Group #30774231 — subgroups

Subgroups — #30774231

Order 17152.

430 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 139 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×#16863224	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863200	C₂	1	2	yes	maximal
3	C₂×#16863171	C₂	1	1	yes	maximal, characteristic
4	#22561071	C₂	1	2	yes	maximal
5	C₂²×Q₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#14523977	C₂²	1	2	yes	—
8	C₂×#14523967	—	2	2	no	—
9	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
10	#16863303	—	2	2	no	—
11	#16863224	—	2	2	no	—
12	#16863200	—	2	4	no	—
13	#16863171	—	2	2	no	—
14	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
15	C₂×Q₃₂×C₆₇	—	2	2	no	—
16	C₂×Q₃₂×C₆₇	—	2	2	no	—
17	C₂×Q₃₂×C₆₇	C₄	1	4	yes	complemented
18	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₆₇	—	2	2	no	—
21	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
22	C₂×C₆₇⋊C₁₆	—	2	1	no	—
23	C₂×C₆₇⋊C₁₆	—	2	1	no	—
24	C₂×C₆₇⋊C₁₆	D₄	1	2	yes	—
25	#14523977	—	2	2	no	—
26	#14523977	—	2	2	no	—
27	#14523967	—	4	4	no	—
28	C₈×Dic₆₇	—	2	1	no	—
29	C₈×Dic₆₇	—	2	1	no	—
30	C₆₇⋊#95	—	4	4	no	—
31	C₂²×Q₈×C₆₇	—	2	2	no	—
32	C₂×Q₁₆×C₆₇	—	2	2	no	—
33	C₂×Q₁₆×C₆₇	—	2	2	no	—
34	C₂×Q₁₆×C₆₇	—	2	2	no	—
35	C₂×Q₁₆×C₆₇	—	2	2	no	—
36	C₂×Q₁₆×C₆₇	—	2	2	no	—
37	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
39	Q₃₂×C₆₇	—	2	8	no	—
40	C₂×C₁₆×C₆₇	C₂×C₄	1	2	yes	—
41	C₂×C₁₆×C₆₇	D₄	1	2	yes	—
42	C₂×C₁₆×C₆₇	D₄	1	2	yes	—
43	C₂²×Dic₆₇	—	4	2	no	—
44	C₂²×Dic₆₇	D₈	1	2	yes	—
45	C₂×C₆₇⋊C₈	—	2	1	no	—
46	C₂×C₆₇⋊C₈	—	2	1	no	—
47	C₂×C₆₇⋊C₈	D₈	1	2	yes	—
48	C₄⋊Dic₆₇	—	4	2	no	—
49	C₄⋊Dic₆₇	—	4	2	no	—
50	C₄×Dic₆₇	—	2	1	no	—
51	C₄×Dic₆₇	—	2	1	no	—
52	C₆₇⋊C₁₆	—	2	2	no	—
53	C₂×Q₈×C₆₇	—	2	4	no	—
54	C₂×Q₈×C₆₇	—	4	2	no	—
55	C₂×Q₈×C₆₇	—	4	2	no	—
56	C₂×Q₈×C₆₇	—	4	2	no	—
57	C₂×Q₈×C₆₇	—	4	2	no	—
58	C₂×Q₈×C₆₇	—	4	2	no	—
59	C₂²×C₄×C₆₇	—	4	2	no	—
60	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₆₇	—	2	4	no	—
62	Q₁₆×C₆₇	—	2	4	no	—
63	Q₁₆×C₆₇	—	4	2	no	—
64	Q₁₆×C₆₇	—	4	2	no	—
65	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
70	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
71	C₁₆×C₆₇	C₂²⋊C₄	1	4	yes	—
72	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
73	Q₈×C₆₇	—	4	4	no	—
74	Q₈×C₆₇	—	4	4	no	—
75	Q₈×C₆₇	—	8	2	no	—
76	Q₈×C₆₇	—	8	2	no	—
77	C₂×C₄×C₆₇	—	4	4	no	—
78	C₂×C₄×C₆₇	—	8	2	no	—
79	C₂×C₄×C₆₇	—	8	2	no	—
80	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
82	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
83	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
85	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
86	C₂×Dic₆₇	—	2	2	no	—
87	C₂×Dic₆₇	—	2	4	no	—
88	C₂×Dic₆₇	—	8	2	no	—
89	C₂×Dic₆₇	—	8	4	no	—
90	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
92	C₈×C₆₇	#121	1	1	yes	characteristic
93	C₈×C₆₇	#124	1	1	yes	characteristic
94	C₆₇⋊C₈	—	2	2	no	—
95	C₂²×C₆₇	C₄×D₈	1	1	yes	characteristic
96	C₂²×C₆₇	#466	1	1	yes	characteristic
97	C₂²×C₆₇	#493	1	1	yes	characteristic
98	C₂²×C₆₇	#510	1	4	yes	—
99	C₄×C₆₇	—	8	4	no	—
100	C₄×C₆₇	#390	1	1	yes	characteristic
101	C₄×C₆₇	C₄×D₈	1	1	yes	characteristic
102	C₄×C₆₇	#466	1	1	yes	characteristic
103	C₄×C₆₇	#495	1	1	yes	characteristic
104	Dic₆₇	—	4	2	no	—
105	Dic₆₇	—	16	2	no	—
106	#13240	—	67	1	no	maximal, Sylow
107	C₂×C₆₇	#1970	1	1	yes	characteristic
