Group #24916248 — subgroups

Subgroups — C₂×#19127806 #24916248

Order 10624.

480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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×#13050580	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic
3	#19127806	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14581723	C₂	1	1	yes	maximal, characteristic
5	C₂×#14581716	C₂	1	1	yes	maximal, characteristic
6	C₂×#14581715	C₂	1	1	yes	maximal, characteristic
7	C₂×#14581703	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Q₈×C₈₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₁₆₆	C₂²	1	1	yes	characteristic
10	C₂×#13050580	C₄	1	8	yes	complemented
11	C₂×#13050580	C₂²	1	4	yes	—
12	C₂²×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₄×Dic₁₆₆	—	2	2	no	—
15	C₄×Dic₁₆₆	C₂²	1	4	yes	—
16	C₂×C₄⋊Dic₈₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₈₃⋊C₄	—	2	1	no	—
18	C₂×C₄×Dic₈₃	—	2	1	no	—
19	#14581723	C₂²	1	4	yes	—
20	#14581716	C₂²	1	4	yes	—
21	#14581715	C₂²	1	4	yes	—
22	#14581703	C₂²	1	4	yes	—
23	C₂²×Q₈×C₈₃	C₂²	1	1	yes	characteristic
24	C₄×Q₈×C₈₃	—	2	2	no	—
25	C₄×Q₈×C₈₃	C₂²	1	4	yes	—
26	C₂×C₄⋊C₄×C₈₃	—	2	1	no	—
27	C₂×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₈₃	—	2	1	no	—
29	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
30	C₂×Dic₁₆₆	—	2	1	no	—
31	C₂×Dic₁₆₆	—	2	2	no	—
32	C₂×Dic₁₆₆	C₂×C₄	1	4	yes	—
33	C₂×Dic₁₆₆	C₂³	1	2	yes	—
34	C₂²×Dic₈₃	—	2	1	no	—
35	C₂²×Dic₈₃	—	2	1	no	—
36	#13050580	C₂×C₄	1	16	yes	complemented
37	C₂×C₈₃⋊C₈	—	2	2	no	—
38	C₂×C₈₃⋊C₈	C₂×C₄	1	4	yes	—
39	C₂×C₈₃⋊C₈	C₂³	1	2	yes	—
40	C₂×C₈₃⋊C₈	C₂³	1	2	yes	—
41	C₄⋊Dic₈₃	—	2	1	no	—
42	C₄⋊Dic₈₃	C₂³	1	2	yes	—
43	Dic₈₃⋊C₄	—	2	4	no	—
44	C₄×Dic₈₃	—	2	4	no	—
45	C₂×Q₈×C₈₃	—	2	1	no	—
46	C₂×Q₈×C₈₃	—	2	2	no	—
47	C₂×Q₈×C₈₃	C₂×C₄	1	4	yes	—
48	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
49	C₂²×C₄×C₈₃	—	2	1	no	—
50	C₂²×C₄×C₈₃	—	2	1	no	—
51	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
52	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
53	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₄×C₈₃	—	2	4	no	—
55	C₄⋊C₄×C₈₃	—	2	1	no	—
