Group #34096167 — subgroups

Subgroups — #1809×C₁₅₇ #34096167

Order 20096.

316 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 136 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×M₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#107×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#106×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#380×C₁₅₇	C₂	1	2	yes	maximal
5	#340×C₁₅₇	C₂	1	2	yes	maximal, complemented
6	C₂³×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₅₇	—	2	2	no	—
8	C₂×M₁₆×C₁₅₇	—	2	2	no	—
9	C₂×M₁₆×C₁₅₇	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
14	C₂×C₂²⋊C₄×C₁₅₇	—	2	2	no	—
15	#107×C₁₅₇	—	2	2	no	—
16	#106×C₁₅₇	—	2	2	no	—
17	#95×C₁₅₇	—	2	2	no	—
18	C₂⁴×C₁₅₇	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₅₇	—	2	1	no	—
20	C₂²×C₄×C₁₅₇	—	2	1	no	—
21	C₂²×C₄×C₁₅₇	—	2	1	no	—
22	C₂²×C₄×C₁₅₇	—	2	1	no	—
23	C₂²×C₄×C₁₅₇	—	2	2	no	—
24	C₂²×C₄×C₁₅₇	—	2	2	no	—
25	C₂²×C₄×C₁₅₇	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₅₇	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₅₇	Q₈	1	2	yes	—
28	C₂²×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
29	M₁₆×C₁₅₇	—	2	8	no	—
30	C₂×C₈×C₁₅₇	—	2	1	no	—
31	C₂×C₈×C₁₅₇	—	2	1	no	—
32	C₂×C₈×C₁₅₇	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₁₅₇	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₁₅₇	D₄	1	2	yes	—
35	C₂×C₈×C₁₅₇	D₄	1	2	yes	—
36	C₄⋊C₄×C₁₅₇	—	2	2	no	—
37	C₄⋊C₄×C₁₅₇	—	2	2	no	—
38	C₄⋊C₄×C₁₅₇	—	2	2	no	—
39	C₄⋊C₄×C₁₅₇	—	2	2	no	—
40	C₂²⋊C₄×C₁₅₇	—	4	4	no	—
41	C₂³×C₁₅₇	—	2	1	no	—
42	C₂³×C₁₅₇	—	2	1	no	—
43	C₂³×C₁₅₇	—	2	2	no	—
44	C₂³×C₁₅₇	—	2	2	no	—
45	C₂³×C₁₅₇	C₄⋊C₄	1	2	yes	—
46	C₂³×C₁₅₇	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₅₇	—	2	1	no	—
48	C₂×C₄×C₁₅₇	—	2	1	no	—
49	C₂×C₄×C₁₅₇	—	2	2	no	—
50	C₂×C₄×C₁₅₇	—	2	2	no	—
51	C₂×C₄×C₁₅₇	—	2	2	no	—
52	C₂×C₄×C₁₅₇	—	2	2	no	—
53	C₂×C₄×C₁₅₇	—	4	2	no	—
54	C₂×C₄×C₁₅₇	—	4	2	no	—
55	C₂×C₄×C₁₅₇	—	4	2	no	—
56	C₂×C₄×C₁₅₇	—	4	2	no	—
57	C₂×C₄×C₁₅₇	—	4	2	no	—
58	C₂×C₄×C₁₅₇	—	4	2	no	—
59	C₂×C₄×C₁₅₇	C₄⋊C₄	1	2	yes	—
60	C₂×C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₅₇	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₄×C₁₅₇	#41	1	1	yes	characteristic
65	C₂×C₄×C₁₅₇	#41	1	1	yes	characteristic
66	C₈×C₁₅₇	—	2	2	no	—
67	C₈×C₁₅₇	C₂²⋊C₄	1	4	yes	complemented
68	C₂²×C₁₅₇	—	2	2	no	—
69	C₂²×C₁₅₇	—	2	4	no	—
70	C₂²×C₁₅₇	—	4	2	no	—
71	C₂²×C₁₅₇	—	4	1	no	—
72	C₂²×C₁₅₇	—	4	1	no	—
73	C₂²×C₁₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₁₅₇	#121	1	1	yes	characteristic
75	C₂²×C₁₅₇	#121	1	1	yes	characteristic
76	C₂²×C₁₅₇	AGL(1,ℤ/8)	1	2	yes	—
77	C₂²×C₁₅₇	#137	1	2	yes	—
78	C₄×C₁₅₇	—	2	2	no	—
79	C₄×C₁₅₇	—	8	2	no	—
80	C₄×C₁₅₇	—	8	2	no	—
81	C₄×C₁₅₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₄×C₁₅₇	#117	1	1	yes	characteristic
83	C₄×C₁₅₇	C₂²⋊Q₈	1	1	yes	characteristic
84	C₄×C₁₅₇	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₁₅₇	—	4	2	no	—
86	C₂×C₁₅₇	#380	1	1	yes	characteristic
