Group #22550559 — subgroups

Subgroups — #22550559

Order 8128.

214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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	#16861204	C₂	1	1	yes	maximal, characteristic, complemented
2	#16861203	C₂	1	1	yes	maximal, characteristic, complemented
3	#16861201	C₂	1	1	yes	maximal, characteristic, complemented
4	#16861199	C₂	1	1	yes	maximal, characteristic, complemented
5	#16861199	C₂	1	1	yes	maximal, characteristic, complemented
6	#16861193	C₂	1	1	yes	maximal, characteristic
7	#16861192	C₂	1	1	yes	maximal, characteristic
8	#16861187	C₂	1	1	yes	maximal, characteristic, complemented
9	#16861186	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×Dic₂₅₄	C₂	1	1	yes	maximal, characteristic, complemented
11	(C₂²⋊D₁₂₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
12	#16861166	C₂	1	1	yes	maximal, characteristic, complemented
13	#16861165	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×Dic₁₂₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	#117×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Dic₂₅₄	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₂₇	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₂₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
21	C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic
22	C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic
23	C₄⋊Dic₁₂₇	C₂²	1	1	yes	characteristic
24	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
25	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
26	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
27	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
28	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
29	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
30	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
31	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
32	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
33	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
34	Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²⋊Dic₁₂₇	C₂²	1	1	yes	characteristic
36	(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
42	C₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
43	C₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄×C₁₂₇	C₂²	1	1	yes	characteristic
45	C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
46	C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
47	C₂²⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
48	C₂²⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
49	C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
50	C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
51	C₂²×D₁₂₇	C₂³	1	1	yes	characteristic
52	Dic₂₅₄	—	2	2	no	—
53	C₂²⋊D₁₂₇	—	2	2	no	—
54	C₂×Dic₁₂₇	—	2	2	no	—
55	C₂×Dic₁₂₇	—	2	2	no	—
56	C₂×Dic₁₂₇	C₂³	1	1	yes	characteristic
57	C₂×Dic₁₂₇	C₂³	1	1	yes	characteristic
58	C₂×Dic₁₂₇	C₂³	1	1	yes	characteristic
59	C₂×Dic₁₂₇	C₂³	1	1	yes	characteristic
60	C₂×Dic₁₂₇	C₂³	1	1	yes	characteristic
61	C₂×Dic₁₂₇	C₂³	1	1	yes	characteristic
62	C₂×Dic₁₂₇	C₂³	1	1	yes	characteristic
63	C₄×D₁₂₇	—	2	2	no	—
64	C₂³×C₁₂₇	C₂³	1	1	yes	characteristic
65	C₂×C₄×C₁₂₇	—	2	2	no	—
66	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
67	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
68	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
69	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
70	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
71	C₂×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
