

—

120

C₂²×C₃

C₃²×D₉

yes

characteristic

121

C₂²×C₃

D₃×3₋¹⁺²

yes

characteristic

122

C₂×D₃

—

123

C₃²

—

124

C₃²

—

125

C₃²

—

126

C₃²

C₂²×C₃×D₉

yes

characteristic

127

C₃²

C₂²×C₃²×D₃

yes

characteristic

128

C₉

—

129

C₉

—

130

C₉

—

131

C₉

—

132

C₉

C₂²×C₃×D₉

yes

complemented

133

C₉

C₂³×3₋¹⁺²

yes

characteristic, complemented

134

C₂³

—

Sylow

135

C₂×C₃

—

136

C₂×C₃

—

137

C₂×C₃

—

138

C₂×C₃

—

139

C₂×C₃

—

140

C₂×C₃

C₂×C₃²×D₉

yes

—

141

C₂×C₃

C₂×D₃×3₋¹⁺²

yes

—

142

D₃

—

143

C₂²

—

144

C₂²

D₉×3₋¹⁺²

yes

characteristic, direct product factor

145

C₃

—

146

C₃

—

147

C₃

—

148

C₃

C₂²×C₃²×D₉

yes

characteristic

149

C₃

C₂²×D₃×3₋¹⁺²

yes

characteristic

150

C₂

—

151

C₂

C₂×D₉×3₋¹⁺²

yes

direct product factor

	subgroup	G/H
center	C₂²×C₃	C₃²×D₉
commutator, cosocle	C₃×C₉	C₂³×C₃²
Frattini	C₃²	C₂²×C₃²×D₃
Fitting	C₂²×C₉×3₋¹⁺²	C₂
socle	C₂²×C₃²	C₃²×D₃
prime radical	C₂²×C₃²×D₉	C₃
hypercenter	C₂²×3₋¹⁺²	D₉
hypocenter	C₉	C₂³×3₋¹⁺²
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×3₋¹⁺²

subgroup

G/H

center

C₂²×C₃

C₃²×D₉

commutator, cosocle

C₃×C₉

C₂³×C₃²

Frattini

C₃²

C₂²×C₃²×D₃

Fitting

C₂²×C₉×3₋¹⁺²

C₂

socle

C₂²×C₃²

C₃²×D₃

prime radical

C₂²×C₃²×D₉

C₃

hypercenter

C₂²×3₋¹⁺²

D₉

hypocenter

C₉

C₂³×3₋¹⁺²

LCS

G ▷ C₃×C₉ ▷ C₉

UCS

C₁ ◁ C₂²×C₃ ◁ C₂²×3₋¹⁺²

N	H ≅ G/N	type
1. C₂²×C₉×3₋¹⁺²	C₂	semidirect
2. C₂×D₉×3₋¹⁺²	C₂	direct (N × H)
5. C₂²×C₉×D₉	C₃	semidirect
6. C₂×C₉×3₋¹⁺²	C₂²	semidirect
7. D₉×3₋¹⁺²	C₂²	direct (N × H)
14. C₂²×C₉²	C₂×C₃	semidirect
15. C₂×C₉×D₉	C₂×C₃	semidirect
16. C₉×3₋¹⁺²	C₂³	semidirect
28. C₂×C₉²	C₂²×C₃	semidirect
29. C₉×D₉	C₂²×C₃	semidirect
35. C₂²×3₋¹⁺²	D₉	direct (N × H)
49. C₉²	C₂³×C₃	semidirect
54. C₂²×D₉	3₋¹⁺²	direct (N × H)
60. C₂×3₋¹⁺²	C₂×D₉	direct (N × H)
83. C₂²×C₉	C₃×D₉	semidirect
84. C₂²×C₉	C₂×3₋¹⁺²	semidirect
85. C₂×D₉	C₂×3₋¹⁺²	direct (N × H)
89. 3₋¹⁺²	C₂²×D₉	direct (N × H)
112. C₂×C₉	C₂×C₃×D₉	semidirect
113. C₂×C₉	C₂²×3₋¹⁺²	semidirect
114. D₉	C₂²×3₋¹⁺²	direct (N × H)
132. C₉	C₂²×C₃×D₉	semidirect
133. C₉	C₂³×3₋¹⁺²	semidirect
144. C₂²	D₉×3₋¹⁺²	direct (N × H)
151. C₂	C₂×D₉×3₋¹⁺²	direct (N × H)

H ≅ G/N

type

1. C₂²×C₉×3₋¹⁺²

C₂

semidirect

2. C₂×D₉×3₋¹⁺²

C₂

direct (N × H)

5. C₂²×C₉×D₉

C₃

semidirect

6. C₂×C₉×3₋¹⁺²

C₂²

semidirect

7. D₉×3₋¹⁺²

C₂²

direct (N × H)

14. C₂²×C₉²

C₂×C₃

semidirect

15. C₂×C₉×D₉

C₂×C₃

semidirect

16. C₉×3₋¹⁺²

C₂³

semidirect

28. C₂×C₉²

C₂²×C₃

semidirect

29. C₉×D₉

C₂²×C₃

semidirect

35. C₂²×3₋¹⁺²

D₉

direct (N × H)

49. C₉²

C₂³×C₃

semidirect

54. C₂²×D₉

3₋¹⁺²

direct (N × H)

60. C₂×3₋¹⁺²

C₂×D₉

direct (N × H)

83. C₂²×C₉

C₃×D₉

semidirect

84. C₂²×C₉

C₂×3₋¹⁺²

semidirect

85. C₂×D₉

C₂×3₋¹⁺²

direct (N × H)

89. 3₋¹⁺²

C₂²×D₉

direct (N × H)

112. C₂×C₉

C₂×C₃×D₉

semidirect

113. C₂×C₉

C₂²×3₋¹⁺²

semidirect

114. D₉

C₂²×3₋¹⁺²

direct (N × H)

132. C₉

C₂²×C₃×D₉

semidirect

133. C₉

C₂³×3₋¹⁺²

semidirect

144. C₂²

D₉×3₋¹⁺²

direct (N × H)

151. C₂

C₂×D₉×3₋¹⁺²

direct (N × H)

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

subgroup	index
C₂²×C₉×3₋¹⁺²	2
C₂×D₉×3₋¹⁺²	2
C₂²×D₃×3₋¹⁺²	3
C₂²×C₃²×D₉	3
C₂²×C₉×D₉	3

subgroup

index

C₂²×C₉×3₋¹⁺²

C₂×D₉×3₋¹⁺²

C₂²×D₃×3₋¹⁺²

C₂²×C₃²×D₉

C₂²×C₉×D₉

Subgroups — C₂²×D₉×3₋¹⁺² #14518463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C22×D9×3−1+2 #14518463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₉×3₋¹⁺² #14518463