87	C₂×C₁₅₇	#428	1	2	yes	—
88	C₂×C₁₅₇	#468	1	2	yes	—
89	C₂×C₁₅₇	#469	1	1	yes	characteristic
90	C₂×C₁₅₇	#470	1	1	yes	characteristic
91	C₁₅₇	#1809	1	1	yes	characteristic, direct product factor, Sylow
92	#1809	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂²×M₁₆	C₂×C₁₅₇	1	1	yes	characteristic
94	C₂×#107	C₂×C₁₅₇	1	1	yes	characteristic, complemented
95	C₂×#106	C₂×C₁₅₇	1	1	yes	characteristic, complemented
96	#380	C₂×C₁₅₇	1	2	yes	—
97	#340	C₂×C₁₅₇	1	2	yes	complemented
98	C₂³×C₄	C₂²×C₁₅₇	1	1	yes	characteristic
99	C₂×M₁₆	—	2	2	no	—
100	C₂×M₁₆	—	2	2	no	—
101	C₂×M₁₆	C₄×C₁₅₇	1	4	yes	complemented
102	C₂²×C₈	C₂²×C₁₅₇	1	1	yes	characteristic
103	C₂²×C₈	C₂²×C₁₅₇	1	1	yes	characteristic
104	C₂×C₄⋊C₄	C₂²×C₁₅₇	1	2	yes	—
105	C₂×C₄⋊C₄	C₂²×C₁₅₇	1	2	yes	—
106	C₂×C₂²⋊C₄	—	2	2	no	—
107	#107	—	2	2	no	—
108	#106	—	2	2	no	—
109	#95	—	2	2	no	—
110	C₂⁴	D₄×C₁₅₇	1	1	yes	characteristic
111	C₂²×C₄	—	2	1	no	—
112	C₂²×C₄	—	2	1	no	—
113	C₂²×C₄	—	2	1	no	—
114	C₂²×C₄	—	2	1	no	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	—	2	2	no	—
117	C₂²×C₄	C₂×C₄×C₁₅₇	1	2	yes	—
118	C₂²×C₄	D₄×C₁₅₇	1	1	yes	characteristic
119	C₂²×C₄	Q₈×C₁₅₇	1	2	yes	—
120	C₂²×C₄	C₂³×C₁₅₇	1	1	yes	characteristic
121	M₁₆	—	2	8	no	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	2	1	no	—
124	C₂×C₈	C₂×C₄×C₁₅₇	1	2	yes	—
125	C₂×C₈	C₂×C₄×C₁₅₇	1	2	yes	—
126	C₂×C₈	D₄×C₁₅₇	1	2	yes	—
127	C₂×C₈	D₄×C₁₅₇	1	2	yes	—
128	C₄⋊C₄	—	2	2	no	—
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	2	2	no	—
131	C₄⋊C₄	—	2	2	no	—
132	C₂²⋊C₄	—	4	4	no	—
133	C₂³	—	2	1	no	—
134	C₂³	—	2	1	no	—
135	C₂³	—	2	2	no	—
136	C₂³	—	2	2	no	—
137	C₂³	C₄⋊C₄×C₁₅₇	1	2	yes	—
138	C₂³	C₂×D₄×C₁₅₇	1	1	yes	characteristic
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	4	2	no	—
146	C₂×C₄	—	4	2	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	—	4	2	no	—
151	C₂×C₄	C₄⋊C₄×C₁₅₇	1	2	yes	—
152	C₂×C₄	C₂²×C₄×C₁₅₇	1	1	yes	characteristic
153	C₂×C₄	C₂×D₄×C₁₅₇	1	1	yes	characteristic
154	C₂×C₄	C₂×D₄×C₁₅₇	1	1	yes	characteristic
155	C₂×C₄	C₂×Q₈×C₁₅₇	1	1	yes	characteristic
156	C₂×C₄	#41×C₁₅₇	1	1	yes	characteristic
157	C₂×C₄	#41×C₁₅₇	1	1	yes	characteristic
158	C₈	—	2	2	no	—
159	C₈	C₂²⋊C₄×C₁₅₇	1	4	yes	complemented
160	C₂²	—	2	4	no	—
161	C₂²	—	2	2	no	—
162	C₂²	—	4	2	no	—
163	C₂²	—	4	1	no	—
164	C₂²	—	4	1	no	—
165	C₂²	C₂×C₄⋊C₄×C₁₅₇	1	1	yes	characteristic
166	C₂²	#121×C₁₅₇	1	1	yes	characteristic
167	C₂²	#121×C₁₅₇	1	1	yes	characteristic
168	C₂²	AGL(1,ℤ/8)×C₁₅₇	1	2	yes	—
169	C₂²	#137×C₁₅₇	1	2	yes	—
170	C₄	—	2	2	no	—
171	C₄	—	8	2	no	—
172	C₄	—	8	2	no	—
173	C₄	C₂×C₂²⋊C₄×C₁₅₇	1	1	yes	characteristic
174	C₄	#117×C₁₅₇	1	1	yes	characteristic
175	C₄	C₂²⋊Q₈×C₁₅₇	1	1	yes	characteristic
176	C₄	C₂²⋊Q₈×C₁₅₇	1	1	yes	characteristic
177	C₂	—	4	2	no	—
178	C₂	#380×C₁₅₇	1	1	yes	characteristic
179	C₂	#428×C₁₅₇	1	2	yes	—
180	C₂	#468×C₁₅₇	1	2	yes	—
181	C₂	#469×C₁₅₇	1	1	yes	characteristic
182	C₂	#470×C₁₅₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×M₁₆×C₁₅₇

