Group #20304667 — subgroups

Subgroups — C₂₉×#9767 #20304667

Order 7424.

414 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 174 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×C₂₉×#498	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1848	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1549	C₂	1	2	yes	maximal
4	C₂₉×#1548	C₂	1	2	yes	maximal
5	C₂₉×#1450	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂₉×#498	—	2	1	no	—
8	C₂₉×#498	—	2	1	no	—
9	C₂₉×#498	C₄	1	4	yes	—
10	C₂₉×#431	C₂²	1	2	yes	—
11	C₂×C₂₉×#108	—	2	2	no	—
12	C₂×C₂₉×#106	—	2	2	no	—
13	C₂₉×#423	C₂²	1	1	yes	characteristic
14	C₂₉×#423	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#333	—	2	4	no	—
17	C₂₉×#332	—	2	4	no	—
18	C₂₉×#322	—	2	1	no	—
19	C₈²×C₂₉	—	2	1	no	—
20	C₂²×Q₈×C₂₉	—	2	2	no	—
21	C₂×M₁₆×C₂₉	—	2	1	no	—
22	C₂×M₁₆×C₂₉	—	2	1	no	—
23	C₂²×C₈×C₂₉	D₄	1	2	yes	—
24	C₂₉×C₄⋊Q₈	—	2	2	no	—
25	C₂₉×C₄⋊Q₈	—	2	2	no	—
26	C₂₉×C₄⋊Q₈	—	2	2	no	—
27	C₂₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
28	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
30	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
31	C₂₉×#108	—	4	4	no	—
32	C₂₉×#106	—	2	4	no	—
33	C₂₉×#106	—	2	4	no	—
34	C₂₉×C₄⋊C₈	—	2	2	no	—
35	C₂₉×C₄⋊C₈	—	2	2	no	—
36	C₂₉×C₄⋊C₈	D₄	1	4	yes	—
37	C₂₉×C₂²⋊C₈	—	2	2	no	—
38	C₄×C₈×C₂₉	—	2	2	no	—
39	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
42	C₂×Q₈×C₂₉	—	2	4	no	—
43	C₂×Q₈×C₂₉	—	4	2	no	—
44	C₂×Q₈×C₂₉	—	8	4	no	—
45	C₂²×C₄×C₂₉	—	4	2	no	—
46	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₂₉	#41	1	2	yes	—
48	M₁₆×C₂₉	—	4	2	no	—
49	M₁₆×C₂₉	—	4	2	no	—
50	C₂×C₈×C₂₉	—	2	4	no	—
51	C₂×C₈×C₂₉	—	4	1	no	—
52	C₂×C₈×C₂₉	—	4	1	no	—
53	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
54	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₂₉	SD₁₆	1	4	yes	—
56	C₂×C₈×C₂₉	Q₁₆	1	4	yes	—
57	C₄⋊C₄×C₂₉	—	2	4	no	—
58	C₄⋊C₄×C₂₉	—	2	4	no	—
59	C₄⋊C₄×C₂₉	—	4	2	no	—
60	C₄⋊C₄×C₂₉	—	4	2	no	—
61	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₂₉	C₂×D₄	1	2	yes	—
64	#9767	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂³×C₂₉	#124	1	1	yes	characteristic
66	Q₈×C₂₉	—	8	4	no	—
67	Q₈×C₂₉	—	8	4	no	—
68	C₂×C₄×C₂₉	—	2	4	no	—
69	C₂×C₄×C₂₉	—	4	4	no	—
70	C₂×C₄×C₂₉	—	8	4	no	—
71	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
73	C₂×C₄×C₂₉	#121	1	2	yes	—
74	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
75	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
76	C₂×C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
77	C₈×C₂₉	—	4	4	no	—
78	C₈×C₂₉	—	8	1	no	—
79	C₈×C₂₉	—	8	1	no	—
80	C₈×C₂₉	#103	1	4	yes	—
81	C₈×C₂₉	#103	1	4	yes	—
82	C₂×#498	C₂×C₂₉	1	1	yes	characteristic
83	#1848	C₂×C₂₉	1	1	yes	characteristic
84	#1549	C₂×C₂₉	1	2	yes	—
85	#1548	C₂×C₂₉	1	2	yes	—
86	#1450	C₂×C₂₉	1	1	yes	characteristic
87	C₂²×C₂₉	—	2	2	no	—
88	C₂²×C₂₉	#390	1	1	yes	characteristic
89	C₂²×C₂₉	#487	1	2	yes	—