72	C₂²×C₁₂₇	—	2	1	no	—
73	C₂²×C₁₂₇	—	2	1	no	—
74	C₂²×C₁₂₇	#41	1	2	yes	—
75	C₂²×C₁₂₇	C₂⁴	1	1	yes	characteristic
76	C₂×D₁₂₇	—	2	1	no	—
77	C₂×D₁₂₇	—	2	1	no	—
78	C₂×D₁₂₇	—	2	1	no	—
79	C₄×C₁₂₇	—	2	1	no	—
80	C₄×C₁₂₇	—	2	1	no	—
81	C₄×C₁₂₇	—	2	1	no	—
82	C₄×C₁₂₇	—	2	1	no	—
83	C₄×C₁₂₇	—	2	1	no	—
84	C₄×C₁₂₇	—	2	1	no	—
85	Dic₁₂₇	—	2	1	no	—
86	Dic₁₂₇	—	2	1	no	—
87	Dic₁₂₇	—	2	1	no	—
88	Dic₁₂₇	—	2	1	no	—
89	Dic₁₂₇	—	2	1	no	—
90	Dic₁₂₇	—	2	1	no	—
91	Dic₁₂₇	#41	1	2	yes	—
92	C₂×C₁₂₇	—	2	2	no	—
93	C₂×C₁₂₇	C₂×#41	1	1	yes	characteristic
94	C₂×C₁₂₇	C₂×#41	1	1	yes	characteristic
95	C₂×C₁₂₇	2₋¹⁺⁴	1	1	yes	characteristic
96	D₁₂₇	—	4	1	no	—
97	C₁₂₇	#552	1	1	yes	characteristic, complemented, Sylow
98	#552	—	127	1	no	maximal, Sylow
99	#126	—	127	1	no	—
100	#126	—	127	1	no	—
101	#125	—	127	1	no	—
102	#125	—	127	1	no	—
103	#125	—	127	1	no	—
104	#123	—	127	1	no	—
105	#123	—	127	1	no	—
106	C₂²⋊Q₈	—	127	1	no	—
107	C₂²⋊Q₈	—	127	1	no	—
108	C₄×Q₈	—	127	1	no	—
109	C₄×D₄	—	127	1	no	—
110	#117	—	127	1	no	—
111	#117	—	127	1	no	—
112	#117	D₁₂₇	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₄	—	127	1	no	—
114	C₂×Q₈	—	127	1	no	—
115	C₂×D₄	—	127	1	no	—
116	C₂²×C₄	—	127	1	no	—
117	C₂²×C₄	—	127	1	no	—
118	C₂²×C₄	—	127	1	no	—
119	C₂²×C₄	C₂×D₁₂₇	1	1	yes	characteristic
120	C₄⋊C₄	—	127	1	no	—
121	C₄⋊C₄	—	127	1	no	—
122	C₄⋊C₄	—	127	1	no	—
123	C₄⋊C₄	—	127	1	no	—
124	C₄⋊C₄	—	127	1	no	—
125	C₄⋊C₄	—	127	1	no	—
126	C₄⋊C₄	—	127	1	no	—
127	C₄⋊C₄	—	127	1	no	—
128	C₄⋊C₄	—	127	1	no	—
129	C₄⋊C₄	—	127	1	no	—
130	C₄⋊C₄	—	127	1	no	—
131	C₄⋊C₄	—	127	1	no	—
132	C₄⋊C₄	—	127	1	no	—
133	C₄⋊C₄	—	127	1	no	—
134	C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
135	C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
136	C₂²⋊C₄	—	127	1	no	—
137	C₂²⋊C₄	—	127	1	no	—
138	C₂²⋊C₄	—	127	1	no	—
139	C₂²⋊C₄	—	127	1	no	—
140	C₂²⋊C₄	—	127	1	no	—
141	C₂²⋊C₄	—	127	1	no	—
142	C₂²⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
143	C₂²⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
144	C₄²	—	127	1	no	—
145	C₄²	—	127	1	no	—
146	C₄²	—	127	1	no	—
147	C₄²	C₂×D₁₂₇	1	1	yes	characteristic
148	C₄²	C₂×D₁₂₇	1	1	yes	characteristic
149	C₂³	—	127	1	no	—
150	C₂³	C₂²×D₁₂₇	1	1	yes	characteristic
151	Q₈	—	254	2	no	—
152	D₄	—	254	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	127	1	no	—
155	C₂×C₄	—	127	1	no	—
156	C₂×C₄	—	127	1	no	—
157	C₂×C₄	—	127	1	no	—
158	C₂×C₄	—	127	1	no	—
159	C₂×C₄	—	127	1	no	—
160	C₂×C₄	—	127	1	no	—
161	C₂×C₄	—	254	2	no	—
162	C₂×C₄	—	254	2	no	—
163	C₂×C₄	—	254	2	no	—
164	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
165	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
166	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
167	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
168	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
169	C₂×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
170	C₂²	—	2	1	no	—
171	C₂²	—	2	1	no	—
172	C₂²	—	254	1	no	—
173	C₂²	—	254	1	no	—
174	C₂²	—	254	1	no	—
175	C₂²	#14523248	1	2	yes	—
176	C₂²	C₂³×D₁₂₇	1	1	yes	characteristic
177	C₄	—	2	1	no	—
178	C₄	—	2	1	no	—
179	C₄	—	2	1	no	—
180	C₄	—	2	1	no	—
181	C₄	—	2	1	no	—
182	C₄	—	2	1	no	—
183	C₄	—	127	2	no	—
184	C₄	—	254	1	no	—
185	C₄	—	254	1	no	—
186	C₄	—	254	1	no	—
187	C₄	—	254	1	no	—
188	C₄	—	254	1	no	—
189	C₄	—	254	1	no	—
190	C₂	—	2	2	no	—
191	C₂	—	508	1	no	—
192	C₂	#41×D₁₂₇	1	1	yes	characteristic
193	C₂	C₂×#14523248	1	1	yes	characteristic
194	C₂	#16861256	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16861204

