Group #30765151 — subgroups

Subgroups — #30765151

Order 17152.

418 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 131 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	#22562012	C₂	1	2	yes	maximal, complemented
2	#22558133	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₆₇⋊C₁₆)	—	2	2	no	—
5	C₂²⋊(C₆₇⋊C₁₆)	C₂²	1	4	yes	—
6	#16863172	—	2	2	no	—
7	C₂³×C₈×C₆₇	C₄	1	2	yes	—
8	C₂×C₄×D₄×C₆₇	C₄	1	1	yes	characteristic
9	C₈×D₄×C₆₇	—	2	2	no	—
10	C₈×D₄×C₆₇	—	2	2	no	—
11	C₂×C₄⋊C₈×C₆₇	C₄	1	1	yes	characteristic
12	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₆₇⋊C₁₆	—	2	4	no	—
15	C₂²×D₄×C₆₇	C₈	1	1	yes	characteristic
16	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₆₇	—	2	2	no	—
18	C₂²×C₈×C₆₇	—	2	2	no	—
19	C₂²×C₈×C₆₇	—	4	4	no	—
20	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
23	C₄×D₄×C₆₇	—	2	2	no	—
24	C₄×D₄×C₆₇	—	2	2	no	—
25	C₂×C₄⋊C₄×C₆₇	C₈	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₆₇	C₈	1	2	yes	—
27	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
28	C₄⋊C₈×C₆₇	—	2	2	no	—
29	C₂²⋊C₈×C₆₇	—	2	4	no	—
30	C₄×C₈×C₆₇	D₄	1	2	yes	—
31	C₄×C₈×C₆₇	D₄	1	2	yes	—
32	C₆₇⋊C₁₆	—	4	4	no	—
33	C₂⁴×C₆₇	C₂×C₈	1	2	yes	—
34	C₂×D₄×C₆₇	—	2	4	no	—
35	C₂×D₄×C₆₇	—	2	2	no	—
36	C₂²×C₄×C₆₇	—	2	2	no	—
37	C₂²×C₄×C₆₇	—	2	2	no	—
38	C₂²×C₄×C₆₇	—	4	2	no	—
39	C₂²×C₄×C₆₇	—	4	2	no	—
40	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₆₇	C₂×C₈	1	2	yes	—
42	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₆₇	—	2	2	no	—
45	C₂×C₈×C₆₇	—	2	2	no	—
46	C₂×C₈×C₆₇	—	4	1	no	—
47	C₂×C₈×C₆₇	—	4	4	no	—
48	C₂×C₈×C₆₇	—	4	4	no	—
49	C₂×C₈×C₆₇	—	4	2	no	—
50	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
53	C₄⋊C₄×C₆₇	—	2	2	no	—
54	C₂²⋊C₄×C₆₇	—	2	4	no	—
55	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₆₇	M₁₆	1	2	yes	—
57	C₂³×C₆₇	—	2	2	no	—
58	C₂³×C₆₇	—	2	2	no	—
59	C₂³×C₆₇	—	4	2	no	—
60	C₂³×C₆₇	—	4	2	no	—
61	C₂³×C₆₇	M₃₂	1	4	yes	—
62	C₂³×C₆₇	C₂²×C₈	1	1	yes	characteristic
63	D₄×C₆₇	—	2	8	no	—
64	C₂×C₄×C₆₇	—	2	2	no	—
65	C₂×C₄×C₆₇	—	2	1	no	—
66	C₂×C₄×C₆₇	—	2	1	no	—
67	C₂×C₄×C₆₇	—	2	2	no	—
68	C₂×C₄×C₆₇	—	4	1	no	—
69	C₂×C₄×C₆₇	—	4	4	no	—
70	C₂×C₄×C₆₇	—	4	2	no	—
71	C₂×C₄×C₆₇	—	4	2	no	—
72	C₂×C₄×C₆₇	—	4	2	no	—
73	C₂×C₄×C₆₇	C₂²⋊C₈	1	2	yes	—
74	C₂×C₄×C₆₇	C₂²⋊C₈	1	2	yes	—
75	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
77	C₈×C₆₇	—	2	2	no	—
78	C₈×C₆₇	—	2	1	no	—
79	C₈×C₆₇	—	4	2	no	—
80	C₈×C₆₇	#100	1	2	yes	—
81	C₂²×C₆₇	—	2	1	no	—
82	C₂²×C₆₇	—	2	1	no	—
83	C₂²×C₆₇	—	2	4	no	—
84	C₂²×C₆₇	—	4	4	no	—
85	C₂²×C₆₇	—	4	4	no	—
86	C₂²×C₆₇	—	4	2	no	—
87	C₂²×C₆₇	—	4	2	no	—
88	C₂²×C₆₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
89	C₂²×C₆₇	C₂×M₃₂	1	2	yes	—
90	C₄×C₆₇	—	2	2	no	—
91	C₄×C₆₇	—	2	2	no	—
92	C₄×C₆₇	—	2	1	no	—
93	C₄×C₆₇	—	4	2	no	—
94	C₄×C₆₇	#410	1	1	yes	characteristic
95	C₄×C₆₇	C₂×#100	1	1	yes	characteristic
96	#11488	—	67	1	no	maximal, Sylow
97	C₂×C₆₇	—	2	2	no	—
98	C₂×C₆₇	—	4	4	no	—
99	C₂×C₆₇	#1460	1	1	yes	characteristic
