Group #24923889 — subgroups

Subgroups — #24923889

Order 10688.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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	#19128830	C₂	1	1	yes	maximal, characteristic, complemented
2	#19128827	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128825	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128821	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128818	C₂	1	1	yes	maximal, characteristic, complemented
6	#19128818	C₂	1	1	yes	maximal, characteristic, complemented
7	#19128817	C₂	1	1	yes	maximal, characteristic, complemented
8	#19128815	C₂	1	1	yes	maximal, characteristic, complemented
9	#19128810	C₂	1	1	yes	maximal, characteristic, complemented
10	#19128810	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128805	C₂	1	1	yes	maximal, characteristic
12	#19128797	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂²⋊D₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#19128790	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²⋊Q₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Dic₃₃₄	C₂²	1	1	yes	characteristic
17	C₂×Dic₃₃₄	C₂²	1	1	yes	characteristic
18	C₂×D₆₆₈	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊D₁₆₇	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊D₁₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₁₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₁₆₇	C₂²	1	1	yes	characteristic
23	C₄⋊Dic₁₆₇	C₂²	1	1	yes	characteristic
24	Dic₁₆₇⋊C₄	C₂²	1	1	yes	characteristic
25	Dic₁₆₇⋊C₄	C₂²	1	1	yes	characteristic
26	Dic₁₆₇⋊C₄	C₂²	1	1	yes	characteristic
27	Dic₁₆₇⋊C₄	C₂²	1	1	yes	characteristic
28	Dic₁₆₇⋊C₄	C₂²	1	1	yes	characteristic
29	Dic₁₆₇⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²⋊Dic₁₆₇	C₂²	1	1	yes	characteristic
31	C₂²⋊Dic₁₆₇	C₂²	1	1	yes	characteristic
32	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
33	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
34	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
35	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
36	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×D₁₆₇)⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×Dic₁₆₇	C₂²	1	1	yes	characteristic
41	C₄×Dic₁₆₇	C₂²	1	1	yes	characteristic
42	C₄×Dic₁₆₇	C₂²	1	1	yes	characteristic
43	C₄×Dic₁₆₇	C₂²	1	1	yes	characteristic
44	C₂×Q₈×C₁₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₄×C₁₆₇	C₂²	1	1	yes	characteristic
46	C₄⋊C₄×C₁₆₇	C₂²	1	1	yes	characteristic
47	C₄⋊C₄×C₁₆₇	C₂²	1	1	yes	characteristic
48	C₄⋊C₄×C₁₆₇	C₂²	1	1	yes	characteristic
49	C₂²⋊C₄×C₁₆₇	C₂²	1	1	yes	characteristic
50	C₂²⋊C₄×C₁₆₇	C₂²	1	1	yes	characteristic
51	C₂²×D₁₆₇	C₂³	1	1	yes	characteristic
52	C₂²×D₁₆₇	C₂³	1	1	yes	characteristic
53	Dic₃₃₄	—	2	2	no	—
54	Dic₃₃₄	—	4	1	no	—
55	D₆₆₈	—	4	1	no	—
56	C₂²⋊D₁₆₇	—	2	2	no	—
57	C₂²⋊D₁₆₇	—	4	1	no	—
58	C₂×Dic₁₆₇	C₂³	1	1	yes	characteristic
59	C₂×Dic₁₆₇	C₂³	1	1	yes	characteristic
60	C₂×Dic₁₆₇	C₂³	1	1	yes	characteristic
61	C₂×Dic₁₆₇	C₂³	1	1	yes	characteristic
62	C₂×Dic₁₆₇	C₂³	1	1	yes	characteristic
63	C₂×Dic₁₆₇	C₂³	1	1	yes	characteristic
64	C₄×D₁₆₇	—	2	2	no	—
65	C₄×D₁₆₇	—	4	1	no	—
66	C₂³×C₁₆₇	C₂³	1	1	yes	characteristic
67	Q₈×C₁₆₇	—	4	1	no	—
68	C₂×C₄×C₁₆₇	—	4	1	no	—
69	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
70	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
71	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
72	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
73	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
74	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
75	C₂²×C₁₆₇	—	2	1	no	—
