Group #11785450 — subgroups

Subgroups — #11785450

Order 1152.

408 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 126 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×#3663	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588808	C₂	1	2	yes	maximal
4	C₂×#63372	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588231	C₂	1	2	yes	maximal, complemented
6	#70712	—	3	1	no	maximal
7	C₂²×C₄×D₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂×#3667	C₂²	1	2	yes	—
11	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#3663	—	2	2	no	—
13	C₂×#3663	—	2	2	no	—
14	C₂×#3663	C₄	1	4	yes	—
15	C₉×#108	—	2	2	no	—
16	(C₂×D₉)⋊C₈	—	2	4	no	—
17	#63372	—	2	2	no	—
18	C₂²×ΓL(1,𝔽₂₅)	—	3	1	no	—
19	C₂×C₃×#108	D₃	1	1	yes	characteristic
20	#5126	—	3	2	no	—
21	C₂×#819	—	3	1	no	—
22	#4558	—	3	2	no	—
23	C₂³×D₉	Q₈	1	1	yes	characteristic
24	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₉	Q₈	1	1	yes	characteristic
26	C₂×C₄×D₉	—	2	1	no	—
27	C₂×C₄×D₉	—	2	1	no	—
28	C₂×C₄×D₉	—	2	1	no	—
29	C₂×C₄×D₉	—	2	1	no	—
30	C₂×C₄×D₉	C₂×C₄	1	2	yes	—
31	C₂×C₄×D₉	D₄	1	2	yes	—
32	C₉×M₁₆	—	2	2	no	—
33	C₉×M₁₆	—	2	2	no	—
34	C₂×C₈×C₉	—	2	2	no	—
35	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
36	C₂×C₈×C₉	D₄	1	2	yes	—
37	C₂×C₈×C₉	D₄	1	2	yes	—
38	#3667	—	2	2	no	—
39	#3667	—	2	2	no	—
40	C₂×C₉⋊C₈	—	2	1	no	—
41	C₂×C₉⋊C₈	—	2	1	no	—
42	C₂×C₉⋊C₈	—	2	2	no	—
43	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
44	#3663	—	2	8	no	—
45	#1811	—	9	1	no	Sylow
46	C₂²×C₄×D₃	—	3	1	no	—
47	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
48	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
49	C₂×#208	—	3	2	no	—
50	C₂²×C₃⋊C₈	—	3	1	no	—
51	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
52	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
53	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
54	C₃×#108	—	2	2	no	—
55	(C₂×D₃)⋊C₈	—	6	4	no	—
56	#819	—	6	2	no	—
57	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
58	C₂²×D₉	—	2	1	no	—
59	C₂²×D₉	—	2	1	no	—
60	C₂²×D₉	—	4	2	no	—
61	C₂²×D₉	C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×C₉	#41	1	1	yes	characteristic
67	C₂×C₄×C₉	#41	1	1	yes	characteristic
68	C₂×Dic₉	—	2	1	no	—
69	C₂×Dic₉	—	2	1	no	—
70	C₂×Dic₉	C₄⋊C₄	1	2	yes	—
71	C₄×D₉	—	2	2	no	—
72	C₄×D₉	—	2	2	no	—
73	C₄×D₉	—	2	2	no	—
74	C₄×D₉	—	2	2	no	—
75	C₈×C₉	—	4	2	no	—
76	C₈×C₉	C₂²⋊C₄	1	4	yes	—
77	C₉⋊C₈	—	2	2	no	—
78	C₉⋊C₈	—	4	2	no	—
79	C₂²×M₁₆	—	9	1	no	—
80	C₂×#108	—	9	1	no	—
81	C₂×#108	D₉	1	1	yes	characteristic, complemented
82	#407	—	9	2	no	—
83	#341	—	9	2	no	—
84	C₂³×D₃	—	3	1	no	—
85	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
86	C₂²×Dic₃	—	3	1	no	—
87	C₂×C₄×D₃	—	3	2	no	—
88	C₂×C₄×D₃	—	3	2	no	—
89	C₂×C₄×D₃	—	6	1	no	—
90	C₂×C₄×D₃	—	6	1	no	—
91	C₂×C₄×D₃	—	6	1	no	—
92	C₂×C₄×D₃	—	6	1	no	—
93	C₃×M₁₆	—	2	2	no	—
94	C₃×M₁₆	—	2	2	no	—
95	C₂×C₃×C₈	—	2	2	no	—
96	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
97	C₂×C₃×C₈	D₁₂	1	2	yes	—
98	C₂×C₃×C₈	#67	1	2	yes	—
99	#208	—	6	2	no	—
100	#208	—	6	2	no	—
101	C₂×C₃⋊C₈	—	3	2	no	—
102	C₂×C₃⋊C₈	—	6	1	no	—
103	C₂×C₃⋊C₈	—	6	1	no	—
104	C₂×C₃⋊C₈	—	6	2	no	—
105	ΓL(1,𝔽₂₅)	—	6	8	no	—
106	C₂²×C₉	—	2	2	no	—
107	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
109	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
110	C₂×D₉	—	2	2	no	—
111	C₂×D₉	—	2	4	no	—
112	C₂×D₉	—	4	2	no	—
113	C₂×D₉	—	4	2	no	—
114	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₄×C₉	#117	1	1	yes	characteristic
116	C₄×C₉	#121	1	1	yes	characteristic
117	C₄×C₉	#121	1	1	yes	characteristic
118	Dic₉	—	2	2	no	—
