Group #13145278 — subgroups

Subgroups — C₂×3₋¹⁺²×SD₃₂ #13145278

Order 1728.

360 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 175 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	C₂×Q₁₆×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
3	3₋¹⁺²×SD₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃²×SD₃₂	C₃	1	1	yes	maximal, characteristic
6	C₂×C₉×SD₃₂	C₃	1	3	yes	maximal, complemented
7	C₂×Q₈×3₋¹⁺²	—	2	1	no	—
8	C₂×D₄×3₋¹⁺²	—	2	1	no	—
9	Q₁₆×3₋¹⁺²	—	2	1	no	—
10	Q₁₆×3₋¹⁺²	C₂²	1	2	yes	complemented
11	D₈×3₋¹⁺²	—	2	1	no	—
12	D₈×3₋¹⁺²	C₂²	1	2	yes	—
13	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
14	C₁₆×3₋¹⁺²	C₂²	1	2	yes	complemented
15	C₂×C₃²×Q₁₆	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃²×D₈	C₂×C₃	1	1	yes	characteristic
17	C₃²×SD₃₂	C₂×C₃	1	4	yes	—
18	C₂×C₃²×C₁₆	C₂×C₃	1	1	yes	characteristic
19	C₂×C₉×Q₁₆	C₂×C₃	1	3	yes	complemented
20	C₂×C₉×D₈	C₂×C₃	1	3	yes	—
21	C₉×SD₃₂	C₂×C₃	1	12	yes	complemented
22	C₂×C₉×C₁₆	C₂×C₃	1	3	yes	complemented
23	C₂³×3₋¹⁺²	—	4	1	no	—
24	Q₈×3₋¹⁺²	—	2	2	no	—
25	Q₈×3₋¹⁺²	—	4	1	no	—
26	D₄×3₋¹⁺²	—	2	2	no	—
27	D₄×3₋¹⁺²	—	4	1	no	—
28	C₂×C₄×3₋¹⁺²	—	4	1	no	—
29	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
30	C₈×3₋¹⁺²	D₄	1	1	yes	characteristic
31	C₈×3₋¹⁺²	C₂³	1	1	yes	characteristic
32	C₂×C₃×SD₃₂	—	3	1	no	—
33	C₂×C₃×SD₃₂	C₃²	1	1	yes	characteristic
34	C₂×C₃²×Q₈	—	2	1	no	—
35	C₂×C₃²×D₄	—	2	1	no	—
36	C₃²×Q₁₆	—	2	1	no	—
37	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
38	C₃²×D₈	—	2	1	no	—
39	C₃²×D₈	C₂²×C₃	1	2	yes	—
40	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
41	C₂×Q₈×C₉	—	2	3	no	—
42	C₂×D₄×C₉	—	2	3	no	—
43	C₃²×C₁₆	C₂²×C₃	1	2	yes	—
44	C₉×Q₁₆	—	2	3	no	—
45	C₉×Q₁₆	C₂²×C₃	1	6	yes	complemented
46	C₉×D₈	—	2	3	no	—
47	C₉×D₈	C₂²×C₃	1	6	yes	—
48	C₂×C₈×C₉	C₂²×C₃	1	3	yes	—
49	C₉×C₁₆	C₂²×C₃	1	6	yes	complemented
50	C₂²×3₋¹⁺²	—	4	2	no	—
51	C₂²×3₋¹⁺²	—	8	2	no	—
52	C₂²×3₋¹⁺²	D₈	1	1	yes	characteristic
53	C₄×3₋¹⁺²	—	4	2	no	—
54	C₄×3₋¹⁺²	D₈	1	1	yes	characteristic
55	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