76	C₂²×C₁₆₇	—	2	1	no	—
77	C₂²×C₁₆₇	—	2	1	no	—
78	C₂²×C₁₆₇	C₂⁴	1	1	yes	characteristic
79	C₂×D₁₆₇	—	2	1	no	—
80	C₂×D₁₆₇	—	2	1	no	—
81	C₂×D₁₆₇	—	2	1	no	—
82	C₂×D₁₆₇	—	2	1	no	—
83	C₂×D₁₆₇	—	2	1	no	—
84	C₂×D₁₆₇	—	2	1	no	—
85	C₄×C₁₆₇	—	2	1	no	—
86	C₄×C₁₆₇	—	2	1	no	—
87	C₄×C₁₆₇	—	2	1	no	—
88	C₄×C₁₆₇	—	2	1	no	—
89	C₄×C₁₆₇	—	2	1	no	—
90	C₄×C₁₆₇	—	2	1	no	—
91	Dic₁₆₇	—	2	1	no	—
92	Dic₁₆₇	—	2	1	no	—
93	Dic₁₆₇	—	2	1	no	—
94	Dic₁₆₇	—	2	1	no	—
95	Dic₁₆₇	—	2	1	no	—
96	Dic₁₆₇	#41	1	2	yes	—
97	C₂×C₁₆₇	—	4	1	no	—
98	C₂×C₁₆₇	C₂×#41	1	1	yes	characteristic
99	C₂×C₁₆₇	H(5,𝔽₂)	1	1	yes	characteristic
100	C₂×C₁₆₇	2₋¹⁺⁴	1	1	yes	characteristic
101	D₁₆₇	—	4	1	no	—
102	D₁₆₇	—	4	1	no	—
103	C₁₆₇	#542	1	1	yes	characteristic, complemented, Sylow
104	#542	—	167	1	no	maximal, Sylow
105	C₄⋊Q₈	—	167	1	no	—
106	#126	—	167	1	no	—
107	#126	—	167	1	no	—
108	#124	—	167	1	no	—
109	#124	—	167	1	no	—
110	#124	—	167	1	no	—
111	#123	—	167	1	no	—
112	#123	—	167	1	no	—
113	C₂²⋊Q₈	—	167	1	no	—
114	C₂²⋊Q₈	—	167	1	no	—
115	C₂²⋊Q₈	D₁₆₇	1	1	yes	characteristic, complemented
116	#121	—	167	1	no	—
117	C₄×Q₈	—	167	1	no	—
118	C₄×D₄	—	167	1	no	—
119	#117	—	167	1	no	—
120	C₂×Q₈	—	167	1	no	—
121	C₂×Q₈	—	167	1	no	—
122	C₂×Q₈	C₂×D₁₆₇	1	1	yes	characteristic
123	C₂×D₄	—	167	1	no	—
124	C₂×D₄	—	167	1	no	—
125	C₂×D₄	—	167	1	no	—
126	C₂²×C₄	—	167	1	no	—
127	C₂²×C₄	—	167	1	no	—
128	C₂²×C₄	C₂×D₁₆₇	1	1	yes	characteristic
129	C₄⋊C₄	—	167	1	no	—
130	C₄⋊C₄	—	167	1	no	—
131	C₄⋊C₄	—	167	1	no	—
132	C₄⋊C₄	—	167	1	no	—
133	C₄⋊C₄	—	167	1	no	—
134	C₄⋊C₄	—	167	1	no	—
135	C₄⋊C₄	—	167	1	no	—
136	C₄⋊C₄	C₂×D₁₆₇	1	1	yes	characteristic
137	C₄⋊C₄	C₂×D₁₆₇	1	1	yes	characteristic
138	C₄⋊C₄	C₂×D₁₆₇	1	1	yes	characteristic
139	C₂²⋊C₄	—	167	1	no	—
140	C₂²⋊C₄	—	167	1	no	—
141	C₂²⋊C₄	—	167	1	no	—
142	C₂²⋊C₄	—	167	1	no	—
143	C₂²⋊C₄	—	167	1	no	—
144	C₂²⋊C₄	—	167	1	no	—
145	C₂²⋊C₄	—	167	1	no	—
146	C₂²⋊C₄	—	167	1	no	—
147	C₂²⋊C₄	—	167	1	no	—
148	C₂²⋊C₄	—	167	1	no	—
149	C₂²⋊C₄	C₂×D₁₆₇	1	1	yes	characteristic
150	C₂²⋊C₄	C₂×D₁₆₇	1	1	yes	characteristic
151	C₄²	—	167	1	no	—
152	C₄²	—	167	1	no	—
153	C₄²	—	167	1	no	—
154	C₄²	—	167	1	no	—
155	C₂³	—	167	1	no	—
156	C₂³	—	167	1	no	—
157	C₂³	C₂²×D₁₆₇	1	1	yes	characteristic
158	Q₈	—	4	1	no	—
159	Q₈	—	334	2	no	—
160	Q₈	—	668	1	no	—
161	D₄	—	334	2	no	—
162	D₄	—	668	1	no	—
163	D₄	—	668	1	no	—
164	C₂×C₄	—	4	1	no	—
165	C₂×C₄	—	334	2	no	—
166	C₂×C₄	—	668	1	no	—
167	C₂×C₄	—	167	1	no	—
168	C₂×C₄	—	167	1	no	—
169	C₂×C₄	—	167	1	no	—
170	C₂×C₄	—	167	1	no	—
171	C₂×C₄	—	167	1	no	—
172	C₂×C₄	—	167	1	no	—
173	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
174	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
175	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
176	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
177	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
178	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
179	C₂²	—	2	1	no	—
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	—	334	1	no	—
183	C₂²	—	334	1	no	—
184	C₂²	—	334	1	no	—
185	C₂²	—	334	1	no	—
186	C₂²	—	334	1	no	—
187	C₂²	—	334	1	no	—
188	C₂²	C₂³×D₁₆₇	1	1	yes	characteristic
189	C₄	—	2	1	no	—
190	C₄	—	2	1	no	—
191	C₄	—	2	1	no	—
192	C₄	—	2	1	no	—
193	C₄	—	2	1	no	—
194	C₄	—	2	1	no	—
195	C₄	—	334	1	no	—
196	C₄	—	334	1	no	—
197	C₄	—	334	1	no	—
198	C₄	—	334	1	no	—
199	C₄	—	334	1	no	—
200	C₄	—	167	2	no	—
201	C₂	—	4	1	no	—
202	C₂	—	668	1	no	—
203	C₂	—	668	1	no	—
204	C₂	#41×D₁₆₇	1	1	yes	characteristic
205	C₂	#19128877	1	1	yes	characteristic
206	C₂	#19128880	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19128830