108	C₂×C₆₇	#2176	1	2	yes	—
109	C₂×C₆₇	#2219	1	2	yes	—
110	C₂×C₆₇	#2251	1	2	yes	—
111	C₂²×Q₃₂	D₆₇	1	1	yes	characteristic
112	C₂×#367	—	67	1	no	—
113	C₂×#358	—	67	2	no	—
114	C₂×#346	—	67	1	no	—
115	#1969	—	67	2	no	—
116	C₆₇	#13240	1	1	yes	characteristic, complemented, Sylow
117	C₂²×Q₁₆	C₂×D₆₇	1	2	yes	—
118	C₂×Q₃₂	—	2	2	no	—
119	C₂×Q₃₂	—	2	2	no	—
120	C₂×Q₃₂	Dic₆₇	1	4	yes	complemented
121	C₂²×C₁₆	—	67	1	no	—
122	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
123	C₂×#107	—	67	2	no	—
124	C₂×#103	—	134	2	no	—
125	C₂×C₄×C₈	—	67	1	no	—
126	#391	—	134	2	no	—
127	#367	—	134	2	no	—
128	#358	—	134	4	no	—
129	#346	—	134	2	no	—
130	C₂²×Q₈	—	2	2	no	—
131	C₂×Q₁₆	—	2	2	no	—
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×Q₁₆	C₂×Dic₆₇	1	4	yes	—
137	C₂²×C₈	—	67	1	no	—
138	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	134	2	no	—
140	C₂×C₄²	—	67	1	no	—
141	Q₃₂	—	2	8	no	—
142	C₂×C₁₆	—	67	2	no	—
143	C₂×C₁₆	—	134	1	no	—
144	C₂×C₁₆	—	134	1	no	—
145	C₂×C₁₆	C₂×Dic₆₇	1	2	yes	—
146	C₂×C₁₆	C₂²⋊D₆₇	1	2	yes	—
147	C₂×C₁₆	C₂²⋊D₆₇	1	2	yes	—
148	#107	—	134	2	no	—
149	#107	—	134	2	no	—
150	#103	—	268	4	no	—
151	C₄×C₈	—	134	1	no	—
152	C₄×C₈	—	134	1	no	—
153	#95	—	268	4	no	—
154	C₂×Q₈	—	2	4	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂²×C₄	—	4	2	no	—
161	C₂²×C₄	—	268	2	no	—
162	C₂²×C₄	—	67	2	no	—
163	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
164	Q₁₆	—	2	4	no	—
165	Q₁₆	—	2	4	no	—
166	Q₁₆	—	4	2	no	—
167	Q₁₆	—	4	2	no	—
168	C₂×C₈	—	67	2	no	—
169	C₂×C₈	—	134	1	no	—
170	C₂×C₈	—	134	1	no	—
171	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
172	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
173	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
174	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
175	C₂×C₈	#11761627	1	1	yes	characteristic
176	C₂×C₈	#11761627	1	1	yes	characteristic
177	C₄⋊C₄	—	268	2	no	—
178	C₄⋊C₄	—	268	2	no	—
179	C₄²	—	134	1	no	—
180	C₄²	—	134	1	no	—
181	C₁₆	—	134	2	no	—
182	C₁₆	C₂²⋊Dic₆₇	1	4	yes	—
183	C₂³	D₈×D₆₇	1	1	yes	characteristic
184	Q₈	—	4	4	no	—
185	Q₈	—	4	4	no	—
186	Q₈	—	8	2	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	2	no	—
191	C₂×C₄	—	536	2	no	—
192	C₂×C₄	—	536	4	no	—
193	C₂×C₄	—	134	4	no	—
194	C₂×C₄	—	134	2	no	—
195	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
196	C₂×C₄	#14524014	1	1	yes	characteristic
197	C₂×C₄	#14524039	1	1	yes	characteristic
198	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
199	C₂×C₄	#14524062	1	1	yes	characteristic
200	C₂×C₄	#14524062	1	1	yes	characteristic
201	C₈	—	134	2	no	—
202	C₈	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
203	C₈	D₄×Dic₆₇	1	1	yes	characteristic
204	C₈	#14524014	1	1	yes	characteristic
205	C₈	#14524030	1	1	yes	characteristic
206	C₂²	D₈×Dic₆₇	1	1	yes	characteristic
207	C₂²	#16863629	1	1	yes	characteristic
208	C₂²	#16863771	1	1	yes	characteristic
209	C₂²	#16863838	1	4	yes	—
210	C₄	—	8	4	no	—
211	C₄	—	268	2	no	—
212	C₄	—	1072	2	no	—
213	C₄	#16863299	1	1	yes	characteristic
214	C₄	D₈×Dic₆₇	1	1	yes	characteristic
215	C₄	#16863629	1	1	yes	characteristic
216	C₄	#16863779	1	1	yes	characteristic
217	C₂	#22561076	1	1	yes	characteristic
218	C₂	#22562080	1	2	yes	—
219	C₂	#22562314	1	2	yes	—
220	C₂	#22562477	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16863224

