Group #34097407 — subgroups

Subgroups — C₂×#467×C₁₅₇ #34097407

Order 20096.

512 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 232 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	C₂²×Q₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₈×C₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊Q₈×C₁₅₇	C₂	1	2	yes	maximal
4	#467×C₁₅₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×#107×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#103×C₁₅₇	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₈×C₁₅₇	C₂²	1	2	yes	—
8	C₂³×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
9	C₂×Q₁₆×C₁₅₇	—	2	4	no	—
10	C₂×Q₁₆×C₁₅₇	C₂²	1	4	yes	complemented
11	C₂²×C₈×C₁₅₇	—	2	4	no	—
12	C₂²×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₅₇	C₂²	1	4	yes	—
14	C₂²×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
15	C₂²⋊Q₈×C₁₅₇	—	2	4	no	—
16	C₂²⋊Q₈×C₁₅₇	C₂²	1	8	yes	—
17	C₂×C₄⋊C₄×C₁₅₇	—	2	2	no	—
18	C₂×C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₄×C₁₅₇	—	2	2	no	—
20	#107×C₁₅₇	C₂²	1	4	yes	complemented
21	#103×C₁₅₇	C₂²	1	8	yes	complemented
22	C₂⁴×C₁₅₇	D₄	1	1	yes	characteristic
23	C₂×Q₈×C₁₅₇	—	2	2	no	—
24	C₂×Q₈×C₁₅₇	—	2	4	no	—
25	C₂×Q₈×C₁₅₇	—	2	4	no	—
26	C₂×Q₈×C₁₅₇	C₂³	1	4	yes	—
27	C₂²×C₄×C₁₅₇	—	2	2	no	—
28	C₂²×C₄×C₁₅₇	—	2	2	no	—
29	C₂²×C₄×C₁₅₇	—	2	2	no	—
30	C₂²×C₄×C₁₅₇	—	2	2	no	—
31	C₂²×C₄×C₁₅₇	D₄	1	2	yes	—
32	C₂²×C₄×C₁₅₇	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₅₇	C₂³	1	2	yes	—
34	C₂²×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
35	Q₁₆×C₁₅₇	—	2	8	no	—
36	C₂×C₈×C₁₅₇	—	2	2	no	—
37	C₂×C₈×C₁₅₇	—	2	8	no	—
38	C₂×C₈×C₁₅₇	D₄	1	4	yes	—
39	C₂×C₈×C₁₅₇	C₂³	1	2	yes	—
40	C₂×C₈×C₁₅₇	C₂³	1	2	yes	—
41	C₄⋊C₄×C₁₅₇	—	2	8	no	—
42	C₄⋊C₄×C₁₅₇	—	2	2	no	—
43	C₄⋊C₄×C₁₅₇	C₂³	1	4	yes	—
44	C₂²⋊C₄×C₁₅₇	—	2	8	no	—
45	C₂³×C₁₅₇	—	2	2	no	—
46	C₂³×C₁₅₇	—	2	2	no	—
47	C₂³×C₁₅₇	Q₁₆	1	4	yes	complemented
48	C₂³×C₁₅₇	C₂×D₄	1	2	yes	—
49	C₂³×C₁₅₇	C₂×D₄	1	1	yes	characteristic
50	Q₈×C₁₅₇	—	2	4	no	—
51	Q₈×C₁₅₇	—	2	4	no	—
52	Q₈×C₁₅₇	—	4	4	no	—
53	C₂×C₄×C₁₅₇	—	2	2	no	—
54	C₂×C₄×C₁₅₇	—	2	4	no	—
55	C₂×C₄×C₁₅₇	—	2	2	no	—
56	C₂×C₄×C₁₅₇	—	2	2	no	—
57	C₂×C₄×C₁₅₇	—	2	4	no	—
58	C₂×C₄×C₁₅₇	—	2	4	no	—
59	C₂×C₄×C₁₅₇	—	4	4	no	—
60	C₂×C₄×C₁₅₇	—	4	4	no	—
61	C₂×C₄×C₁₅₇	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₅₇	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₁₅₇	#41	1	2	yes	—
65	C₂×C₄×C₁₅₇	C₂⁴	1	1	yes	characteristic
66	C₈×C₁₅₇	—	2	2	no	—
67	C₈×C₁₅₇	C₂×D₄	1	4	yes	—
68	C₂²×C₁₅₇	—	2	2	no	—
69	C₂²×C₁₅₇	—	2	2	no	—
70	C₂²×C₁₅₇	—	2	8	no	—
71	C₂²×C₁₅₇	#121	1	2	yes	—
72	C₂²×C₁₅₇	C₂×Q₁₆	1	2	yes	—
73	C₂²×C₁₅₇	C₂×Q₁₆	1	4	yes	complemented
74	C₂²×C₁₅₇	#135	1	2	yes	—
75	C₂²×C₁₅₇	C₂²×D₄	1	1	yes	characteristic
76	C₄×C₁₅₇	—	2	2	no	—
77	C₄×C₁₅₇	—	4	4	no	—
78	C₄×C₁₅₇	—	4	4	no	—
79	C₄×C₁₅₇	#121	1	2	yes	—
80	C₄×C₁₅₇	C₂²×D₄	1	1	yes	characteristic
81	C₄×C₁₅₇	C₂×#41	1	1	yes	characteristic
82	C₂×C₁₅₇	—	2	4	no	—
83	C₂×C₁₅₇	#467	1	4	yes	direct product factor