C₂

yes

maximal, characteristic, complemented

#16861203

C₂

yes

maximal, characteristic, complemented

#16861201

C₂

yes

maximal, characteristic, complemented

#16861199

C₂

yes

maximal, characteristic, complemented

#16861199

C₂

yes

maximal, characteristic, complemented

#16861193

C₂

yes

maximal, characteristic

#16861192

C₂

yes

maximal, characteristic

#16861187

C₂

yes

maximal, characteristic, complemented

#16861186

C₂

yes

maximal, characteristic, complemented

C₄×Dic₂₅₄

C₂

yes

maximal, characteristic, complemented

(C₂²⋊D₁₂₇)⋊C₄

C₂

yes

maximal, characteristic

#16861166

C₂

yes

maximal, characteristic, complemented

#16861165

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₂₇⋊C₄

C₂

yes

maximal, characteristic, complemented

#117×C₁₂₇

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₅₄

C₂²

yes

characteristic

C₂×C₂²⋊D₁₂₇

C₂²

yes

characteristic

C₂²×Dic₁₂₇

C₂²

yes

characteristic

C₂²×Dic₁₂₇

C₂²

yes

characteristic

C₂×C₄×D₁₂₇

C₂²

yes

characteristic

C₄⋊Dic₁₂₇

C₂²

yes

characteristic

C₄⋊Dic₁₂₇

C₂²

yes

characteristic

C₄⋊Dic₁₂₇

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

Dic₁₂₇⋊C₄

C₂²

yes

characteristic

C₂²⋊Dic₁₂₇

C₂²

yes

characteristic

(C₂×D₁₂₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₂₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₂₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₂₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₂₇)⋊C₄