C₂

yes

maximal, characteristic, complemented

#19128827

C₂

yes

maximal, characteristic, complemented

#19128825

C₂

yes

maximal, characteristic, complemented

#19128821

C₂

yes

maximal, characteristic, complemented

#19128818

C₂

yes

maximal, characteristic, complemented

#19128818

C₂

yes

maximal, characteristic, complemented

#19128817

C₂

yes

maximal, characteristic, complemented

#19128815

C₂

yes

maximal, characteristic, complemented

#19128810

C₂

yes

maximal, characteristic, complemented

#19128810

C₂

yes

maximal, characteristic, complemented

#19128805

C₂

yes

maximal, characteristic

#19128797

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₁₆₇

C₂

yes

maximal, characteristic, complemented

#19128790

C₂

yes

maximal, characteristic, complemented

C₂²⋊Q₈×C₁₆₇

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₃₄

C₂²

yes

characteristic

C₂×Dic₃₃₄

C₂²

yes

characteristic

C₂×D₆₆₈

C₂²

yes

characteristic

C₂×C₂²⋊D₁₆₇

C₂²

yes

characteristic

C₂×C₂²⋊D₁₆₇

C₂²

yes

characteristic

C₂×C₄×D₁₆₇

C₂²

yes

characteristic

C₂×C₄×D₁₆₇

C₂²

yes

characteristic

C₄⋊Dic₁₆₇

C₂²

yes

characteristic

Dic₁₆₇⋊C₄

C₂²

yes

characteristic

Dic₁₆₇⋊C₄

C₂²

yes

characteristic

Dic₁₆₇⋊C₄

C₂²

yes

characteristic

Dic₁₆₇⋊C₄

C₂²

yes

characteristic

Dic₁₆₇⋊C₄

C₂²

yes

characteristic

Dic₁₆₇⋊C₄

C₂²

yes

characteristic

C₂²⋊Dic₁₆₇

C₂²

yes

characteristic

C₂²⋊Dic₁₆₇

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

(C₂×D₁₆₇)⋊C₄

C₂²

yes

characteristic

C₄×Dic₁₆₇

C₂²

yes

characteristic

C₄×Dic₁₆₇

C₂²

yes

characteristic

C₄×Dic₁₆₇

C₂²

yes

characteristic

C₄×Dic₁₆₇

C₂²

yes

characteristic

C₂×Q₈×C₁₆₇

C₂²

yes

characteristic

C₂²×C₄×C₁₆₇

C₂²

yes

characteristic

C₄⋊C₄×C₁₆₇

C₂²

yes

characteristic

C₄⋊C₄×C₁₆₇

C₂²

yes

characteristic

C₄⋊C₄×C₁₆₇

C₂²

yes

characteristic

C₂²⋊C₄×C₁₆₇

C₂²

yes

characteristic

C₂²⋊C₄×C₁₆₇

C₂²

yes

characteristic

C₂²×D₁₆₇

C₂³

yes

characteristic

C₂²×D₁₆₇

C₂³

yes

characteristic

Dic₃₃₄

—

Dic₃₃₄

—

D₆₆₈

—

C₂²⋊D₁₆₇

—

C₂²⋊D₁₆₇

—

C₂×Dic₁₆₇

C₂³

yes

characteristic

C₂×Dic₁₆₇

C₂³

yes

characteristic

C₂×Dic₁₆₇

C₂³

yes

characteristic

C₂×Dic₁₆₇

C₂³

yes

characteristic

C₂×Dic₁₆₇

C₂³

yes

characteristic

C₂×Dic₁₆₇

C₂³

yes

characteristic

C₄×D₁₆₇

—

C₄×D₁₆₇

—

C₂³×C₁₆₇

C₂³

yes

characteristic

Q₈×C₁₆₇

—

C₂×C₄×C₁₆₇

—

C₂×C₄×C₁₆₇

C₂³

yes

characteristic

C₂×C₄×C₁₆₇

C₂³

yes

characteristic

C₂×C₄×C₁₆₇

C₂³

yes

characteristic

C₂×C₄×C₁₆₇

C₂³

yes

characteristic

C₂×C₄×C₁₆₇

C₂³

yes

characteristic

C₂×C₄×C₁₆₇

C₂³

yes

characteristic

C₂²×C₁₆₇

—

C₂²×C₁₆₇

—

C₂²×C₁₆₇

—

C₂²×C₁₆₇

C₂⁴

yes

characteristic

C₂×D₁₆₇

—

C₂×D₁₆₇

—

C₂×D₁₆₇

—

C₂×D₁₆₇

—

C₂×D₁₆₇

—

C₂×D₁₆₇

—

C₄×C₁₆₇

—

C₄×C₁₆₇

—

C₄×C₁₆₇

—

C₄×C₁₆₇

—

C₄×C₁₆₇

—

C₄×C₁₆₇

—

Dic₁₆₇

—

Dic₁₆₇

—

Dic₁₆₇

—

Dic₁₆₇

—

Dic₁₆₇

—

Dic₁₆₇

#41

yes

—

C₂×C₁₆₇

—

C₂×C₁₆₇

C₂×#41

yes

characteristic

C₂×C₁₆₇

H(5,𝔽₂)