C₂

yes

maximal, characteristic

C₂×#107×C₁₅₇

C₂

yes

maximal, characteristic, complemented

C₂×#106×C₁₅₇

C₂

yes

maximal, characteristic, complemented

#380×C₁₅₇

C₂

yes

maximal

#340×C₁₅₇

C₂

yes

maximal, complemented

C₂³×C₄×C₁₅₇

C₂²

yes

characteristic

C₂×M₁₆×C₁₅₇

—

C₂×M₁₆×C₁₅₇

—

C₂×M₁₆×C₁₅₇

C₄

yes

complemented

C₂²×C₈×C₁₅₇

C₂²

yes

characteristic

C₂²×C₈×C₁₅₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₅₇

C₂²

yes

—

C₂×C₄⋊C₄×C₁₅₇

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₅₇

—

#107×C₁₅₇

—

#106×C₁₅₇

—

#95×C₁₅₇

—

C₂⁴×C₁₅₇

D₄

yes

characteristic

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

—

C₂²×C₄×C₁₅₇

C₂×C₄

yes

—

C₂²×C₄×C₁₅₇

D₄

yes

characteristic

C₂²×C₄×C₁₅₇

Q₈

yes

—

C₂²×C₄×C₁₅₇

C₂³

yes

characteristic

M₁₆×C₁₅₇

—

C₂×C₈×C₁₅₇

—

C₂×C₈×C₁₅₇

—

C₂×C₈×C₁₅₇

C₂×C₄

yes

—

C₂×C₈×C₁₅₇

C₂×C₄

yes

—

C₂×C₈×C₁₅₇

D₄

yes

—

C₂×C₈×C₁₅₇

D₄

yes

—

C₄⋊C₄×C₁₅₇

—

C₄⋊C₄×C₁₅₇

—

C₄⋊C₄×C₁₅₇

—

C₄⋊C₄×C₁₅₇

—

C₂²⋊C₄×C₁₅₇

—

C₂³×C₁₅₇

—

C₂³×C₁₅₇

—

C₂³×C₁₅₇

—

C₂³×C₁₅₇

—

C₂³×C₁₅₇

C₄⋊C₄

yes

—

C₂³×C₁₅₇

C₂×D₄

yes

characteristic

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×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₅₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₅₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₅₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₅₇