84	C₂×C₁₅₇	C₂×#121	1	1	yes	characteristic
85	C₂×C₁₅₇	C₂²×Q₁₆	1	1	yes	characteristic
86	C₂×C₁₅₇	C₂×#135	1	1	yes	characteristic
87	C₁₅₇	C₂×#467	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×#467	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂²×Q₁₆	C₂×C₁₅₇	1	1	yes	characteristic, complemented
90	C₂³×C₈	C₂×C₁₅₇	1	1	yes	characteristic
91	C₂×C₂²⋊Q₈	C₂×C₁₅₇	1	2	yes	—
92	#467	C₂×C₁₅₇	1	8	yes	direct product factor
93	C₂×#107	C₂×C₁₅₇	1	1	yes	characteristic, complemented
94	C₂×#103	C₂×C₁₅₇	1	2	yes	complemented
95	C₂²×Q₈	C₂²×C₁₅₇	1	2	yes	—
96	C₂³×C₄	C₂²×C₁₅₇	1	1	yes	characteristic
97	C₂×Q₁₆	—	2	4	no	—
98	C₂×Q₁₆	C₂²×C₁₅₇	1	4	yes	complemented
99	C₂²×C₈	—	2	4	no	—
100	C₂²×C₈	C₂²×C₁₅₇	1	1	yes	characteristic
101	C₂²×C₈	C₂²×C₁₅₇	1	4	yes	—
102	C₂²×C₈	C₂²×C₁₅₇	1	1	yes	characteristic
103	C₂²⋊Q₈	—	2	4	no	—
104	C₂²⋊Q₈	C₂²×C₁₅₇	1	8	yes	—
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	C₂²×C₁₅₇	1	2	yes	—
107	C₂×C₂²⋊C₄	—	2	2	no	—
108	#107	C₂²×C₁₅₇	1	4	yes	complemented
109	#103	C₂²×C₁₅₇	1	8	yes	complemented
110	C₂⁴	D₄×C₁₅₇	1	1	yes	characteristic
111	C₂×Q₈	—	2	2	no	—
112	C₂×Q₈	—	2	4	no	—
113	C₂×Q₈	—	2	4	no	—
114	C₂×Q₈	C₂³×C₁₅₇	1	4	yes	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	—	2	2	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	2	2	no	—
119	C₂²×C₄	D₄×C₁₅₇	1	1	yes	characteristic
120	C₂²×C₄	D₄×C₁₅₇	1	2	yes	—
121	C₂²×C₄	C₂³×C₁₅₇	1	2	yes	—
122	C₂²×C₄	C₂³×C₁₅₇	1	1	yes	characteristic
123	Q₁₆	—	2	8	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	2	8	no	—
126	C₂×C₈	D₄×C₁₅₇	1	4	yes	—
127	C₂×C₈	C₂³×C₁₅₇	1	2	yes	—
128	C₂×C₈	C₂³×C₁₅₇	1	2	yes	—
129	C₄⋊C₄	—	2	8	no	—
130	C₄⋊C₄	—	2	2	no	—
131	C₄⋊C₄	C₂³×C₁₅₇	1	4	yes	—
132	C₂²⋊C₄	—	2	8	no	—
133	C₂³	—	2	2	no	—
134	C₂³	—	2	2	no	—
135	C₂³	Q₁₆×C₁₅₇	1	4	yes	complemented
136	C₂³	C₂×D₄×C₁₅₇	1	2	yes	—
137	C₂³	C₂×D₄×C₁₅₇	1	1	yes	characteristic
138	Q₈	—	2	4	no	—
139	Q₈	—	2	4	no	—
140	Q₈	—	4	4	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	4	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	4	4	no	—
148	C₂×C₄	—	4	4	no	—
149	C₂×C₄	C₂×D₄×C₁₅₇	1	2	yes	—
150	C₂×C₄	C₂×D₄×C₁₅₇	1	1	yes	characteristic
151	C₂×C₄	C₂×D₄×C₁₅₇	1	2	yes	—
152	C₂×C₄	#41×C₁₅₇	1	2	yes	—
153	C₂×C₄	C₂⁴×C₁₅₇	1	1	yes	characteristic
154	C₈	—	2	2	no	—
155	C₈	C₂×D₄×C₁₅₇	1	4	yes	—
156	C₂²	—	2	8	no	—
157	C₂²	—	2	2	no	—
158	C₂²	—	2	2	no	—
159	C₂²	#121×C₁₅₇	1	2	yes	—
160	C₂²	C₂×Q₁₆×C₁₅₇	1	2	yes	—
161	C₂²	C₂×Q₁₆×C₁₅₇	1	4	yes	complemented
162	C₂²	#135×C₁₅₇	1	2	yes	—
163	C₂²	C₂²×D₄×C₁₅₇	1	1	yes	characteristic
164	C₄	—	2	2	no	—
165	C₄	—	4	4	no	—
166	C₄	—	4	4	no	—
167	C₄	#121×C₁₅₇	1	2	yes	—
168	C₄	C₂²×D₄×C₁₅₇	1	1	yes	characteristic
169	C₄	C₂×#41×C₁₅₇	1	1	yes	characteristic
170	C₂	—	2	4	no	—
171	C₂	#467×C₁₅₇	1	4	yes	direct product factor
172	C₂	C₂×#121×C₁₅₇	1	1	yes	characteristic
173	C₂	C₂²×Q₁₆×C₁₅₇	1	1	yes	characteristic
174	C₂	C₂×#135×C₁₅₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₁₆×C₁₅₇