56	C₄⋊C₄×C₈₃	C₂³	1	2	yes	—
57	C₄²×C₈₃	—	2	4	no	—
58	C₄²×C₈₃	D₄	1	2	yes	—
59	C₄²×C₈₃	C₂³	1	2	yes	—
60	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
61	Q₈×C₈₃	—	2	4	no	—
62	Q₈×C₈₃	—	2	2	no	—
63	Q₈×C₈₃	C₂²×C₄	1	4	yes	—
64	C₂×C₄×C₈₃	—	2	4	no	—
65	C₂×C₄×C₈₃	—	2	2	no	—
66	C₂×C₄×C₈₃	—	2	2	no	—
67	C₂×C₄×C₈₃	—	2	2	no	—
68	C₂×C₄×C₈₃	—	2	2	no	—
69	C₂×C₄×C₈₃	—	4	2	no	—
70	C₂×C₄×C₈₃	C₂²×C₄	1	2	yes	—
71	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₈₃	#41	1	2	yes	—
75	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
76	C₂×Dic₈₃	—	2	4	no	—
77	C₂×Dic₈₃	—	2	2	no	—
78	C₂×Dic₈₃	—	2	2	no	—
79	C₂×Dic₈₃	—	4	2	no	—
80	Dic₁₆₆	—	2	4	no	—
81	Dic₁₆₆	—	2	2	no	—
82	Dic₁₆₆	C₂²×C₄	1	4	yes	—
83	C₈₃⋊C₈	—	2	2	no	—
84	C₈₃⋊C₈	C₂²×C₄	1	4	yes	—
85	C₂²×C₈₃	C₄×D₄	1	2	yes	—
86	C₂²×C₈₃	#137	1	2	yes	—
87	C₂²×C₈₃	#137	1	2	yes	—
88	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
89	C₄×C₈₃	—	2	4	no	—
90	C₄×C₈₃	—	2	2	no	—
91	C₄×C₈₃	—	2	2	no	—
92	C₄×C₈₃	—	4	2	no	—
93	C₄×C₈₃	C₄×D₄	1	2	yes	—
94	C₄×C₈₃	C₂³×C₄	1	1	yes	characteristic
95	C₄×C₈₃	C₂×#41	1	1	yes	characteristic
96	Dic₈₃	—	2	4	no	—
97	Dic₈₃	—	4	2	no	—
98	C₂×C₈₃	#441	1	4	yes	complemented
99	C₂×C₈₃	C₂×C₄×D₄	1	1	yes	characteristic
100	C₂×C₈₃	C₂×#137	1	1	yes	characteristic
101	C₂×C₈₃	C₂×#137	1	1	yes	characteristic
102	C₂×#441	—	83	1	no	maximal, Sylow
103	C₈₃	C₂×#441	1	1	yes	characteristic, complemented, Sylow
104	C₂²×Q₁₆	—	83	1	no	—
105	C₂×C₄×Q₈	—	83	1	no	—
106	C₂×C₄×Q₈	D₈₃	1	1	yes	characteristic
107	#441	—	83	8	no	—
108	C₂×#106	—	83	1	no	—
109	C₂×#103	—	83	1	no	—
110	C₂×#103	—	83	1	no	—
111	C₂×#97	—	83	1	no	—
112	C₂²×Q₈	—	83	1	no	—
113	C₂²×Q₈	C₂×D₈₃	1	1	yes	characteristic
114	C₂×Q₁₆	—	83	8	no	—
115	C₂×Q₁₆	—	83	4	no	—
116	C₂²×C₈	—	83	1	no	—
117	C₂²×C₈	—	83	1	no	—
118	C₄×Q₈	—	2	2	no	—
119	C₄×Q₈	—	83	4	no	—
120	C₄×Q₈	—	166	2	no	—
121	C₄×Q₈	C₂×D₈₃	1	4	yes	—
122	C₂×C₄⋊C₄	—	2	1	no	—
123	C₂×C₄⋊C₄	—	83	1	no	—
124	C₂×C₄⋊C₄	—	166	1	no	—
125	C₂×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic
126	C₂×C₄²	—	2	1	no	—
127	C₂×C₄²	—	166	1	no	—
128	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