56	C₂×C₃×Q₁₆	—	3	1	no	—
57	C₂×C₃×Q₁₆	C₂×C₃²	1	1	yes	characteristic
58	C₂×C₃×D₈	—	3	1	no	—
59	C₂×C₃×D₈	C₂×C₃²	1	1	yes	characteristic
60	C₃×SD₃₂	—	3	4	no	—
61	C₃×SD₃₂	C₂×C₃²	1	4	yes	—
62	C₂×C₃×C₁₆	—	3	1	no	—
63	C₂×C₃×C₁₆	C₂×C₃²	1	1	yes	characteristic
64	C₂³×C₃²	—	4	1	no	—
65	C₃²×Q₈	—	2	2	no	—
66	C₃²×Q₈	—	4	1	no	—
67	C₃²×D₄	—	2	2	no	—
68	C₃²×D₄	—	4	1	no	—
69	C₂×C₃²×C₄	—	4	1	no	—
70	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
71	C₂³×C₉	—	4	3	no	—
72	C₃²×C₈	C₃×D₄	1	1	yes	characteristic
73	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
74	Q₈×C₉	—	2	6	no	—
75	Q₈×C₉	—	4	3	no	—
76	D₄×C₉	—	2	6	no	—
77	D₄×C₉	—	4	3	no	—
78	C₂×C₄×C₉	—	4	3	no	—
79	C₂×C₄×C₉	C₃×D₄	1	3	yes	—
80	C₈×C₉	C₃×D₄	1	3	yes	—
81	C₈×C₉	C₂³×C₃	1	3	yes	—
82	C₂×SD₃₂	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×3₋¹⁺²	—	8	2	no	—
84	C₂×3₋¹⁺²	SD₃₂	1	2	yes	direct product factor
85	C₂×3₋¹⁺²	C₂×D₈	1	1	yes	characteristic
86	C₂×C₃×Q₈	—	2	1	no	—
87	C₂×C₃×Q₈	—	6	1	no	—
88	C₂×C₃×D₄	—	2	1	no	—
89	C₂×C₃×D₄	—	6	1	no	—
90	C₃×Q₁₆	—	2	1	no	—
91	C₃×Q₁₆	—	3	2	no	—
92	C₃×Q₁₆	—	6	1	no	—
93	C₃×Q₁₆	C₂²×C₃²	1	2	yes	—
94	C₃×D₈	—	2	1	no	—
95	C₃×D₈	—	3	2	no	—
96	C₃×D₈	—	6	1	no	—
97	C₃×D₈	C₂²×C₃²	1	2	yes	—
98	C₂×C₃×C₈	—	3	1	no	—
99	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
100	C₃×C₁₆	—	3	2	no	—
101	C₃×C₁₆	C₂²×C₃²	1	2	yes	—
102	C₂²×C₃²	—	4	2	no	—
103	C₂²×C₃²	—	8	2	no	—
104	C₂²×C₃²	C₃×D₈	1	1	yes	characteristic
105	C₃²×C₄	—	4	2	no	—
106	C₃²×C₄	C₃×D₈	1	1	yes	characteristic
107	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
108	C₂²×C₉	—	4	6	no	—
109	C₂²×C₉	—	8	6	no	—
110	C₂²×C₉	C₃×D₈	1	3	yes	—
111	C₄×C₉	—	4	6	no	—
112	C₄×C₉	C₃×D₈	1	3	yes	—
113	C₄×C₉	C₂×C₃×D₄	1	3	yes	—
114	C₂×Q₁₆	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
115	C₂×D₈	C₂×3₋¹⁺²	1	1	yes	characteristic
116	SD₃₂	C₂×3₋¹⁺²	1	4	yes	direct product factor
117	C₂×C₁₆	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
118	3₋¹⁺²	C₂×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
119	C₂³×C₃	—	4	1	no	—
120	C₂³×C₃	—	12	1	no	—
121	C₃×Q₈	—	2	2	no	—