100	C₂×C₆₇	#2112	1	1	yes	characteristic
101	C₂×C₆₇	#2115	1	1	yes	characteristic
102	C₂×C₈×D₄	D₆₇	1	1	yes	characteristic
103	#2163	—	67	2	no	—
104	#1314	—	67	4	no	—
105	C₆₇	#11488	1	1	yes	characteristic, complemented, Sylow
106	C₂³×C₈	Dic₆₇	1	2	yes	—
107	C₂×C₄×D₄	Dic₆₇	1	1	yes	characteristic
108	C₈×D₄	—	2	2	no	—
109	C₈×D₄	—	2	2	no	—
110	C₂×C₄⋊C₈	Dic₆₇	1	1	yes	characteristic
111	C₂×C₂²⋊C₈	C₂×D₆₇	1	2	yes	—
112	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
113	C₄⋊C₁₆	—	134	2	no	—
114	C₂²⋊C₁₆	—	67	4	no	—
115	#346	—	134	2	no	—
116	C₂²×D₄	C₆₇⋊C₈	1	1	yes	characteristic
117	C₂³×C₄	C₂×Dic₆₇	1	2	yes	—
118	C₂²×C₈	—	2	2	no	—
119	C₂²×C₈	—	2	2	no	—
120	C₂²×C₈	—	4	4	no	—
121	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
122	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
123	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
124	C₄×D₄	—	2	2	no	—
125	C₄×D₄	—	2	2	no	—
126	C₂×C₄⋊C₄	C₆₇⋊C₈	1	1	yes	characteristic
127	C₂×C₂²⋊C₄	C₆₇⋊C₈	1	2	yes	—
128	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
129	C₂×C₁₆	—	134	4	no	—
130	C₄⋊C₈	—	2	2	no	—
131	C₂²⋊C₈	—	2	4	no	—
132	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
133	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
134	C₂⁴	C₂×C₆₇⋊C₈	1	2	yes	—
135	C₂×D₄	—	2	4	no	—
136	C₂×D₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	C₂×C₆₇⋊C₈	1	1	yes	characteristic
142	C₂²×C₄	C₂×C₆₇⋊C₈	1	2	yes	—
143	C₂²×C₄	C₂×C₆₇⋊C₈	1	1	yes	characteristic
144	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	4	1	no	—
148	C₂×C₈	—	4	4	no	—
149	C₂×C₈	—	4	4	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
152	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
153	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
154	C₄⋊C₄	—	2	2	no	—
155	C₂²⋊C₄	—	2	4	no	—
156	C₄²	C₂²⋊Dic₆₇	1	2	yes	—
157	C₄²	#11761612	1	2	yes	—
158	C₁₆	—	268	4	no	—
159	C₂³	—	2	2	no	—
160	C₂³	—	2	2	no	—
161	C₂³	—	4	2	no	—
162	C₂³	—	4	2	no	—
163	C₂³	#14523983	1	4	yes	—
164	C₂³	C₂²×C₆₇⋊C₈	1	1	yes	characteristic
165	D₄	—	2	8	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	C₂²⋊(C₆₇⋊C₈)	1	2	yes	—
176	C₂×C₄	C₂²⋊(C₆₇⋊C₈)	1	2	yes	—
177	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
178	C₂×C₄	C₂×#11761612	1	1	yes	characteristic
179	C₈	—	2	2	no	—
180	C₈	—	2	1	no	—
181	C₈	—	4	2	no	—
182	C₈	#14523960	1	2	yes	—
183	C₂²	—	2	1	no	—
184	C₂²	—	2	1	no	—
185	C₂²	—	2	4	no	—
186	C₂²	—	4	4	no	—
187	C₂²	—	4	4	no	—
188	C₂²	—	4	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	C₂×C₂²⋊(C₆₇⋊C₈)	1	1	yes	characteristic
191	C₂²	C₂×#14523983	1	2	yes	—
192	C₄	—	2	2	no	—
193	C₄	—	2	2	no	—
194	C₄	—	2	1	no	—
195	C₄	—	4	2	no	—
196	C₄	#16863370	1	1	yes	characteristic
197	C₄	C₂×#14523960	1	1	yes	characteristic
198	C₂	—	2	2	no	—
199	C₂	—	4	4	no	—
200	C₂	#22558530	1	1	yes	characteristic
201	C₂	#22561820	1	1	yes	characteristic
202	C₂	#22561830	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22562012