129	#106	—	83	4	no	—
130	#103	—	83	4	no	—
131	#103	—	83	4	no	—
132	#97	—	83	4	no	—
133	C₂×Q₈	—	2	1	no	—
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	83	4	no	—
136	C₂×Q₈	—	83	2	no	—
137	C₂×Q₈	—	166	1	no	—
138	C₂×Q₈	—	166	2	no	—
139	C₂×Q₈	C₄×D₈₃	1	4	yes	—
140	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	—	166	1	no	—
144	C₂²×C₄	—	166	1	no	—
145	C₂²×C₄	C₂²⋊D₈₃	1	1	yes	characteristic
146	C₂²×C₄	C₂²⋊D₈₃	1	1	yes	characteristic
147	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
148	Q₁₆	—	83	16	no	—
149	C₂×C₈	—	83	4	no	—
150	C₂×C₈	—	83	2	no	—
151	C₂×C₈	—	83	2	no	—
152	C₂×C₈	—	166	2	no	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	2	1	no	—
155	C₄⋊C₄	—	83	2	no	—
156	C₄⋊C₄	—	166	1	no	—
157	C₄⋊C₄	—	166	4	no	—
158	C₄⋊C₄	C₂²×D₈₃	1	2	yes	—
159	C₄²	—	2	4	no	—
160	C₄²	—	166	4	no	—
161	C₄²	C₂²⋊D₈₃	1	2	yes	—
162	C₄²	C₂²×D₈₃	1	2	yes	—
163	C₂³	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
164	Q₈	—	2	2	no	—
165	Q₈	—	2	4	no	—
166	Q₈	—	83	4	no	—
167	Q₈	—	166	2	no	—
168	Q₈	—	166	4	no	—
169	Q₈	C₂×C₄×D₈₃	1	4	yes	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	—	332	2	no	—
177	C₂×C₄	—	166	2	no	—
178	C₂×C₄	—	166	2	no	—
179	C₂×C₄	—	166	4	no	—
180	C₂×C₄	C₂×C₄×D₈₃	1	2	yes	—
181	C₂×C₄	C₂×C₂²⋊D₈₃	1	2	yes	—
182	C₂×C₄	C₂×C₂²⋊D₈₃	1	2	yes	—
183	C₂×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
184	C₂×C₄	#13050590	1	2	yes	—
185	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
186	C₈	—	83	4	no	—
187	C₈	—	166	2	no	—
188	C₂²	C₄×C₂²⋊D₈₃	1	2	yes	—
189	C₂²	#14581822	1	2	yes	—
190	C₂²	#14581823	1	2	yes	—
191	C₂²	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
192	C₄	—	2	4	no	—
193	C₄	—	2	2	no	—
194	C₄	—	2	2	no	—
195	C₄	—	4	2	no	—
196	C₄	—	332	2	no	—
197	C₄	—	166	4	no	—
198	C₄	C₄×C₂²⋊D₈₃	1	2	yes	—
199	C₄	C₂²×C₄×D₈₃	1	1	yes	characteristic
200	C₄	C₂×#13050590	1	1	yes	characteristic
201	C₂	#19127806	1	4	yes	direct product factor
202	C₂	C₂×C₄×C₂²⋊D₈₃	1	1	yes	characteristic
203	C₂	C₂×#14581822	1	1	yes	characteristic
204	C₂	C₂×#14581823	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#13050580