C₂

yes

maximal, characteristic, complemented

C₂³×C₈×C₁₅₇

C₂

yes

maximal, characteristic

C₂×C₂²⋊Q₈×C₁₅₇

C₂

yes

maximal

#467×C₁₅₇

C₂

yes

maximal, direct product factor

C₂×#107×C₁₅₇

C₂

yes

maximal, characteristic, complemented

C₂×#103×C₁₅₇

C₂

yes

maximal, complemented

C₂²×Q₈×C₁₅₇

C₂²

yes

—

C₂³×C₄×C₁₅₇

C₂²

yes

characteristic

C₂×Q₁₆×C₁₅₇

—

C₂×Q₁₆×C₁₅₇

C₂²

yes

complemented

C₂²×C₈×C₁₅₇

—

C₂²×C₈×C₁₅₇

C₂²

yes

characteristic

C₂²×C₈×C₁₅₇

C₂²

yes

—

C₂²×C₈×C₁₅₇

C₂²

yes

characteristic

C₂²⋊Q₈×C₁₅₇

—

C₂²⋊Q₈×C₁₅₇

C₂²

yes

—

C₂×C₄⋊C₄×C₁₅₇

—

C₂×C₄⋊C₄×C₁₅₇

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₅₇

—

#107×C₁₅₇

C₂²

yes

complemented

#103×C₁₅₇

C₂²

yes

complemented

C₂⁴×C₁₅₇

D₄

yes

characteristic

C₂×Q₈×C₁₅₇

—

C₂×Q₈×C₁₅₇

—

C₂×Q₈×C₁₅₇

—

C₂×Q₈×C₁₅₇

C₂³

yes

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

D₄

yes

—

C₂²×C₄×C₁₅₇

D₄

yes

characteristic

C₂²×C₄×C₁₅₇

C₂³

yes

—

C₂²×C₄×C₁₅₇

C₂³

yes

characteristic

Q₁₆×C₁₅₇

—

C₂×C₈×C₁₅₇

—

C₂×C₈×C₁₅₇

—

C₂×C₈×C₁₅₇

D₄

yes

—

C₂×C₈×C₁₅₇

C₂³

yes

—

C₂×C₈×C₁₅₇

C₂³

yes

—

C₄⋊C₄×C₁₅₇

—

C₄⋊C₄×C₁₅₇

—

C₄⋊C₄×C₁₅₇

C₂³

yes

—

C₂²⋊C₄×C₁₅₇

—

C₂³×C₁₅₇

—

C₂³×C₁₅₇

—

C₂³×C₁₅₇

Q₁₆

yes

complemented

C₂³×C₁₅₇

C₂×D₄

yes

—

C₂³×C₁₅₇

C₂×D₄

yes

characteristic

Q₈×C₁₅₇

—

Q₈×C₁₅₇

—

Q₈×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

C₂×D₄

yes

—

C₂×C₄×C₁₅₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₅₇

C₂×D₄

yes

—

C₂×C₄×C₁₅₇

#41

yes

—

C₂×C₄×C₁₅₇

C₂⁴

yes

characteristic

C₈×C₁₅₇

—

C₈×C₁₅₇

C₂×D₄

yes

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

#121

yes

—

C₂²×C₁₅₇

C₂×Q₁₆

yes

—

C₂²×C₁₅₇

C₂×Q₁₆

yes

complemented

C₂²×C₁₅₇

#135

yes

—

C₂²×C₁₅₇

C₂²×D₄

yes

characteristic

C₄×C₁₅₇

—

C₄×C₁₅₇

—

C₄×C₁₅₇

—

C₄×C₁₅₇

#121

yes

—

C₄×C₁₅₇

C₂²×D₄

yes

characteristic

C₄×C₁₅₇

C₂×#41

yes

characteristic

C₂×C₁₅₇

—

C₂×C₁₅₇

#467

yes

direct product factor

C₂×C₁₅₇

C₂×#121

yes

characteristic

C₂×C₁₅₇

C₂²×Q₁₆

yes

C₂×C₁₅₇

yes

C₁₅₇

yes

characteristic, direct product factor, Sylow

C₂×#467

C₁₅₇

yes

maximal, characteristic, direct product factor, Sylow

C₂²×Q₁₆

C₂×C₁₅₇

yes

characteristic, complemented

C₂³×C₈

C₂×C₁₅₇

yes

characteristic

C₂×C₂²⋊Q₈

C₂×C₁₅₇

yes

—