yes

characteristic

100

C₂×C₁₆₇

2₋¹⁺⁴

yes

characteristic

101

D₁₆₇

—

102

D₁₆₇

—

103

C₁₆₇

#542

yes

characteristic, complemented, Sylow

104

#542

—

167

maximal, Sylow

105

C₄⋊Q₈

—

167

—

106

#126

—

167

—

107

#126

—

167

—

108

#124

—

167

—

109

#124

—

167

—

110

#124

—

167

—

111

#123

—

167

—

112

#123

—

167

—

113

C₂²⋊Q₈

—

167

—

114

C₂²⋊Q₈

—

167

—

115

C₂²⋊Q₈

D₁₆₇

yes

characteristic, complemented

116

#121

—

167

—

117

C₄×Q₈

—

167

—

118

C₄×D₄

—

167

—

119

#117

—

167

—

120

C₂×Q₈

—

167

—

121

C₂×Q₈

—

167

—

122

C₂×Q₈

C₂×D₁₆₇

yes

characteristic

123

C₂×D₄

—

167

—

124

C₂×D₄

—

167

—

125

C₂×D₄

—

167

—

126

C₂²×C₄

—

167

—

127

C₂²×C₄

—

167

—

128

C₂²×C₄

C₂×D₁₆₇

yes

characteristic

129

C₄⋊C₄

—

167

—

130

C₄⋊C₄

—

167

—

131

C₄⋊C₄

—

167

—

132

C₄⋊C₄

—

167

—

133

C₄⋊C₄

—

167

—

134

C₄⋊C₄

—

167

—

135

C₄⋊C₄

—

167

—

136

C₄⋊C₄

C₂×D₁₆₇

yes

characteristic

137

C₄⋊C₄

C₂×D₁₆₇

yes

characteristic

138

C₄⋊C₄

C₂×D₁₆₇

yes

characteristic

139

C₂²⋊C₄

—

167

—

140

C₂²⋊C₄

—

167

—

141

C₂²⋊C₄

—

167

—

142

C₂²⋊C₄

—

167

—

143

C₂²⋊C₄

—

167

—

144

C₂²⋊C₄

—

167

—

145

C₂²⋊C₄

—

167

—

146

C₂²⋊C₄

—

167

—

147

C₂²⋊C₄

—

167

—

148

C₂²⋊C₄

—

167

—

149

C₂²⋊C₄

C₂×D₁₆₇

yes

characteristic

150

C₂²⋊C₄

C₂×D₁₆₇

yes

characteristic

151

C₄²

—

167

—

152

C₄²

—

167

—

153

C₄²

—

167

—

154

C₄²

—

167

—

155

C₂³

—

167

—

156

C₂³

—

167

—

157

C₂³

C₂²×D₁₆₇

yes

characteristic

158

Q₈

—

159

Q₈

—

334

—

160

Q₈

—

668

—

161

D₄

—

334

—

162

D₄

—

668

—

163

D₄

—

668

—

164

C₂×C₄

—

165

C₂×C₄

—

334

—

166

C₂×C₄

—

668

—

167

C₂×C₄

—

167

—

168

C₂×C₄

—

167

—

169

C₂×C₄

—

167

—

170

C₂×C₄

—

167

—

171

C₂×C₄

—

167

—

172

C₂×C₄

—

167

—

173

C₂×C₄

C₂²×D₁₆₇

yes

characteristic

174

C₂×C₄

C₂²×D₁₆₇

yes

characteristic

175

C₂×C₄

C₂²×D₁₆₇

yes

characteristic

176

C₂×C₄

C₂²×D₁₆₇

yes

characteristic