C₂²

yes

characteristic

C₄×Dic₁₂₇

C₂²

yes

characteristic

C₄×Dic₁₂₇

C₂²

yes

characteristic

C₄×Dic₁₂₇

C₂²

yes

characteristic

C₂²×C₄×C₁₂₇

C₂²

yes

characteristic

C₄⋊C₄×C₁₂₇

C₂²

yes

characteristic

C₄⋊C₄×C₁₂₇

C₂²

yes

characteristic

C₂²⋊C₄×C₁₂₇

C₂²

yes

characteristic

C₂²⋊C₄×C₁₂₇

C₂²

yes

characteristic

C₄²×C₁₂₇

C₂²

yes

characteristic

C₄²×C₁₂₇

C₂²

yes

characteristic

C₂²×D₁₂₇

C₂³

yes

characteristic

Dic₂₅₄

—

C₂²⋊D₁₂₇

—

C₂×Dic₁₂₇

—

C₂×Dic₁₂₇

—

C₂×Dic₁₂₇

C₂³

yes

characteristic

C₂×Dic₁₂₇

C₂³

yes

characteristic

C₂×Dic₁₂₇

C₂³

yes

characteristic

C₂×Dic₁₂₇

C₂³

yes

characteristic

C₂×Dic₁₂₇

C₂³

yes

characteristic

C₂×Dic₁₂₇

C₂³

yes

characteristic

C₂×Dic₁₂₇

C₂³

yes

characteristic

C₄×D₁₂₇

—

C₂³×C₁₂₇

C₂³

yes

characteristic

C₂×C₄×C₁₂₇

—

C₂×C₄×C₁₂₇

C₂³

yes

characteristic

C₂×C₄×C₁₂₇

C₂³

yes

characteristic

C₂×C₄×C₁₂₇

C₂³

yes

characteristic

C₂×C₄×C₁₂₇

C₂³

yes

characteristic

C₂×C₄×C₁₂₇

C₂³

yes

characteristic

C₂×C₄×C₁₂₇

C₂³

yes

characteristic

C₂²×C₁₂₇

—

C₂²×C₁₂₇

—

C₂²×C₁₂₇

#41

yes

—

C₂²×C₁₂₇

C₂⁴

yes

characteristic

C₂×D₁₂₇

—

C₂×D₁₂₇

—

C₂×D₁₂₇

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

C₄×C₁₂₇

—

Dic₁₂₇

—

Dic₁₂₇

—

Dic₁₂₇

—

Dic₁₂₇

—

Dic₁₂₇

—

Dic₁₂₇

—

Dic₁₂₇

#41

yes

—

C₂×C₁₂₇

—

C₂×C₁₂₇

C₂×#41

yes

characteristic

C₂×C₁₂₇

C₂×#41

yes

characteristic

C₂×C₁₂₇

2₋¹⁺⁴

yes

characteristic

D₁₂₇

—

C₁₂₇

#552

yes

characteristic, complemented, Sylow

#552

—

127

maximal, Sylow

#126

—

127

—

100

#126

—

127

—

101

#125

—

127

—

102

#125

—

127

—

103

#125

—

127

—

104

#123

—

127

—

105

#123

—

127

—

106

C₂²⋊Q₈

—

127

—

107

C₂²⋊Q₈

—

127

—

108

C₄×Q₈

—

127

—

109

C₄×D₄

—

127

—

110

#117

—

127

—

111

#117

—

127

—

112

#117

D₁₂₇

yes

characteristic, complemented

113

C₂×C₄⋊C₄

—

127

—

114

C₂×Q₈

—

127

—

115

C₂×D₄

—

127

—

116

C₂²×C₄

—

127

—

117

C₂²×C₄

—

127

—

118

C₂²×C₄

—

127

—

119

C₂²×C₄

C₂×D₁₂₇

yes

characteristic

120

C₄⋊C₄

—

127

—

121

C₄⋊C₄

—

127

—

122

C₄⋊C₄

—

127

—

123

C₄⋊C₄

—

127

—

124

C₄⋊C₄

—

127

—

125

C₄⋊C₄

—

127

—

126

C₄⋊C₄

—

127

—

127

C₄⋊C₄

—

127

—

128

C₄⋊C₄

—

127

—

129

C₄⋊C₄

—

127

—

130

C₄⋊C₄

—

127

—

131

C₄⋊C₄

—

127

—

132

C₄⋊C₄

—

127

—

133

C₄⋊C₄

—

127

—

134

C₄⋊C₄

C₂×D₁₂₇

yes

characteristic

135

C₄⋊C₄

C₂×D₁₂₇

yes

characteristic

136

C₂²⋊C₄

—

127

—

137

C₂²⋊C₄

—

127

—

138

C₂²⋊C₄

—

127

—

139

C₂²⋊C₄

—

127

—

140

C₂²⋊C₄

—

127

—

141

C₂²⋊C₄

—