C₂

yes

maximal, characteristic

C₂×#16863200

C₂

yes

maximal

C₂×#16863171

C₂

yes

maximal, characteristic

#22561071

C₂

yes

maximal

C₂²×Q₃₂×C₆₇

C₂

yes

maximal, characteristic

C₂²×C₆₇⋊C₁₆

C₂²

yes

characteristic

C₂×#14523977

C₂²

yes

—

C₂×#14523967

—

C₂×C₈×Dic₆₇

C₂²

yes

—

—

—

—

C₂²×Q₁₆×C₆₇

C₂²

yes

—

C₂×Q₃₂×C₆₇

—

C₂×Q₃₂×C₆₇

—

C₂×Q₃₂×C₆₇

C₄

yes

complemented

C₂²×C₁₆×C₆₇

C₂²

yes

characteristic

C₂²×C₆₇⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₆₇

—

C₂×C₄×Dic₆₇

D₄

yes

characteristic

C₂×C₆₇⋊C₁₆

—

C₂×C₆₇⋊C₁₆

—

C₂×C₆₇⋊C₁₆

D₄

yes

—

#14523977

—

#14523977

—

#14523967

—

C₈×Dic₆₇

—

C₈×Dic₆₇

—

C₆₇⋊#95

—

C₂²×Q₈×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

—

C₂×Q₁₆×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

Q₃₂×C₆₇

—

C₂×C₁₆×C₆₇

C₂×C₄

yes

—

C₂×C₁₆×C₆₇

D₄

yes

—

C₂×C₁₆×C₆₇

D₄

yes

—

C₂²×Dic₆₇

—

C₂²×Dic₆₇

D₈

yes

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

D₈

yes

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₆₇⋊C₁₆

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

Q₁₆×C₆₇

—

C₂×C₈×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

C₂×C₈×C₆₇

yes

C₂×C₈×C₆₇

yes

C₁₆×C₆₇

C₂²⋊C₄

yes

—

C₂³×C₆₇

C₂×D₈

yes

characteristic

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₄×D₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

C₂×D₈

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₈×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₆₇