119	C₂³×C₄	—	9	1	no	—
120	C₂×M₁₆	—	9	4	no	—
121	C₂×M₁₆	—	9	2	no	—
122	C₂×M₁₆	—	18	2	no	—
123	C₂×M₁₆	—	18	2	no	—
124	C₂×M₁₆	C₂×D₉	1	2	yes	—
125	C₂²×C₈	—	9	1	no	—
126	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
127	#108	—	2	2	no	—
128	#108	—	18	2	no	—
129	C₂²⋊C₈	—	18	4	no	—
130	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
131	C₂²×D₃	—	3	2	no	—
132	C₂²×D₃	—	6	1	no	—
133	C₂²×D₃	—	6	1	no	—
134	C₂²×D₃	—	12	2	no	—
135	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
136	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
137	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄	#237	1	1	yes	characteristic
139	C₂×C₃×C₄	#239	1	1	yes	characteristic
140	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
141	C₂×Dic₃	—	3	2	no	—
142	C₂×Dic₃	—	6	1	no	—
143	C₂×Dic₃	—	6	1	no	—
144	C₄×D₃	—	6	2	no	—
145	C₄×D₃	—	6	2	no	—
146	C₄×D₃	—	6	2	no	—
147	C₄×D₃	—	6	2	no	—
148	C₃×C₈	—	4	2	no	—
149	C₃×C₈	(C₂×D₃)⋊C₄	1	4	yes	—
150	C₃⋊C₈	—	6	2	no	—
151	C₃⋊C₈	—	12	2	no	—
152	C₂×C₉	—	2	1	no	—
153	C₂×C₉	—	2	1	no	—
154	C₂×C₉	#380	1	1	yes	characteristic
155	C₂×C₉	#430	1	2	yes	—
156	D₉	—	4	2	no	—
157	C₂⁴	—	9	1	no	—
158	C₂²×C₄	—	9	1	no	—
159	C₂²×C₄	—	9	2	no	—
160	C₂²×C₄	—	9	2	no	—
161	C₂²×C₄	—	18	1	no	—
162	C₂²×C₄	—	18	1	no	—
163	C₂²×C₄	—	18	1	no	—
164	C₂²×C₄	—	18	1	no	—
165	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
166	M₁₆	—	2	2	no	—
167	M₁₆	—	2	2	no	—
168	M₁₆	—	18	8	no	—
169	M₁₆	—	18	2	no	—
170	M₁₆	—	18	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	9	2	no	—
173	C₂×C₈	—	18	1	no	—
174	C₂×C₈	—	18	1	no	—
175	C₂×C₈	—	18	2	no	—
176	C₂×C₈	C₄×D₉	1	2	yes	—
177	C₂×C₈	D₃₆	1	2	yes	—
178	C₂×C₈	#611	1	2	yes	—
179	C₂²×C₃	—	2	2	no	—
180	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
181	C₂²×C₃	#897	1	1	yes	characteristic
182	C₂²×C₃	#946	1	1	yes	characteristic
183	C₂×D₃	—	6	4	no	—
184	C₂×D₃	—	6	2	no	—
185	C₂×D₃	—	12	2	no	—
186	C₂×D₃	—	12	2	no	—
187	C₃×C₄	#892	1	1	yes	characteristic
188	C₃×C₄	#895	1	1	yes	characteristic
189	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
190	C₃×C₄	#938	1	1	yes	characteristic
191	Dic₃	—	6	2	no	—
192	C₉	#1811	1	1	yes	characteristic, complemented, Sylow
193	C₂³	—	9	2	no	—
194	C₂³	—	18	1	no	—
195	C₂³	—	18	1	no	—
196	C₂³	—	36	2	no	—
197	C₂³	Q₈×D₉	1	1	yes	characteristic
198	C₂×C₄	—	9	2	no	—
199	C₂×C₄	—	18	1	no	—
200	C₂×C₄	—	18	1	no	—
201	C₂×C₄	—	18	2	no	—
202	C₂×C₄	—	18	2	no	—
203	C₂×C₄	—	18	2	no	—
204	C₂×C₄	—	18	2	no	—
205	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
206	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
207	C₂×C₄	D₄×D₉	1	1	yes	characteristic
208	C₂×C₄	#3699	1	1	yes	characteristic
209	C₂×C₄	#3701	1	1	yes	characteristic
210	C₂×C₄	C₂×#611	1	1	yes	characteristic
211	C₈	—	4	2	no	—
212	C₈	—	18	2	no	—
213	C₈	—	36	2	no	—
214	C₈	(C₂×D₉)⋊C₄	1	4	yes	—
215	C₂×C₃	—	2	1	no	—
216	C₂×C₃	—	2	1	no	—
217	C₂×C₃	#4893	1	2	yes	—
218	C₂×C₃	#4987	1	1	yes	characteristic
219	D₃	—	12	2	no	—
220	C₂²	—	2	2	no	—
221	C₂²	—	18	4	no	—
222	C₂²	—	18	2	no	—
223	C₂²	—	36	2	no	—
224	C₂²	—	36	2	no	—
225	C₂²	C₄⋊C₄×D₉	1	1	yes	characteristic
226	C₂²	#63459	1	1	yes	characteristic
227	C₂²	#63508	1	1	yes	characteristic
228	C₄	—	18	2	no	—
229	C₄	#63454	1	1	yes	characteristic
230	C₄	#63457	1	1	yes	characteristic
231	C₄	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
232	C₄	#63500	1	1	yes	characteristic
233	C₃	#70712	1	1	yes	characteristic
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	—	36	2	no	—
237	C₂	#10588573	1	2	yes	—
238	C₂	#10588667	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#3663