122	C₃×Q₈	—	4	1	no	—
123	C₃×Q₈	—	6	2	no	—
124	C₃×Q₈	—	12	1	no	—
125	C₃×D₄	—	2	2	no	—
126	C₃×D₄	—	4	1	no	—
127	C₃×D₄	—	6	2	no	—
128	C₃×D₄	—	12	1	no	—
129	C₂×C₃×C₄	—	3	1	no	—
130	C₂×C₃×C₄	—	4	1	no	—
131	C₂×C₃×C₄	—	12	1	no	—
132	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
133	C₃×C₈	—	3	1	no	—
134	C₃×C₈	—	3	1	no	—
135	C₃×C₈	C₃²×D₄	1	1	yes	characteristic
136	C₃×C₈	C₂³×C₃²	1	1	yes	characteristic
137	C₂×C₃²	—	8	2	no	—
138	C₂×C₃²	C₃×SD₃₂	1	2	yes	—
139	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
140	C₂×C₉	—	8	6	no	—
141	C₂×C₉	C₃×SD₃₂	1	6	yes	complemented
142	C₂×C₉	C₂×C₃×D₈	1	3	yes	—
143	C₂×Q₈	—	2	1	no	—
144	C₂×D₄	—	2	1	no	—
145	Q₁₆	—	2	1	no	—
146	Q₁₆	C₂²×3₋¹⁺²	1	2	yes	complemented
147	D₈	—	2	1	no	—
148	D₈	C₂²×3₋¹⁺²	1	2	yes	—
149	C₂×C₈	C₂²×3₋¹⁺²	1	1	yes	characteristic
150	C₁₆	C₂²×3₋¹⁺²	1	2	yes	complemented
151	C₂²×C₃	—	3	1	no	—
152	C₂²×C₃	—	4	2	no	—
153	C₂²×C₃	—	8	2	no	—
154	C₂²×C₃	—	12	2	no	—
155	C₂²×C₃	—	24	2	no	—
156	C₂²×C₃	C₃²×D₈	1	1	yes	characteristic
157	C₃×C₄	—	3	1	no	—
158	C₃×C₄	—	3	1	no	—
159	C₃×C₄	—	4	2	no	—
160	C₃×C₄	—	12	2	no	—
161	C₃×C₄	C₃²×D₈	1	1	yes	characteristic
162	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
163	C₃²	C₂×C₃×SD₃₂	1	1	yes	characteristic
164	C₉	C₂×C₃×SD₃₂	1	3	yes	complemented
165	C₂³	—	4	1	no	—
166	Q₈	—	2	2	no	—
167	Q₈	—	4	1	no	—
168	D₄	—	2	2	no	—
169	D₄	—	4	1	no	—
170	C₂×C₄	—	4	1	no	—
171	C₂×C₄	D₄×3₋¹⁺²	1	1	yes	characteristic
172	C₈	D₄×3₋¹⁺²	1	1	yes	characteristic
173	C₈	C₂³×3₋¹⁺²	1	1	yes	characteristic
174	C₂×C₃	—	3	2	no	—
175	C₂×C₃	—	3	1	no	—
176	C₂×C₃	—	8	2	no	—
177	C₂×C₃	—	24	2	no	—
178	C₂×C₃	C₃²×SD₃₂	1	2	yes	—
179	C₂×C₃	C₂×C₃²×D₈	1	1	yes	characteristic
180	C₂²	—	4	2	no	—
181	C₂²	—	8	2	no	—
182	C₂²	D₈×3₋¹⁺²	1	1	yes	characteristic
183	C₄	—	4	2	no	—
184	C₄	D₈×3₋¹⁺²	1	1	yes	characteristic
185	C₄	C₂×D₄×3₋¹⁺²	1	1	yes	characteristic
186	C₃	—	3	1	no	—
187	C₃	C₂×C₃²×SD₃₂	1	1	yes	characteristic
188	C₂	—	8	2	no	—
189	C₂	3₋¹⁺²×SD₃₂	1	2	yes	direct product factor
190	C₂	C₂×D₈×3₋¹⁺²	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×3₋¹⁺²