127

—

142

C₂²⋊C₄

C₂×D₁₂₇

yes

characteristic

143

C₂²⋊C₄

C₂×D₁₂₇

yes

characteristic

144

C₄²

—

127

—

145

C₄²

—

127

—

146

C₄²

—

127

—

147

C₄²

C₂×D₁₂₇

yes

characteristic

148

C₄²

C₂×D₁₂₇

yes

characteristic

149

C₂³

—

127

—

150

C₂³

C₂²×D₁₂₇

yes

characteristic

151

Q₈

—

254

—

152

D₄

—

254

—

153

C₂×C₄

—

154

C₂×C₄

—

127

—

155

C₂×C₄

—

127

—

156

C₂×C₄

—

127

—

157

C₂×C₄

—

127

—

158

C₂×C₄

—

127

—

159

C₂×C₄

—

127

—

160

C₂×C₄

—

127

—

161

C₂×C₄

—

254

—

162

C₂×C₄

—

254

—

163

C₂×C₄

—

254

—

164

C₂×C₄

C₂²×D₁₂₇

yes

characteristic

165

C₂×C₄

C₂²×D₁₂₇

yes

characteristic

166

C₂×C₄

C₂²×D₁₂₇

yes

characteristic

167

C₂×C₄

C₂²×D₁₂₇

yes

characteristic

168

C₂×C₄

C₂²×D₁₂₇

yes

characteristic

169

C₂×C₄

C₂²×D₁₂₇

yes

characteristic

170

C₂²

—

171

C₂²

—

172

C₂²

—

254

—

173

C₂²

—

254

—

174

C₂²

—

254

—

175

C₂²

#14523248

yes

—

176

C₂²

C₂³×D₁₂₇

yes

characteristic

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

—

127

—

184

C₄

—

254

—

185

C₄

—

254

—

186

C₄

—

254

—

187

C₄

—

254

—

188

C₄

—

254

—

189

C₄

—

254

—

190

C₂

—

191

C₂

—

508

—

192

C₂

#41×D₁₂₇

yes

characteristic

193

C₂

C₂×#14523248

yes

characteristic

194

C₂

#16861256

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₂₇
commutator, socle	C₂²×C₁₂₇	C₂⁴
Fitting	#117×C₁₂₇	C₂
hypercenter	#117	D₁₂₇
hypocenter	C₁₂₇	#552
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #117

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₂₇

commutator, socle

C₂²×C₁₂₇

C₂⁴

Fitting

#117×C₁₂₇

C₂

D₁₂₇

C₁₂₇

G ▷ C₂²×C₁₂₇ ▷ C₁₂₇

C₁ ◁ C₂² ◁ #117

N	H ≅ G/N	type
1. #16861204	C₂	semidirect
2. #16861203	C₂	semidirect
3. #16861201	C₂	semidirect
4. #16861199	C₂	semidirect
5. #16861199	C₂	semidirect
8. #16861187	C₂	semidirect
9. #16861186	C₂	semidirect
10. C₄×Dic₂₅₄	C₂	semidirect
12. #16861166	C₂	semidirect
13. #16861165	C₂	semidirect
14. C₂×Dic₁₂₇⋊C₄	C₂	semidirect
15. #117×C₁₂₇	C₂	semidirect
97. C₁₂₇	#552	semidirect
112. #117	D₁₂₇	semidirect

H ≅ G/N

type

1. #16861204

C₂

semidirect

2. #16861203

C₂

semidirect

3. #16861201

C₂

semidirect

4. #16861199

C₂

semidirect

5. #16861199

C₂

semidirect

8. #16861187

C₂

semidirect

9. #16861186

C₂

semidirect

10. C₄×Dic₂₅₄

C₂

semidirect

12. #16861166

C₂

semidirect

13. #16861165

C₂

semidirect

14. C₂×Dic₁₂₇⋊C₄

C₂

semidirect

15. #117×C₁₂₇

C₂

semidirect

97. C₁₂₇

#552

semidirect

112. #117

D₁₂₇

semidirect

Subgroups — #22550559

Conjugacy classes of subgroups

Complements