C₂

yes

maximal, characteristic

C₂×C₉×#108

C₂

yes

maximal, characteristic, complemented

#10588808

C₂

yes

maximal

C₂×#63372

C₂

yes

maximal, characteristic, complemented

#10588231

C₂

yes

maximal, complemented

#70712

—

maximal

C₂²×C₄×D₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂²×C₈×C₉

C₂²

yes

characteristic

C₂×#3667

C₂²

yes

—

C₂²×C₉⋊C₈

C₂²

yes

—

—

C₄

yes

—

C₉×#108

—

(C₂×D₉)⋊C₈

—

#63372

—

C₂²×ΓL(1,𝔽₂₅)

—

C₂×C₃×#108

D₃

yes

—

—

—

C₂³×D₉

Q₈

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

Q₈

yes

characteristic

C₂×C₄×D₉

—

C₂×C₄×D₉

—

C₂×C₄×D₉

—

C₂×C₄×D₉

—

C₂×C₄×D₉

C₂×C₄

yes

—

C₂×C₄×D₉

D₄

yes

—

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂×C₄

yes

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

D₄

yes

—

#3667

—

#3667

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

#3663

—

#1811

—

Sylow

C₂²×C₄×D₃

—

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₂×#208

—

C₂²×C₃⋊C₈

—

C₂×ΓL(1,𝔽₂₅)

—

C₂×ΓL(1,𝔽₂₅)

—

C₂×ΓL(1,𝔽₂₅)

—

C₃×#108

—

(C₂×D₃)⋊C₈

—

#819

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂²×D₉

—

C₂²×D₉

—

C₂²×D₉

—

C₂²×D₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

C₂×C₄×C₉

yes

C₂×C₄×C₉

yes

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

C₄⋊C₄

yes

—

C₄×D₉

—

C₄×D₉

—

C₄×D₉

—

C₄×D₉

—

C₈×C₉

—

C₈×C₉

C₂²⋊C₄

yes

—

C₉⋊C₈

—

C₉⋊C₈

—

C₂²×M₁₆

—

C₂×#108

—

C₂×#108

D₉

yes

characteristic, complemented

#407

—

#341

—

C₂³×D₃

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₄×D₃

yes

—

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃×C₈

#67

yes

—

#208

—

100

#208

—

101

C₂×C₃⋊C₈

—

102

C₂×C₃⋊C₈

—

103

C₂×C₃⋊C₈

—

104

C₂×C₃⋊C₈

—

105

ΓL(1,𝔽₂₅)