C₂

yes

maximal, characteristic, complemented

C₂×D₈×3₋¹⁺²

C₂

yes

maximal, characteristic

3₋¹⁺²×SD₃₂

C₂

yes

maximal, direct product factor

C₂×C₁₆×3₋¹⁺²

C₂

yes

maximal, characteristic, complemented

C₂×C₃²×SD₃₂

C₃

yes

maximal, characteristic

C₂×C₉×SD₃₂

C₃

yes

maximal, complemented

C₂×Q₈×3₋¹⁺²

—

C₂×D₄×3₋¹⁺²

—

Q₁₆×3₋¹⁺²

—

Q₁₆×3₋¹⁺²

C₂²

yes

complemented

D₈×3₋¹⁺²

—

D₈×3₋¹⁺²

C₂²

yes

—

C₂×C₈×3₋¹⁺²

C₂²

yes

characteristic

C₁₆×3₋¹⁺²

C₂²

yes

complemented

C₂×C₃²×Q₁₆

C₂×C₃

yes

characteristic

C₂×C₃²×D₈

C₂×C₃

yes

characteristic

C₃²×SD₃₂

C₂×C₃

yes

—

C₂×C₃²×C₁₆

C₂×C₃

yes

characteristic

C₂×C₉×Q₁₆

C₂×C₃

yes

complemented

C₂×C₉×D₈

C₂×C₃

yes

—

C₉×SD₃₂

C₂×C₃

yes

complemented

C₂×C₉×C₁₆

C₂×C₃

yes

complemented

C₂³×3₋¹⁺²

—

Q₈×3₋¹⁺²

—

Q₈×3₋¹⁺²

—

D₄×3₋¹⁺²

—

D₄×3₋¹⁺²

—

C₂×C₄×3₋¹⁺²

—

C₂×C₄×3₋¹⁺²

D₄

yes

characteristic

C₈×3₋¹⁺²

D₄

yes

characteristic

C₈×3₋¹⁺²

C₂³

yes

characteristic

C₂×C₃×SD₃₂

—

C₂×C₃×SD₃₂

C₃²

yes

characteristic

C₂×C₃²×Q₈

—

C₂×C₃²×D₄

—

C₃²×Q₁₆

—

C₃²×Q₁₆

C₂²×C₃

yes

—

C₃²×D₈

—

C₃²×D₈

C₂²×C₃

yes

—

C₂×C₃²×C₈

C₂²×C₃

yes

characteristic

C₂×Q₈×C₉

—

C₂×D₄×C₉

—

C₃²×C₁₆

C₂²×C₃

yes

—

C₉×Q₁₆

—

C₉×Q₁₆

C₂²×C₃

yes

complemented

C₉×D₈

—

C₉×D₈

C₂²×C₃

yes

—

C₂×C₈×C₉

C₂²×C₃

yes

—

C₉×C₁₆

C₂²×C₃

yes

complemented

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

—

C₂²×3₋¹⁺²

D₈

yes

characteristic

C₄×3₋¹⁺²

—

C₄×3₋¹⁺²

D₈

yes

characteristic

C₄×3₋¹⁺²

C₂×D₄

yes

characteristic

C₂×C₃×Q₁₆

—

C₂×C₃×Q₁₆

C₂×C₃²

yes

characteristic

C₂×C₃×D₈

—

C₂×C₃×D₈

C₂×C₃²

yes

characteristic

C₃×SD₃₂

—

C₃×SD₃₂

C₂×C₃²

yes

—

C₂×C₃×C₁₆

—

C₂×C₃×C₁₆

C₂×C₃²

yes

characteristic

C₂³×C₃²

—

C₃²×Q₈

—

C₃²×Q₈

—

C₃²×D₄

—

C₃²×D₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₃×D₄

yes

characteristic

C₂³×C₉

—

C₃²×C₈

C₃×D₄

yes

characteristic

C₃²×C₈

C₂³×C₃

yes

characteristic

Q₈×C₉

—

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₃×D₄

yes

—

C₈×C₉

C₃×D₄

yes

—

C₈×C₉

C₂³×C₃

yes

—

C₂×SD₃₂

3₋¹⁺²

yes

characteristic, direct product factor, Sylow

C₂×3₋¹⁺²

—

C₂×3₋¹⁺²

SD₃₂

yes

direct product factor

C₂×3₋¹⁺²

C₂×D₈

yes

characteristic

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₃×Q₁₆

C₂²×C₃²

yes

—

C₃×D₈

—

C₃×D₈

—

C₃×D₈

—

C₃×D₈

C₂²×C₃²

yes

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂²×C₃²

yes

characteristic

100

C₃×C₁₆

—

101

C₃×C₁₆

C₂²×C₃²

yes

—

102

C₂²×C₃²

—

103

C₂²×C₃²

—

104

C₂²×C₃²

C₃×D₈

yes

characteristic

105

C₃²×C₄

—

106

C₃²×C₄

C₃×D₈

yes

characteristic

107

C₃²×C₄