C₂×Q₈

yes

C₂×C₄×C₁₅₇

yes

C₂×C₄×C₁₅₇

yes

C₈×C₁₅₇

—

C₈×C₁₅₇

C₂²⋊C₄

yes

complemented

C₂²×C₁₅₇

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

C₂×C₄⋊C₄

yes

C₂²×C₁₅₇

yes

C₂²×C₁₅₇

yes

C₂²×C₁₅₇

yes

—

C₂²×C₁₅₇

#137

yes

—

C₄×C₁₅₇

—

C₄×C₁₅₇

—

C₄×C₁₅₇

—

C₄×C₁₅₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₅₇

#117

yes

characteristic

C₄×C₁₅₇

C₂²⋊Q₈

yes

characteristic

C₄×C₁₅₇

C₂²⋊Q₈

yes

characteristic

C₂×C₁₅₇

—

C₂×C₁₅₇

#380

yes

characteristic

C₂×C₁₅₇

#428

yes

—

C₂×C₁₅₇

#468

yes

—

C₂×C₁₅₇

yes

C₂×C₁₅₇

yes

C₁₅₇

yes

characteristic, direct product factor, Sylow

#1809

C₁₅₇

yes

maximal, characteristic, direct product factor, Sylow

C₂²×M₁₆

C₂×C₁₅₇

yes

characteristic

C₂×#107

C₂×C₁₅₇

yes

characteristic, complemented

C₂×#106

C₂×C₁₅₇

yes

characteristic, complemented

#380

C₂×C₁₅₇

yes

—

#340

C₂×C₁₅₇

yes

complemented

C₂³×C₄

C₂²×C₁₅₇

yes

characteristic

C₂×M₁₆

—

100

C₂×M₁₆

—

101

C₂×M₁₆

C₄×C₁₅₇

yes

complemented

102

C₂²×C₈

C₂²×C₁₅₇

yes

characteristic

103

C₂²×C₈

C₂²×C₁₅₇

yes

characteristic

104

C₂×C₄⋊C₄

C₂²×C₁₅₇

yes

—

105

C₂×C₄⋊C₄

C₂²×C₁₅₇

yes

—

106

C₂×C₂²⋊C₄

—

107

#107

—

108

#106

—

109

#95

—

110

C₂⁴

D₄×C₁₅₇

yes

characteristic

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂×C₄×C₁₅₇

yes

—

118

C₂²×C₄

D₄×C₁₅₇

yes

characteristic

119

C₂²×C₄

Q₈×C₁₅₇

yes

—

120

C₂²×C₄

C₂³×C₁₅₇

yes

characteristic

121

M₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

C₂×C₄×C₁₅₇

yes

—

125

C₂×C₈

C₂×C₄×C₁₅₇

yes

—

126

C₂×C₈

D₄×C₁₅₇

yes

—

127

C₂×C₈

D₄×C₁₅₇

yes

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₂²⋊C₄

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

C₄⋊C₄×C₁₅₇

yes

—

138

C₂³

C₂×D₄×C₁₅₇

yes

characteristic

139

C₂×C₄

—

140

C₂×C₄

—

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

—

150

C₂×C₄

—

151

C₂×C₄

C₄⋊C₄×C₁₅₇

yes

—

152

C₂×C₄

C₂²×C₄×C₁₅₇

yes

characteristic

153

C₂×C₄

C₂×D₄×C₁₅₇

yes

characteristic

154

C₂×C₄

C₂×D₄×C₁₅₇

yes

characteristic

155

C₂×C₄

C₂×Q₈×C₁₅₇

yes

characteristic

156

C₂×C₄

#41×C₁₅₇

yes

characteristic

157