C₄×D₄

yes

C₈×C₆₇

yes

C₈×C₆₇

yes

C₆₇⋊C₈

—

C₂²×C₆₇

C₄×D₈

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

—

C₄×C₆₇

—

100

C₄×C₆₇

#390

yes

characteristic

101

C₄×C₆₇

C₄×D₈

yes

characteristic

102

C₄×C₆₇

#466

yes

characteristic

103

C₄×C₆₇

#495

yes

characteristic

104

Dic₆₇

—

105

Dic₆₇

—

106

#13240

—

maximal, Sylow

107

C₂×C₆₇

#1970

yes

characteristic

108

C₂×C₆₇

#2176

yes

—

109

C₂×C₆₇

#2219

yes

—

110

C₂×C₆₇

#2251

yes

—

111

C₂²×Q₃₂

D₆₇

yes

characteristic

112

C₂×#367

—

113

C₂×#358

—

114

C₂×#346

—

115

#1969

—

116

C₆₇

#13240

yes

characteristic, complemented, Sylow

117

C₂²×Q₁₆

C₂×D₆₇

yes

—

118

C₂×Q₃₂

—

119

C₂×Q₃₂

—

120

C₂×Q₃₂

Dic₆₇

yes

complemented

121

C₂²×C₁₆

—

122

C₂²×C₁₆

C₂×D₆₇

yes

characteristic

123

C₂×#107

—

124

C₂×#103

—

134

—

125

C₂×C₄×C₈

—

126

#391

—

134

—

127

#367

—

134

—

128

#358

—

134

—

129

#346

—

134

—

130

C₂²×Q₈

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

C₂×Dic₆₇

yes

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂²×D₆₇

yes

characteristic

139

C₂×C₄⋊C₄

—

134

—

140

C₂×C₄²

—

141

Q₃₂

—

142

C₂×C₁₆

—

143

C₂×C₁₆

—

134

—

144

C₂×C₁₆

—

134

—

145

C₂×C₁₆

C₂×Dic₆₇

yes

—

146

C₂×C₁₆

C₂²⋊D₆₇

yes

—

147

C₂×C₁₆

C₂²⋊D₆₇

yes

—

148

#107

—

134

—

149

#107

—

134

—

150

#103

—

268

—

151

C₄×C₈

—

134

—

152

C₄×C₈

—

134

—

153

#95

—

268

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂²×C₄

—

161

C₂²×C₄

—

268

—

162

C₂²×C₄

—

163

C₂²×C₄

D₄×D₆₇

yes

characteristic

164

Q₁₆

—

165

Q₁₆

—

166

Q₁₆

—

167

Q₁₆

—

168

C₂×C₈

—

169

C₂×C₈

—

134

—

170

C₂×C₈

—

134

—

171

C₂×C₈

C₂²×Dic₆₇

yes

characteristic

172

C₂×C₈

D₄×D₆₇

yes

characteristic

173

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

174

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

175

C₂×C₈

#11761627

yes

characteristic

176

C₂×C₈

#11761627

yes

characteristic

177

C₄⋊C₄

—

268

—

178

C₄⋊C₄

—

268

—

179

C₄²

—

134

—

180

C₄²

—

134

—

181

C₁₆

—

134

—

182

C₁₆

C₂²⋊Dic₆₇

yes

—

183

C₂³

D₈×D₆₇

yes

characteristic

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

536

—

192

C₂×C₄

—

536

—

193

C₂×C₄

—

134

—

194

C₂×C₄

—

134

—

195

C₂×C₄

D₄×Dic₆₇

yes

characteristic

196

C₂×C₄

#14524014

yes

characteristic

197

C₂×C₄

#14524039

yes

characteristic

198

C₂×C₄

D₈×D₆₇

yes

characteristic

199

C₂×C₄

#14524062

yes

characteristic

200

C₂×C₄

#14524062

yes

characteristic

201

C₈

—

134

—

202

C₈

C₂×C₂²⋊Dic₆₇

yes

characteristic

203

C₈

D₄×Dic₆₇

yes

characteristic

204

C₈

#14524014

yes

characteristic

205

C₈

#14524030

yes

characteristic

206

C₂²

D₈×Dic₆₇

yes

characteristic

207

C₂²

#16863629

yes

characteristic

208

C₂²

#16863771

yes

characteristic

209

C₂²

#16863838

yes

—

210

C₄

—

211

C₄

—

268

—

212

C₄

—

1072

—

213

C₄

#16863299

yes

characteristic

214

C₄

D₈×Dic₆₇

yes

characteristic

215

C₄

#16863629

yes

characteristic

216

C₄

#16863779

yes

characteristic

217

C₂

#22561076

yes

characteristic

218

C₂

#22562080

yes

—

219

C₂

#22562314

yes

—

220

C₂

#22562477

yes

—

	subgroup	G/H
center	C₂³	D₈×D₆₇
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂²×Q₃₂×C₆₇	C₂
socle, prime radical	C₂³×C₆₇	C₂×D₈
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂²×Q₃₂	D₆₇
hypocenter	C₆₇	#13240
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂³

D₈×D₆₇

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₂²×Q₃₂×C₆₇

C₂

socle, prime radical

C₂³×C₆₇

C₂×D₈

cosocle

C₂²×C₈×C₆₇

C₂³

hypercenter

C₂²×Q₃₂

D₆₇

hypocenter

C₆₇

#13240

LCS

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
17. C₂×Q₃₂×C₆₇	C₄	semidirect
116. C₆₇	#13240	semidirect
120. C₂×Q₃₂	Dic₆₇	semidirect

H ≅ G/N

type

17. C₂×Q₃₂×C₆₇

C₄

semidirect

116. C₆₇

#13240

semidirect

120. C₂×Q₃₂

Dic₆₇

semidirect

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

subgroup	index
C₂×#16863224	2
C₂×#16863200	2
C₂×#16863171	2
#22561071	2
C₂²×Q₃₂×C₆₇	2
#13240	67

subgroup

index

C₂²×Q₃₂×C₆₇

Subgroups — #30774231

Conjugacy classes of subgroups

Complements

Maximal subgroups