C₂×C₃×D₄

yes

characteristic

108

C₂²×C₉

—

109

C₂²×C₉

—

110

C₂²×C₉

C₃×D₈

yes

—

111

C₄×C₉

—

112

C₄×C₉

C₃×D₈

yes

—

113

C₄×C₉

C₂×C₃×D₄

yes

—

114

C₂×Q₁₆

C₂×3₋¹⁺²

yes

characteristic, complemented

115

C₂×D₈

C₂×3₋¹⁺²

yes

characteristic

116

SD₃₂

C₂×3₋¹⁺²

yes

direct product factor

117

C₂×C₁₆

C₂×3₋¹⁺²

yes

characteristic, complemented

118

3₋¹⁺²

C₂×SD₃₂

yes

characteristic, direct product factor, Sylow

119

C₂³×C₃

—

120

C₂³×C₃

—

121

C₃×Q₈

—

122

C₃×Q₈

—

123

C₃×Q₈

—

124

C₃×Q₈

—

125

C₃×D₄

—

126

C₃×D₄

—

127

C₃×D₄

—

128

C₃×D₄

—

129

C₂×C₃×C₄

—

130

C₂×C₃×C₄

—

131

C₂×C₃×C₄

—

132

C₂×C₃×C₄

C₃²×D₄

yes

characteristic

133

C₃×C₈

—

134

C₃×C₈

—

135

C₃×C₈

C₃²×D₄

yes

characteristic

136

C₃×C₈

C₂³×C₃²

yes

characteristic

137

C₂×C₃²

—

138

C₂×C₃²

C₃×SD₃₂

yes

—

139

C₂×C₃²

C₂×C₃×D₈

yes

characteristic

140

C₂×C₉

—

141

C₂×C₉

C₃×SD₃₂

yes

complemented

142

C₂×C₉

C₂×C₃×D₈

yes

—

143

C₂×Q₈

—

144

C₂×D₄

—

145

Q₁₆

—

146

Q₁₆

C₂²×3₋¹⁺²

yes

complemented

147

D₈

—

148

D₈

C₂²×3₋¹⁺²

yes

—

149

C₂×C₈

C₂²×3₋¹⁺²

yes

characteristic

150

C₁₆

C₂²×3₋¹⁺²

yes

complemented

151

C₂²×C₃

—

152

C₂²×C₃

—

153

C₂²×C₃

—

154

C₂²×C₃

—

155

C₂²×C₃

—

156

C₂²×C₃

C₃²×D₈

yes

characteristic

157

C₃×C₄

—

158

C₃×C₄

—

159

C₃×C₄

—

160

C₃×C₄

—

161

C₃×C₄

C₃²×D₈

yes

characteristic

162

C₃×C₄

C₂×C₃²×D₄

yes

characteristic

163

C₃²

C₂×C₃×SD₃₂

yes

characteristic

164

C₉

C₂×C₃×SD₃₂

yes

complemented

165

C₂³

—

166

Q₈

—

167

Q₈

—

168

D₄

—

169

D₄

—

170

C₂×C₄

—

171

C₂×C₄

D₄×3₋¹⁺²

yes

characteristic

172

C₈

D₄×3₋¹⁺²

yes

characteristic

173

C₈

C₂³×3₋¹⁺²

yes

characteristic

174

C₂×C₃

—

175

C₂×C₃

—

176

C₂×C₃

—

177

C₂×C₃

—

178

C₂×C₃

C₃²×SD₃₂

yes

—

179

C₂×C₃

C₂×C₃²×D₈

yes

characteristic

180

C₂²

—

181

C₂²

—

182

C₂²

D₈×3₋¹⁺²

yes

characteristic

183

C₄

—

184

C₄

D₈×3₋¹⁺²

yes

characteristic

185

C₄

C₂×D₄×3₋¹⁺²

yes

characteristic

186

C₃

—

187

C₃

C₂×C₃²×SD₃₂

yes

characteristic

188

C₂

—

189

C₂

3₋¹⁺²×SD₃₂

yes

direct product factor

190

C₂

C₂×D₈×3₋¹⁺²

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₃²×D₈
commutator, Frattini, cosocle	C₃×C₈	C₂³×C₃²
prime radical	C₂×C₃²×D₈	C₂×C₃
LCS	G ▷ C₃×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₄×3₋¹⁺² ◁ C₂×C₈×3₋¹⁺² ◁ G

subgroup

G/H

center, socle

C₂²×C₃

C₃²×D₈

commutator, Frattini, cosocle

C₃×C₈

C₂³×C₃²

prime radical

C₂×C₃²×D₈

C₂×C₃

LCS

G ▷ C₃×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₃ ◁ C₂×C₄×3₋¹⁺² ◁ C₂×C₈×3₋¹⁺² ◁ G