90	C₄×C₂₉	—	2	2	no	—
91	C₄×C₂₉	—	8	4	no	—
92	C₄×C₂₉	C₂×#103	1	2	yes	—
93	C₄×C₂₉	#471	1	4	yes	—
94	C₄×C₂₉	#492	1	1	yes	characteristic
95	C₄×C₂₉	#494	1	1	yes	characteristic
96	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
97	#498	—	2	1	no	—
98	#498	—	2	1	no	—
99	#498	C₄×C₂₉	1	4	yes	—
100	#431	C₂²×C₂₉	1	2	yes	—
101	C₂×#108	—	2	2	no	—
102	C₂×#106	—	2	2	no	—
103	#423	C₂²×C₂₉	1	1	yes	characteristic
104	#423	C₂²×C₂₉	1	1	yes	characteristic
105	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
106	#333	—	2	4	no	—
107	#332	—	2	4	no	—
108	#322	—	2	1	no	—
109	C₈²	—	2	1	no	—
110	C₂×C₂₉	—	2	2	no	—
111	C₂×C₂₉	#1956	1	1	yes	characteristic
112	C₂×C₂₉	#1977	1	2	yes	—
113	C₂²×Q₈	—	2	2	no	—
114	C₂×M₁₆	—	2	1	no	—
115	C₂×M₁₆	—	2	1	no	—
116	C₂²×C₈	D₄×C₂₉	1	2	yes	—
117	C₄⋊Q₈	—	2	2	no	—
118	C₄⋊Q₈	—	2	2	no	—
119	C₄⋊Q₈	—	2	2	no	—
120	C₄⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
124	#108	—	4	4	no	—
125	#106	—	2	4	no	—
126	#106	—	2	4	no	—
127	C₄⋊C₈	—	2	2	no	—
128	C₄⋊C₈	—	2	2	no	—
129	C₄⋊C₈	D₄×C₂₉	1	4	yes	—
130	C₂²⋊C₈	—	2	2	no	—
131	C₄×C₈	—	2	2	no	—
132	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
133	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
134	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
135	C₂₉	#9767	1	1	yes	characteristic, direct product factor, Sylow
136	C₂×Q₈	—	2	4	no	—
137	C₂×Q₈	—	4	2	no	—
138	C₂×Q₈	—	8	4	no	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
141	C₂²×C₄	#41×C₂₉	1	2	yes	—
142	M₁₆	—	4	2	no	—
143	M₁₆	—	4	2	no	—
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	—	4	1	no	—
146	C₂×C₈	—	4	1	no	—
147	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
148	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
149	C₂×C₈	SD₁₆×C₂₉	1	4	yes	—
150	C₂×C₈	Q₁₆×C₂₉	1	4	yes	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
156	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
157	C₄²	C₂×D₄×C₂₉	1	2	yes	—
158	C₂³	C₂₉×#124	1	1	yes	characteristic
159	Q₈	—	8	4	no	—
160	Q₈	—	8	4	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	—	8	4	no	—
164	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
165	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
166	C₂×C₄	C₂₉×#121	1	2	yes	—
167	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
168	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
169	C₂×C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
170	C₈	—	4	4	no	—
171	C₈	—	8	1	no	—
172	C₈	—	8	1	no	—
173	C₈	C₂₉×#103	1	4	yes	—
174	C₈	C₂₉×#103	1	4	yes	—
175	C₂²	—	2	2	no	—
176	C₂²	C₂₉×#390	1	1	yes	characteristic
177	C₂²	C₂₉×#487	1	2	yes	—
178	C₄	—	2	2	no	—
179	C₄	—	8	4	no	—
180	C₄	C₂×C₂₉×#103	1	2	yes	—
181	C₄	C₂₉×#471	1	4	yes	—
182	C₄	C₂₉×#492	1	1	yes	characteristic
183	C₄	C₂₉×#494	1	1	yes	characteristic
184	C₂	—	2	2	no	—
185	C₂	C₂₉×#1956	1	1	yes	characteristic
186	C₂	C₂₉×#1977	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂₉×#498