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₆₆

C₂

yes

maximal, characteristic

#19127806

C₂

yes

maximal, direct product factor

C₂×#14581723

C₂

yes

maximal, characteristic

C₂×#14581716

C₂

yes

maximal, characteristic

C₂×#14581715

C₂

yes

maximal, characteristic

C₂×#14581703

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₈₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₆₆

C₂²

yes

characteristic

C₂×#13050580

C₄

yes

complemented

C₂×#13050580

C₂²

yes

—

C₂²×C₈₃⋊C₈

C₂²

yes

characteristic

C₂²×C₈₃⋊C₈

C₂²

yes

characteristic

C₄×Dic₁₆₆

—

C₄×Dic₁₆₆

C₂²

yes

—

C₂×C₄⋊Dic₈₃

C₂²

yes

characteristic

C₂×Dic₈₃⋊C₄

—

C₂×C₄×Dic₈₃

—

#14581723

C₂²

yes

—

#14581716

C₂²

yes

—

#14581715

C₂²

yes

—

#14581703

C₂²

yes

—

C₂²×Q₈×C₈₃

C₂²

yes

characteristic

C₄×Q₈×C₈₃

—

C₄×Q₈×C₈₃

C₂²

yes

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄⋊C₄×C₈₃

C₂²

yes

characteristic

C₂×C₄²×C₈₃

—

C₂×C₄²×C₈₃

C₂²

yes

characteristic

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

C₂×C₄

yes

—

C₂×Dic₁₆₆

C₂³

yes

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

#13050580

C₂×C₄

yes

complemented

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

C₂×C₄

yes

—

C₂×C₈₃⋊C₈

C₂³

yes

—

C₂×C₈₃⋊C₈

C₂³

yes

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

C₂³

yes

—

Dic₈₃⋊C₄

—

C₄×Dic₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

—

C₂×Q₈×C₈₃

C₂×C₄

yes

—

C₂×Q₈×C₈₃

C₂³

yes

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

D₄

yes

characteristic

C₂²×C₄×C₈₃

D₄

yes

characteristic

C₂²×C₄×C₈₃

C₂³

yes

characteristic

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

C₂³

yes

—

C₄²×C₈₃

—

C₄²×C₈₃

D₄

yes

—

C₄²×C₈₃

C₂³

yes

—

C₂³×C₈₃

C₂×D₄

yes

characteristic

Q₈×C₈₃

—

Q₈×C₈₃

—

Q₈×C₈₃

C₂²×C₄

yes

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²×C₄

yes

—

C₂×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₈₃

#41

yes

—

C₂×C₄×C₈₃

C₂⁴

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

Dic₁₆₆

C₂²×C₄

yes

—

C₈₃⋊C₈

—

C₈₃⋊C₈

C₂²×C₄

yes

—

C₂²×C₈₃

C₄×D₄

yes

—

C₂²×C₈₃

#137

yes

—

C₂²×C₈₃

#137

yes

—

C₂²×C₈₃

C₂²×D₄

yes

characteristic

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

C₄×D₄

yes

—

C₄×C₈₃

C₂³×C₄

yes

characteristic

C₄×C₈₃

C₂×#41

yes

characteristic

Dic₈₃

—

Dic₈₃

—

C₂×C₈₃

#441

yes

complemented

C₂×C₈₃

C₂×C₄×D₄

yes

characteristic

100

C₂×C₈₃

C₂×#137

yes

characteristic

101

C₂×C₈₃

yes

102

—

103

C₈₃

C₂×#441

yes

characteristic, complemented, Sylow

104

C₂²×Q₁₆

—

105

C₂×C₄×Q₈

—

106

C₂×C₄×Q₈

D₈₃

yes

characteristic

107

#441

—

108

C₂×#106

—

109

C₂×#103

—

110

C₂×#103

—

111

C₂×#97

—

112

C₂²×Q₈

—

113

C₂²×Q₈

C₂×D₈₃

yes

characteristic

114

C₂×Q₁₆

—

115

C₂×Q₁₆

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

C₄×Q₈

—

119

C₄×Q₈

—

120

C₄×Q₈

—

166

—

121

C₄×Q₈

C₂×D₈₃

yes

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

166

—

125

C₂×C₄⋊C₄

C₂×D₈₃

yes

characteristic

126

C₂×C₄²

—

127

C₂×C₄²

—

166

—

128

C₂×C₄²

C₂×D₈₃

yes

characteristic