C₂

yes

maximal, complemented

#22558133

C₂

yes

maximal, complemented

C₂×C₈×D₄×C₆₇

C₂

yes

maximal, characteristic

C₄⋊(C₆₇⋊C₁₆)

—

C₂²⋊(C₆₇⋊C₁₆)

C₂²

yes

—

#16863172

—

C₂³×C₈×C₆₇

C₄

yes

—

C₂×C₄×D₄×C₆₇

C₄

yes

characteristic

C₈×D₄×C₆₇

—

C₈×D₄×C₆₇

—

C₂×C₄⋊C₈×C₆₇

C₄

yes

characteristic

C₂×C₂²⋊C₈×C₆₇

C₂²

yes

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

C₂×C₆₇⋊C₁₆

—

C₂²×D₄×C₆₇

C₈

yes

characteristic

C₂³×C₄×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

C₄×D₄×C₆₇

—

C₄×D₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

C₈

yes

characteristic

C₂×C₂²⋊C₄×C₆₇

C₈

yes

—

C₂×C₄²×C₆₇

C₂×C₄

yes

characteristic

C₄⋊C₈×C₆₇

—

C₂²⋊C₈×C₆₇

—

C₄×C₈×C₆₇

D₄

yes

—

C₄×C₈×C₆₇

D₄

yes

—

C₆₇⋊C₁₆

—

C₂⁴×C₆₇

C₂×C₈

yes

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₆₇

C₂×C₈

yes

—

C₂²×C₄×C₆₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₆₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₄⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