C₂

yes

maximal, characteristic

C₂₉×#1848

C₂

yes

maximal, characteristic

C₂₉×#1549

C₂

yes

maximal

C₂₉×#1548

C₂

yes

maximal

C₂₉×#1450

C₂

yes

maximal, characteristic

C₂×C₂₉×C₄⋊Q₈

C₂²

yes

—

C₂₉×#498

—

C₂₉×#498

—

C₂₉×#498

C₄

yes

—

C₂₉×#431

C₂²

yes

—

C₂×C₂₉×#108

—

C₂×C₂₉×#106

—

C₂₉×#423

C₂²

yes

characteristic

C₂₉×#423

C₂²

yes

characteristic

C₂×C₄×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#333

—

C₂₉×#332

—

C₂₉×#322

—

C₈²×C₂₉

—

C₂²×Q₈×C₂₉

—

C₂×M₁₆×C₂₉

—

C₂×M₁₆×C₂₉

—

C₂²×C₈×C₂₉

D₄

yes

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄²×C₂₉

C₂³

yes

characteristic

C₂₉×#108

—

C₂₉×#106

—

C₂₉×#106

—

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

D₄

yes

—

C₂₉×C₂²⋊C₈

—

C₄×C₈×C₂₉

—

C₄×C₈×C₂₉

C₂×C₄

yes

—

C₄×C₈×C₂₉

D₄

yes

characteristic

C₄×C₈×C₂₉

D₄

yes

characteristic

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₉

#41

yes

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂²⋊C₄

yes

—

C₂×C₈×C₂₉

C₂²⋊C₄

yes

—

C₂×C₈×C₂₉

SD₁₆

yes

—

C₂×C₈×C₂₉

Q₁₆

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂²×C₄

yes

characteristic

C₄²×C₂₉

C₂×D₄

yes

characteristic

C₄²×C₂₉

C₂×D₄

yes

—

#9767

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

#124

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄×D₄

yes

—

C₂×C₄×C₂₉

#121

yes

—

C₂×C₄×C₂₉

#127

yes

characteristic

C₂×C₄×C₂₉

C₂×SD₁₆

yes

—

C₂×C₄×C₂₉

C₂×Q₁₆

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

#103

yes

—

C₈×C₂₉

#103

yes

—

C₂×#498

C₂×C₂₉

yes

characteristic

#1848

C₂×C₂₉

yes

characteristic

#1549

C₂×C₂₉

yes

—

#1548

C₂×C₂₉

yes

—

#1450

C₂×C₂₉

yes

characteristic

C₂²×C₂₉

—

C₂²×C₂₉

#390

yes

characteristic

C₂²×C₂₉

#487

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×#103

yes

—

C₄×C₂₉

#471

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₂×C₄⋊Q₈

C₂²×C₂₉

yes

—

#498

—

#498

—

#498

C₄×C₂₉

yes

—

100

#431

C₂²×C₂₉

yes

—

101

C₂×#108

—

102

C₂×#106

—

103

#423

C₂²×C₂₉

yes

characteristic

104

#423

C₂²×C₂₉

yes

characteristic

105

C₂×C₄×C₈

C₂²×C₂₉

yes

characteristic

106

#333

—

107

#332

—

108

#322

—

109

C₈²

—

110

C₂×C₂₉

—

111

C₂×C₂₉

#1956

yes

characteristic

112

C₂×C₂₉

#1977

yes

—

113

C₂²×Q₈

—

114

C₂×M₁₆

—

115

C₂×M₁₆

—

116

C₂²×C₈

D₄×C₂₉

yes

—

117

C₄⋊Q₈

—

118

C₄⋊Q₈

—

119

C₄⋊Q₈

—

120

C₄⋊Q₈

C₂×C₄×C₂₉

yes