#467

C₂×C₁₅₇

yes

direct product factor

C₂×#107

C₂×C₁₅₇

yes

characteristic, complemented

C₂×#103

C₂×C₁₅₇

yes

complemented

C₂²×Q₈

C₂²×C₁₅₇

yes

—

C₂³×C₄

C₂²×C₁₅₇

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

C₂²×C₁₅₇

yes

complemented

C₂²×C₈

—

100

C₂²×C₈

C₂²×C₁₅₇

yes

characteristic

101

C₂²×C₈

C₂²×C₁₅₇

yes

—

102

C₂²×C₈

C₂²×C₁₅₇

yes

characteristic

103

C₂²⋊Q₈

—

104

C₂²⋊Q₈

C₂²×C₁₅₇

yes

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

C₂²×C₁₅₇

yes

—

107

C₂×C₂²⋊C₄

—

108

#107

C₂²×C₁₅₇

yes

complemented

109

#103

C₂²×C₁₅₇

yes

complemented

110

C₂⁴

D₄×C₁₅₇

yes

characteristic

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

C₂³×C₁₅₇

yes

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

D₄×C₁₅₇

yes

characteristic

120

C₂²×C₄

D₄×C₁₅₇

yes

—

121

C₂²×C₄

C₂³×C₁₅₇

yes

—

122

C₂²×C₄

C₂³×C₁₅₇

yes

characteristic

123

Q₁₆

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

D₄×C₁₅₇

yes

—

127

C₂×C₈

C₂³×C₁₅₇

yes

—

128

C₂×C₈

C₂³×C₁₅₇

yes

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

C₂³×C₁₅₇

yes

—

132

C₂²⋊C₄

—

133

C₂³

—

134

C₂³

—

135

C₂³

Q₁₆×C₁₅₇

yes

complemented

136

C₂³

C₂×D₄×C₁₅₇

yes

—

137

C₂³

C₂×D₄×C₁₅₇

yes

characteristic

138

Q₈

—

139

Q₈

—

140

Q₈

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

C₂×D₄×C₁₅₇

yes

—

150

C₂×C₄

C₂×D₄×C₁₅₇

yes

characteristic

151

C₂×C₄

C₂×D₄×C₁₅₇

yes

—

152

C₂×C₄

#41×C₁₅₇

yes

—

153

C₂×C₄

C₂⁴×C₁₅₇

yes

characteristic

154

C₈

—

155

C₈

C₂×D₄×C₁₅₇

yes

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

#121×C₁₅₇

yes

—

160

C₂²

C₂×Q₁₆×C₁₅₇

yes

—

161

C₂²

C₂×Q₁₆×C₁₅₇

yes

complemented

162

C₂²

#135×C₁₅₇

yes

—

163

C₂²

C₂²×D₄×C₁₅₇

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

#121×C₁₅₇

yes

—

168

C₄

C₂²×D₄×C₁₅₇

yes

characteristic

169

C₄

C₂×#41×C₁₅₇

yes

characteristic

170

C₂

—

171

C₂

#467×C₁₅₇

yes

direct product factor

172

C₂

C₂×#121×C₁₅₇

yes

characteristic

173

C₂

C₂²×Q₁₆×C₁₅₇

yes

characteristic

174

C₂

C₂×#135×C₁₅₇

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₅₇
prime radical	C₂⁴×C₁₅₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₇ ◁ C₂³×C₄×C₁₅₇ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₅₇