N	H ≅ G/N	type
1. C₂×Q₁₆×3₋¹⁺²	C₂	semidirect
3. 3₋¹⁺²×SD₃₂	C₂	direct (N × H)
4. C₂×C₁₆×3₋¹⁺²	C₂	semidirect
6. C₂×C₉×SD₃₂	C₃	semidirect
10. Q₁₆×3₋¹⁺²	C₂²	semidirect
14. C₁₆×3₋¹⁺²	C₂²	semidirect
19. C₂×C₉×Q₁₆	C₂×C₃	semidirect
21. C₉×SD₃₂	C₂×C₃	semidirect
22. C₂×C₉×C₁₆	C₂×C₃	semidirect
45. C₉×Q₁₆	C₂²×C₃	semidirect
49. C₉×C₁₆	C₂²×C₃	semidirect
82. C₂×SD₃₂	3₋¹⁺²	direct (N × H)
84. C₂×3₋¹⁺²	SD₃₂	direct (N × H)
114. C₂×Q₁₆	C₂×3₋¹⁺²	semidirect
116. SD₃₂	C₂×3₋¹⁺²	direct (N × H)
117. C₂×C₁₆	C₂×3₋¹⁺²	semidirect
118. 3₋¹⁺²	C₂×SD₃₂	direct (N × H)
141. C₂×C₉	C₃×SD₃₂	semidirect
146. Q₁₆	C₂²×3₋¹⁺²	semidirect
150. C₁₆	C₂²×3₋¹⁺²	semidirect
164. C₉	C₂×C₃×SD₃₂	semidirect
189. C₂	3₋¹⁺²×SD₃₂	direct (N × H)

H ≅ G/N

type

1. C₂×Q₁₆×3₋¹⁺²

C₂

semidirect

3. 3₋¹⁺²×SD₃₂

C₂

direct (N × H)

4. C₂×C₁₆×3₋¹⁺²

C₂

semidirect

6. C₂×C₉×SD₃₂

C₃

semidirect

10. Q₁₆×3₋¹⁺²

C₂²

semidirect

14. C₁₆×3₋¹⁺²

C₂²

semidirect

19. C₂×C₉×Q₁₆

C₂×C₃

semidirect

21. C₉×SD₃₂

C₂×C₃

semidirect

22. C₂×C₉×C₁₆

C₂×C₃

semidirect

45. C₉×Q₁₆

C₂²×C₃

semidirect

49. C₉×C₁₆

C₂²×C₃

semidirect

82. C₂×SD₃₂

3₋¹⁺²

direct (N × H)

84. C₂×3₋¹⁺²

SD₃₂

direct (N × H)

114. C₂×Q₁₆

C₂×3₋¹⁺²

semidirect

116. SD₃₂

C₂×3₋¹⁺²

direct (N × H)

117. C₂×C₁₆

C₂×3₋¹⁺²

semidirect

118. 3₋¹⁺²

C₂×SD₃₂

direct (N × H)

141. C₂×C₉

C₃×SD₃₂

semidirect

146. Q₁₆

C₂²×3₋¹⁺²

semidirect

150. C₁₆

C₂²×3₋¹⁺²

semidirect

164. C₉

C₂×C₃×SD₃₂

semidirect

189. C₂

3₋¹⁺²×SD₃₂

direct (N × H)

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

subgroup	index
C₂×Q₁₆×3₋¹⁺²	2
C₂×D₈×3₋¹⁺²	2
3₋¹⁺²×SD₃₂	2
C₂×C₁₆×3₋¹⁺²	2
C₂×C₃²×SD₃₂	3
C₂×C₉×SD₃₂	3

subgroup

index

C₂×Q₁₆×3₋¹⁺²

C₂×D₈×3₋¹⁺²

3₋¹⁺²×SD₃₂

C₂×C₁₆×3₋¹⁺²

C₂×C₃²×SD₃₂

C₂×C₉×SD₃₂

Subgroups — C₂×3₋¹⁺²×SD₃₂ #13145278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×3−1+2×SD32 #13145278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×3₋¹⁺²×SD₃₂ #13145278