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄²

C₂³×C₂₉

yes

characteristic

124

#108

—

125

#106

—

126

#106

—

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

C₄⋊C₈

D₄×C₂₉

yes

—

130

C₂²⋊C₈

—

131

C₄×C₈

—

132

C₄×C₈

C₂×C₄×C₂₉

yes

—

133

C₄×C₈

D₄×C₂₉

yes

characteristic

134

C₄×C₈

D₄×C₂₉

yes

characteristic

135

C₂₉

#9767

yes

characteristic, direct product factor, Sylow

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂²×C₄

—

140

C₂²×C₄

C₂×D₄×C₂₉

yes

characteristic

141

C₂²×C₄

#41×C₂₉

yes

—

142

M₁₆

—

143

M₁₆

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

C₂²⋊C₄×C₂₉

yes

—

148

C₂×C₈

C₂²⋊C₄×C₂₉

yes

—

149

C₂×C₈

SD₁₆×C₂₉

yes

—

150

C₂×C₈

Q₁₆×C₂₉

yes

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄²

C₂²×C₄×C₂₉

yes

characteristic

156

C₄²

C₂×D₄×C₂₉

yes

characteristic

157

C₄²

C₂×D₄×C₂₉

yes

—

158

C₂³

C₂₉×#124

yes

characteristic

159

Q₈

—

160

Q₈

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

C₂×C₂²⋊C₄×C₂₉

yes

characteristic

165

C₂×C₄

C₄×D₄×C₂₉

yes

—

166

C₂×C₄

C₂₉×#121

yes

—

167

C₂×C₄

C₂₉×#127

yes

characteristic

168

C₂×C₄

C₂×SD₁₆×C₂₉

yes

—

169

C₂×C₄

C₂×Q₁₆×C₂₉

yes

—

170

C₈

—

171

C₈

—

172

C₈

—

173

C₈

C₂₉×#103

yes

—

174

C₈

C₂₉×#103

yes

—

175

C₂²

—

176

C₂²

C₂₉×#390

yes

characteristic

177

C₂²

C₂₉×#487

yes

—

178

C₄

—

179

C₄

—

180

C₄

C₂×C₂₉×#103

yes

—

181

C₄

C₂₉×#471

yes

—

182

C₄

C₂₉×#492

yes

characteristic

183

C₄

C₂₉×#494

yes

characteristic

184

C₂

—

185

C₂

C₂₉×#1956

yes

characteristic

186

C₂

C₂₉×#1977

yes

—

	subgroup	G/H
center, socle	C₂²×C₂₉	#390
commutator	C₄²	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂³×C₂₉	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₉

#390

commutator

C₄²

C₂²×C₄×C₂₉

Frattini, cosocle

C₂×C₄²

C₂³×C₂₉

C₂³×C₂₉

G ▷ C₄² ▷ C₂² ▷ C₁

C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
64. #9767	C₂₉	direct (N × H)
135. C₂₉	#9767	direct (N × H)

H ≅ G/N

type

64. #9767

C₂₉

direct (N × H)

135. C₂₉

#9767

direct (N × H)

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

subgroup	index
C₂×C₂₉×#498	2
C₂₉×#1848	2
C₂₉×#1549	2
C₂₉×#1548	2
C₂₉×#1450	2
#9767	29

subgroup

index

C₂×C₂₉×#498

C₂₉×#1848

C₂₉×#1549

C₂₉×#1548

C₂₉×#1450

#9767

Subgroups — C₂₉×#9767 #20304667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#9767 #20304667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9767 #20304667