—

106

C₂²×C₉

—

107

C₂²×C₉

C₂×C₄⋊C₄

yes

characteristic

108

C₂²×C₉

C₂²⋊Q₈

yes

characteristic

109

C₂²×C₉

C₂²⋊Q₈

yes

characteristic

110

C₂×D₉

—

111

C₂×D₉

—

112

C₂×D₉

—

113

C₂×D₉

—

114

C₄×C₉

C₂×C₂²⋊C₄

yes

characteristic

115

C₄×C₉

#117

yes

characteristic

116

C₄×C₉

#121

yes

characteristic

117

C₄×C₉

#121

yes

characteristic

118

Dic₉

—

119

C₂³×C₄

—

120

C₂×M₁₆

—

121

C₂×M₁₆

—

122

C₂×M₁₆

—

123

C₂×M₁₆

—

124

C₂×M₁₆

C₂×D₉

yes

—

125

C₂²×C₈

—

126

C₂²×C₈

C₂×D₉

yes

characteristic

127

#108

—

128

#108

—

129

C₂²⋊C₈

—

130

C₂³×C₃

D₃×Q₈

yes

characteristic

131

C₂²×D₃

—

132

C₂²×D₃

—

133

C₂²×D₃

—

134

C₂²×D₃

—

135

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

136

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

137

C₂×C₃×C₄

D₃×D₄

yes

characteristic

138

C₂×C₃×C₄

#237

yes

characteristic

139

C₂×C₃×C₄

#239

yes

characteristic

140

C₂×C₃×C₄

C₂×#67

yes

characteristic

141

C₂×Dic₃

—

142

C₂×Dic₃

—

143

C₂×Dic₃

—

144

C₄×D₃

—

145

C₄×D₃

—

146

C₄×D₃

—

147

C₄×D₃

—

148

C₃×C₈

—

149

C₃×C₈

(C₂×D₃)⋊C₄

yes

—

150

C₃⋊C₈

—

151

C₃⋊C₈

—

152

C₂×C₉

—

153

C₂×C₉

—

154

C₂×C₉

#380

yes

characteristic

155

C₂×C₉

#430

yes

—

156

D₉

—

157

C₂⁴

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

C₂²×D₉

yes

characteristic

166

M₁₆

—

167

M₁₆

—

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

C₄×D₉

yes

—

177

C₂×C₈

D₃₆

yes

—

178

C₂×C₈

#611

yes

—

179

C₂²×C₃

—

180

C₂²×C₃

D₃×C₄⋊C₄

yes

characteristic

181

C₂²×C₃

#897

yes

characteristic

182

C₂²×C₃

#946

yes

characteristic

183

C₂×D₃

—

184

C₂×D₃

—

185

C₂×D₃

—

186

C₂×D₃

—

187

C₃×C₄

#892

yes

characteristic

188

C₃×C₄

#895

yes

characteristic

189

C₃×C₄

C₂×(C₂×D₃)⋊C₄

yes

characteristic

190

C₃×C₄

#938

yes

characteristic

191

Dic₃

—

192

C₉

#1811

yes

characteristic, complemented, Sylow

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

Q₈×D₉

yes

characteristic

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

C₂×C₄×D₉

yes

characteristic

206

C₂×C₄

C₂×D₃₆

yes

characteristic

207

C₂×C₄

D₄×D₉

yes

characteristic

208

C₂×C₄

#3699

yes

characteristic

209

C₂×C₄

#3701

yes

characteristic

210

C₂×C₄

C₂×#611

yes

characteristic

211

C₈

—

212

C₈

—

213

C₈

—

214

C₈

(C₂×D₉)⋊C₄

yes

—

215

C₂×C₃

—

216

C₂×C₃

—

217

C₂×C₃

#4893

yes

—

218

C₂×C₃

#4987

yes

characteristic

219

D₃

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

C₄⋊C₄×D₉

yes

characteristic

226

C₂²

#63459

yes

characteristic

227

C₂²

#63508

yes

characteristic

228

C₄

—

229

C₄

#63454

yes

characteristic

230

C₄

#63457

yes

characteristic

231

C₄

C₂×(C₂×D₉)⋊C₄

yes

characteristic

232

C₄

#63500

yes

characteristic

233

C₃

#70712

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

—

237

C₂

#10588573

yes

—

238

C₂

#10588667

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₉
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#108	C₂
socle	C₂²×C₃	D₃×C₄⋊C₄
prime radical	C₂³×D₉	Q₈
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#108	D₉
hypocenter	C₉	#1811
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₉

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#108

C₂

socle

C₂²×C₃

D₃×C₄⋊C₄

prime radical

C₂³×D₉

Q₈

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
2. C₂×C₉×#108	C₂	semidirect
4. C₂×#63372	C₂	semidirect
5. #10588231	C₂	semidirect
81. C₂×#108	D₉	semidirect
192. C₉	#1811	semidirect

H ≅ G/N

type

2. C₂×C₉×#108

C₂

semidirect

4. C₂×#63372

C₂

semidirect

5. #10588231

C₂

semidirect

81. C₂×#108

D₉

semidirect

192. C₉

#1811

semidirect

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

subgroup	index
C₂²×#3663	2
C₂×C₉×#108	2
#10588808	2
C₂×#63372	2
#10588231	2
#70712	3

subgroup

index

C₂²×#3663

C₂×C₉×#108

Subgroups — #11785450

Conjugacy classes of subgroups

Complements

Maximal subgroups