C₂×C₄

#41×C₁₅₇

yes

characteristic

158

C₈

—

159

C₈

C₂²⋊C₄×C₁₅₇

yes

complemented

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

—

164

C₂²

—

165

C₂²

C₂×C₄⋊C₄×C₁₅₇

yes

characteristic

166

C₂²

#121×C₁₅₇

yes

characteristic

167

C₂²

#121×C₁₅₇

yes

characteristic

168

C₂²

AGL(1,ℤ/8)×C₁₅₇

yes

—

169

C₂²

#137×C₁₅₇

yes

—

170

C₄

—

171

C₄

—

172

C₄

—

173

C₄

C₂×C₂²⋊C₄×C₁₅₇

yes

characteristic

174

C₄

#117×C₁₅₇

yes

characteristic

175

C₄

C₂²⋊Q₈×C₁₅₇

yes

characteristic

176

C₄

C₂²⋊Q₈×C₁₅₇

yes

characteristic

177

C₂

—

178

C₂

#380×C₁₅₇

yes

characteristic

179

C₂

#428×C₁₅₇

yes

—

180

C₂

#468×C₁₅₇

yes

—

181

C₂

#469×C₁₅₇

yes

characteristic

182

C₂

#470×C₁₅₇

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₅₇
Frattini, cosocle	C₂²×C₄	C₂³×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

C₂×C₄

C₂²×C₄×C₁₅₇

Frattini, cosocle

C₂²×C₄

C₂³×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
2. C₂×#107×C₁₅₇	C₂	semidirect
3. C₂×#106×C₁₅₇	C₂	semidirect
5. #340×C₁₅₇	C₂	semidirect
9. C₂×M₁₆×C₁₅₇	C₄	semidirect
67. C₈×C₁₅₇	C₂²⋊C₄	semidirect
91. C₁₅₇	#1809	direct (N × H)
92. #1809	C₁₅₇	direct (N × H)
94. C₂×#107	C₂×C₁₅₇	semidirect
95. C₂×#106	C₂×C₁₅₇	semidirect
97. #340	C₂×C₁₅₇	semidirect
101. C₂×M₁₆	C₄×C₁₅₇	semidirect
159. C₈	C₂²⋊C₄×C₁₅₇	semidirect

H ≅ G/N

type

2. C₂×#107×C₁₅₇

C₂

semidirect

3. C₂×#106×C₁₅₇

C₂

semidirect

5. #340×C₁₅₇

C₂

semidirect

9. C₂×M₁₆×C₁₅₇

C₄

semidirect

67. C₈×C₁₅₇

C₂²⋊C₄

semidirect

91. C₁₅₇

#1809

direct (N × H)

92. #1809

C₁₅₇

direct (N × H)

94. C₂×#107

C₂×C₁₅₇

semidirect

95. C₂×#106

C₂×C₁₅₇

semidirect

97. #340

C₂×C₁₅₇

semidirect

101. C₂×M₁₆

C₄×C₁₅₇

semidirect

159. C₈

C₂²⋊C₄×C₁₅₇

semidirect

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

subgroup	index
C₂²×M₁₆×C₁₅₇	2
C₂×#107×C₁₅₇	2
C₂×#106×C₁₅₇	2
#380×C₁₅₇	2
#340×C₁₅₇	2
#1809	157

subgroup

index

C₂²×M₁₆×C₁₅₇

C₂×#107×C₁₅₇

C₂×#106×C₁₅₇

#380×C₁₅₇

#340×C₁₅₇

#1809

157

Subgroups — #1809×C₁₅₇ #34096167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1809×C157 #34096167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1809×C₁₅₇ #34096167