C₂²⋊C₄

yes

—

C₄²×C₆₇

M₁₆

yes

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

M₃₂

yes

—

C₂³×C₆₇

C₂²×C₈

yes

characteristic

D₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂²⋊C₈

yes

—

C₂×C₄×C₆₇

C₂²⋊C₈

yes

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₂×M₁₆

yes

characteristic

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

#100

yes

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₆₇

C₂×M₃₂

yes

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

yes

C₄×C₆₇

yes

—

C₂×C₆₇

—

C₂×C₆₇

—

C₂×C₆₇

#1460

yes

characteristic

100

C₂×C₆₇

#2112

yes

characteristic

101

C₂×C₆₇

#2115

yes

characteristic

102

C₂×C₈×D₄

D₆₇

yes

characteristic

103

#2163

—

104

#1314

—

105

C₆₇

#11488

yes

characteristic, complemented, Sylow

106

C₂³×C₈

Dic₆₇

yes

—

107

C₂×C₄×D₄

Dic₆₇

yes

characteristic

108

C₈×D₄

—

109

C₈×D₄

—

110

C₂×C₄⋊C₈

Dic₆₇

yes

characteristic

111

C₂×C₂²⋊C₈

C₂×D₆₇

yes

—

112

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

113

C₄⋊C₁₆

—

134

—

114

C₂²⋊C₁₆

—

115

#346

—

134

—

116

C₂²×D₄

C₆₇⋊C₈

yes

characteristic

117

C₂³×C₄

C₂×Dic₆₇

yes

—

118

C₂²×C₈

—

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₂²×C₈

C₂×Dic₆₇

yes

characteristic

122

C₂²×C₈

C₂×Dic₆₇

yes

—

123

C₂²×C₈

C₂²×D₆₇

yes

characteristic

124

C₄×D₄

—

125

C₄×D₄

—

126

C₂×C₄⋊C₄

C₆₇⋊C₈

yes

characteristic

127

C₂×C₂²⋊C₄

C₆₇⋊C₈

yes

—

128

C₂×C₄²

C₂×Dic₆₇

yes

characteristic

129

C₂×C₁₆

—

134

—

130

C₄⋊C₈

—

131

C₂²⋊C₈

—

132

C₄×C₈

C₂²⋊D₆₇

yes

—

133

C₄×C₈

C₂²⋊D₆₇

yes

—

134

C₂⁴

C₂×C₆₇⋊C₈

yes

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

C₂×C₆₇⋊C₈

yes

characteristic

142

C₂²×C₄

C₂×C₆₇⋊C₈

yes

—

143

C₂²×C₄

C₂×C₆₇⋊C₈

yes

characteristic

144

C₂²×C₄

C₂²×Dic₆₇

yes

characteristic

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

C₂²⋊Dic₆₇

yes

characteristic

152

C₂×C₈

C₂²⋊Dic₆₇

yes

characteristic

153

C₂×C₈

C₂×C₂²⋊D₆₇

yes

—

154

C₄⋊C₄

—

155

C₂²⋊C₄

—

156

C₄²

C₂²⋊Dic₆₇

yes

—

157

C₄²

#11761612

yes

—

158

C₁₆

—

268

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

#14523983

yes

—

164

C₂³

C₂²×C₆₇⋊C₈

yes

characteristic

165

D₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

C₂²⋊(C₆₇⋊C₈)

yes

—

176

C₂×C₄

C₂²⋊(C₆₇⋊C₈)

yes

—

177

C₂×C₄

C₂×C₂²⋊Dic₆₇

yes

characteristic

178

C₂×C₄

C₂×#11761612

yes

characteristic

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

#14523960

yes

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

C₂×C₂²⋊(C₆₇⋊C₈)

yes

characteristic

191

C₂²

C₂×#14523983

yes

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

#16863370

yes

characteristic

197

C₄

C₂×#14523960

yes

characteristic

198

C₂

—

199

C₂

—

200

C₂

#22558530

yes

characteristic

201

C₂

#22561820

yes

characteristic

202

C₂

#22561830

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₆₇
commutator	C₂³×C₆₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂×C₈×D₄×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₂²⋊C₈
prime radical	C₂²×D₄×C₆₇	C₈
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂×C₈×D₄	D₆₇
hypocenter	C₆₇	#11488
LCS	G ▷ C₂³×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×C₈×D₄

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊Dic₆₇

commutator

C₂³×C₆₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₂×C₈×D₄×C₆₇

C₂

socle

C₂²×C₆₇

C₂×C₂²⋊C₈

prime radical

C₂²×D₄×C₆₇

C₈

cosocle

C₂²×C₈×C₆₇

C₂³

hypercenter

C₂×C₈×D₄

D₆₇

hypocenter

C₆₇

#11488

LCS

G ▷ C₂³×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×C₈×D₄

N	H ≅ G/N	type
1. #22562012	C₂	semidirect
2. #22558133	C₂	semidirect
105. C₆₇	#11488	semidirect

H ≅ G/N

type

1. #22562012

C₂

semidirect

2. #22558133

C₂

semidirect

105. C₆₇

#11488

semidirect

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

subgroup	index
#22562012	2
#22558133	2
C₂×C₈×D₄×C₆₇	2
#11488	67

subgroup

index

#22562012

#22558133

C₂×C₈×D₄×C₆₇

#11488

Subgroups — #30765151

Conjugacy classes of subgroups

Complements

Maximal subgroups