C₂×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₁₅₇

prime radical

C₂⁴×C₁₅₇

D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₅₇ ◁ C₂³×C₄×C₁₅₇ ◁ G

N	H ≅ G/N	type
1. C₂²×Q₁₆×C₁₅₇	C₂	semidirect
4. #467×C₁₅₇	C₂	direct (N × H)
5. C₂×#107×C₁₅₇	C₂	semidirect
6. C₂×#103×C₁₅₇	C₂	semidirect
10. C₂×Q₁₆×C₁₅₇	C₂²	semidirect
20. #107×C₁₅₇	C₂²	semidirect
21. #103×C₁₅₇	C₂²	semidirect
47. C₂³×C₁₅₇	Q₁₆	semidirect
73. C₂²×C₁₅₇	C₂×Q₁₆	semidirect
83. C₂×C₁₅₇	#467	direct (N × H)
87. C₁₅₇	C₂×#467	direct (N × H)
88. C₂×#467	C₁₅₇	direct (N × H)
89. C₂²×Q₁₆	C₂×C₁₅₇	semidirect
92. #467	C₂×C₁₅₇	direct (N × H)
93. C₂×#107	C₂×C₁₅₇	semidirect
94. C₂×#103	C₂×C₁₅₇	semidirect
98. C₂×Q₁₆	C₂²×C₁₅₇	semidirect
108. #107	C₂²×C₁₅₇	semidirect
109. #103	C₂²×C₁₅₇	semidirect
135. C₂³	Q₁₆×C₁₅₇	semidirect
161. C₂²	C₂×Q₁₆×C₁₅₇	semidirect
171. C₂	#467×C₁₅₇	direct (N × H)

H ≅ G/N

type

1. C₂²×Q₁₆×C₁₅₇

C₂

semidirect

4. #467×C₁₅₇

C₂

direct (N × H)

5. C₂×#107×C₁₅₇

C₂

semidirect

6. C₂×#103×C₁₅₇

C₂

semidirect

10. C₂×Q₁₆×C₁₅₇

C₂²

semidirect

20. #107×C₁₅₇

C₂²

semidirect

21. #103×C₁₅₇

C₂²

semidirect

47. C₂³×C₁₅₇

Q₁₆

semidirect

73. C₂²×C₁₅₇

C₂×Q₁₆

semidirect

83. C₂×C₁₅₇

#467

direct (N × H)

87. C₁₅₇

C₂×#467

direct (N × H)

88. C₂×#467

C₁₅₇

direct (N × H)

89. C₂²×Q₁₆

C₂×C₁₅₇

semidirect

92. #467

C₂×C₁₅₇

direct (N × H)

93. C₂×#107

C₂×C₁₅₇

semidirect

94. C₂×#103

C₂×C₁₅₇

semidirect

98. C₂×Q₁₆

C₂²×C₁₅₇

semidirect

108. #107

C₂²×C₁₅₇

semidirect

109. #103

C₂²×C₁₅₇

semidirect

135. C₂³

Q₁₆×C₁₅₇

semidirect

161. C₂²

C₂×Q₁₆×C₁₅₇

semidirect

171. C₂

#467×C₁₅₇

direct (N × H)

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

subgroup	index
C₂²×Q₁₆×C₁₅₇	2
C₂³×C₈×C₁₅₇	2
C₂×C₂²⋊Q₈×C₁₅₇	2
#467×C₁₅₇	2
C₂×#107×C₁₅₇	2
C₂×#103×C₁₅₇	2
C₂×#467	157

subgroup

index

C₂²×Q₁₆×C₁₅₇

C₂³×C₈×C₁₅₇

C₂×C₂²⋊Q₈×C₁₅₇

#467×C₁₅₇

C₂×#107×C₁₅₇

C₂×#103×C₁₅₇

C₂×#467

157

Subgroups — C₂×#467×C₁₅₇ #34097407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#467×C157 #34097407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#467×C₁₅₇ #34097407