129

#106

—

130

#103

—

131

#103

—

132

#97

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

166

—

138

C₂×Q₈

—

166

—

139

C₂×Q₈

C₄×D₈₃

yes

—

140

C₂×Q₈

C₂²×D₈₃

yes

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

166

—

144

C₂²×C₄

—

166

—

145

C₂²×C₄

C₂²⋊D₈₃

yes

characteristic

146

C₂²×C₄

C₂²⋊D₈₃

yes

characteristic

147

C₂²×C₄

C₂²×D₈₃

yes

characteristic

148

Q₁₆

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

166

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

166

—

157

C₄⋊C₄

—

166

—

158

C₄⋊C₄

C₂²×D₈₃

yes

—

159

C₄²

—

160

C₄²

—

166

—

161

C₄²

C₂²⋊D₈₃

yes

—

162

C₄²

C₂²×D₈₃

yes

—

163

C₂³

C₂×C₂²⋊D₈₃

yes

characteristic

164

Q₈

—

165

Q₈

—

166

Q₈

—

167

Q₈

—

166

—

168

Q₈

—

166

—

169

Q₈

C₂×C₄×D₈₃

yes

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

332

—

177

C₂×C₄

—

166

—

178

C₂×C₄

—

166

—

179

C₂×C₄

—

166

—

180

C₂×C₄

C₂×C₄×D₈₃

yes

—

181

C₂×C₄

C₂×C₂²⋊D₈₃

yes

—

182

C₂×C₄

C₂×C₂²⋊D₈₃

yes

—

183

C₂×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

184

C₂×C₄

#13050590

yes

—

185

C₂×C₄

C₂³×D₈₃

yes

characteristic

186

C₈

—

187

C₈

—

166

—

188

C₂²

C₄×C₂²⋊D₈₃

yes

—

189

C₂²

#14581822

yes

—

190

C₂²

#14581823

yes

—

191

C₂²

C₂²×C₂²⋊D₈₃

yes

characteristic

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

—

332

—

197

C₄

—

166

—

198

C₄

C₄×C₂²⋊D₈₃

yes

—

199

C₄

C₂²×C₄×D₈₃

yes

characteristic

200

C₄

C₂×#13050590

yes

characteristic

201

C₂

#19127806

yes

direct product factor

202

C₂

C₂×C₄×C₂²⋊D₈₃

yes

characteristic

203

C₂

C₂×#14581822

yes

characteristic

204

C₂

C₂×#14581823

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₈₃
commutator	C₄×C₈₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	C₂×C₄×Q₈×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	C₂×D₄
cosocle	C₂×C₄×C₈₃	C₂⁴
hypercenter	C₂×C₄×Q₈	D₈₃
hypocenter	C₈₃	C₂×#441
LCS	G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₈₃

commutator

C₄×C₈₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₈₃

Fitting

C₂×C₄×Q₈×C₈₃

C₂

socle, prime radical

C₂³×C₈₃

C₂×D₄

cosocle

C₂×C₄×C₈₃

C₂⁴

hypercenter

C₂×C₄×Q₈

D₈₃

hypocenter

C₈₃

C₂×#441

LCS

G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
3. #19127806	C₂	direct (N × H)
10. C₂×#13050580	C₄	semidirect
36. #13050580	C₂×C₄	semidirect
98. C₂×C₈₃	#441	semidirect
103. C₈₃	C₂×#441	semidirect
201. C₂	#19127806	direct (N × H)

H ≅ G/N

type

3. #19127806

C₂

direct (N × H)

10. C₂×#13050580

C₄

semidirect

36. #13050580

C₂×C₄

semidirect

98. C₂×C₈₃

#441

semidirect

103. C₈₃

C₂×#441

semidirect

201. C₂

#19127806

direct (N × H)

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

subgroup	index
C₂²×#13050580	2
C₂×C₄×Dic₁₆₆	2
#19127806	2
C₂×#14581723	2
C₂×#14581716	2
C₂×#14581715	2
C₂×#14581703	2
C₂×C₄×Q₈×C₈₃	2
C₂×#441	83

subgroup

index

C₂×C₄×Dic₁₆₆

C₂×C₄×Q₈×C₈₃

Subgroups — C₂×#19127806 #24916248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#19127806 #24916248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19127806 #24916248