177

C₂×C₄

C₂²×D₁₆₇

yes

characteristic

178

C₂×C₄

C₂²×D₁₆₇

yes

characteristic

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

334

—

183

C₂²

—

334

—

184

C₂²

—

334

—

185

C₂²

—

334

—

186

C₂²

—

334

—

187

C₂²

—

334

—

188

C₂²

C₂³×D₁₆₇

yes

characteristic

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

334

—

196

C₄

—

334

—

197

C₄

—

334

—

198

C₄

—

334

—

199

C₄

—

334

—

200

C₄

—

167

—

201

C₂

—

202

C₂

—

668

—

203

C₂

—

668

—

204

C₂

#41×D₁₆₇

yes

characteristic

205

C₂

#19128877

yes

characteristic

206

C₂

#19128880

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₆₇
commutator, socle, cosocle	C₂²×C₁₆₇	C₂⁴
Fitting	C₂²⋊Q₈×C₁₆₇	C₂
prime radical	#19128805	C₂
hypercenter	C₂²⋊Q₈	D₁₆₇
hypocenter	C₁₆₇	#542
LCS	G ▷ C₂²×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₆₇

commutator, socle, cosocle

C₂²×C₁₆₇

C₂⁴

Fitting

C₂²⋊Q₈×C₁₆₇

C₂

prime radical

#19128805

C₂

hypercenter

C₂²⋊Q₈

D₁₆₇

C₁₆₇

G ▷ C₂²×C₁₆₇ ▷ C₁₆₇

C₁ ◁ C₂² ◁ C₂²⋊Q₈

N	H ≅ G/N	type
1. #19128830	C₂	semidirect
2. #19128827	C₂	semidirect
3. #19128825	C₂	semidirect
4. #19128821	C₂	semidirect
5. #19128818	C₂	semidirect
6. #19128818	C₂	semidirect
7. #19128817	C₂	semidirect
8. #19128815	C₂	semidirect
9. #19128810	C₂	semidirect
10. #19128810	C₂	semidirect
12. #19128797	C₂	semidirect
13. C₄×C₂²⋊D₁₆₇	C₂	semidirect
14. #19128790	C₂	semidirect
15. C₂²⋊Q₈×C₁₆₇	C₂	semidirect
103. C₁₆₇	#542	semidirect
115. C₂²⋊Q₈	D₁₆₇	semidirect

H ≅ G/N

type

1. #19128830

C₂

semidirect

2. #19128827

C₂

semidirect

3. #19128825

C₂

semidirect

4. #19128821

C₂

semidirect

5. #19128818

C₂

semidirect

6. #19128818

C₂

semidirect

7. #19128817

C₂

semidirect

8. #19128815

C₂

semidirect

9. #19128810

C₂

semidirect

10. #19128810

C₂

semidirect

12. #19128797

C₂

semidirect

13. C₄×C₂²⋊D₁₆₇

C₂

semidirect

14. #19128790

C₂

semidirect

15. C₂²⋊Q₈×C₁₆₇

C₂

semidirect

103. C₁₆₇

#542

semidirect

115. C₂²⋊Q₈

D₁₆₇

semidirect

Subgroups — #24923889

Conjugacy classes of subgroups

Complements