Group #11766607 — subgroups

Subgroups — C₉×#1886 #11766607

Order 1152.

486 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 168 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×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₉×#519	C₂	1	1	yes	maximal, characteristic
3	C₉×#419	C₂	1	2	yes	maximal
4	C₂×C₉×#101	C₂	1	1	yes	maximal, characteristic
5	C₉×#339	C₂	1	2	yes	maximal
6	C₃×#1886	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
8	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×M₁₆	C₂²	1	2	yes	—
10	C₉×C₄⋊Q₈	—	2	2	no	—
11	C₉×C₄⋊Q₈	C₄	1	4	yes	complemented
12	C₄×Q₈×C₉	—	2	4	no	—
13	C₉×#117	—	2	2	no	—
14	C₉×#117	C₂²	1	2	yes	—
15	C₂×C₉×C₄⋊C₄	—	2	2	no	—
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₉×#103	—	2	4	no	—
18	C₉×#101	—	2	2	no	—
19	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
20	C₃×#519	C₂×C₃	1	1	yes	characteristic
21	C₃×#419	C₂×C₃	1	2	yes	—
22	C₂×C₃×#101	C₂×C₃	1	1	yes	characteristic
23	C₃×#339	C₂×C₃	1	2	yes	—
24	C₂×Q₈×C₉	—	2	2	no	—
25	C₂×Q₈×C₉	—	2	1	no	—
26	C₂×Q₈×C₉	—	2	2	no	—
27	C₂×Q₈×C₉	—	2	2	no	—
28	C₂×Q₈×C₉	—	2	2	no	—
29	C₂×Q₈×C₉	C₂×C₄	1	2	yes	—
30	C₂×Q₈×C₉	C₂×C₄	1	2	yes	—
31	C₂×Q₈×C₉	D₄	1	2	yes	—
32	C₂²×C₄×C₉	—	2	1	no	—
33	C₂²×C₄×C₉	—	2	1	no	—
34	C₂²×C₄×C₉	D₄	1	2	yes	—
35	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
36	C₉×M₁₆	—	2	2	no	—
37	C₉×M₁₆	—	2	2	no	—
38	C₂×C₈×C₉	—	2	2	no	—
39	C₉×C₄⋊C₄	—	2	4	no	—
40	C₉×C₄⋊C₄	—	2	8	no	—
41	C₉×C₄⋊C₄	D₄	1	4	yes	—
42	C₉×C₂²⋊C₄	—	2	2	no	—
43	C₄²×C₉	—	2	4	no	—
44	C₄²×C₉	—	2	1	no	—
45	C₄²×C₉	—	2	2	no	—
46	C₄²×C₉	C₂×C₄	1	2	yes	—
47	#1886	C₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
50	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
51	C₃×C₄⋊Q₈	—	2	2	no	—
52	C₃×C₄⋊Q₈	C₃×C₄	1	4	yes	—
53	C₃×C₄×Q₈	—	2	4	no	—
54	C₃×#117	—	2	2	no	—
55	C₃×#117	C₂²×C₃	1	2	yes	—
56	C₂×C₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
58	C₃×#103	—	2	4	no	—
59	C₃×#101	—	2	2	no	—
60	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
61	Q₈×C₉	—	2	4	no	—
62	Q₈×C₉	—	2	4	no	—
63	Q₈×C₉	—	2	4	no	—
64	Q₈×C₉	—	4	2	no	—
65	C₂×C₄×C₉	—	2	4	no	—
66	C₂×C₄×C₉	—	2	2	no	—
67	C₂×C₄×C₉	—	2	2	no	—
68	C₂×C₄×C₉	—	2	2	no	—
69	C₂×C₄×C₉	—	2	2	no	—
70	C₂×C₄×C₉	—	2	4	no	—
71	C₂×C₄×C₉	—	4	1	no	—
72	C₂×C₄×C₉	—	4	1	no	—
73	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
74	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₉	#41	1	2	yes	—
78	C₈×C₉	—	4	2	no	—
79	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
80	#519	C₂×C₉	1	1	yes	characteristic
81	#419	C₂×C₉	1	2	yes	—
82	C₂×#101	C₂×C₉	1	1	yes	characteristic
83	#339	C₂×C₉	1	2	yes	—
84	C₂×C₃×Q₈	—	2	2	no	—
85	C₂×C₃×Q₈	—	2	1	no	—
86	C₂×C₃×Q₈	—	2	2	no	—
87	C₂×C₃×Q₈	—	2	2	no	—
88	C₂×C₃×Q₈	—	2	2	no	—
89	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
90	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
91	C₂×C₃×Q₈	C₃×D₄	1	2	yes	—
92	C₂²×C₃×C₄	—	2	1	no	—
93	C₂²×C₃×C₄	—	2	1	no	—
94	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
95	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
96	C₃×M₁₆	—	2	2	no	—
97	C₃×M₁₆	—	2	2	no	—
98	C₂×C₃×C₈	—	2	2	no	—
99	C₃×C₄⋊C₄	—	2	4	no	—
100	C₃×C₄⋊C₄	—	2	8	no	—
101	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
102	C₃×C₂²⋊C₄	—	2	2	no	—
103	C₃×C₄²	—	2	4	no	—
104	C₃×C₄²	—	2	1	no	—
105	C₃×C₄²	—	2	2	no	—
106	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
107	C₂²×C₉	—	2	2	no	—
108	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₉	#120	1	1	yes	characteristic
110	C₂²×C₉	#123	1	1	yes	characteristic
111	C₄×C₉	—	2	4	no	—
112	C₄×C₉	—	2	4	no	—
113	C₄×C₉	—	4	2	no	—
114	C₄×C₉	—	4	4	no	—
115	C₄×C₉	C₄×D₄	1	2	yes	—
116	C₄×C₉	#121	1	2	yes	—
117	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
118	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
119	C₂×M₁₆	C₂²×C₉	1	2	yes	—
120	C₄⋊Q₈	—	2	2	no	—
121	C₄⋊Q₈	C₄×C₉	1	4	yes	complemented
122	C₄×Q₈	—	2	4	no	—
123	#117	—	2	2	no	—
124	#117	C₂²×C₉	1	2	yes	—
125	C₂×C₄⋊C₄	—	2	2	no	—
126	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
127	#103	—	2	4	no	—
128	#101	—	2	2	no	—
129	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
130	C₃×Q₈	—	2	4	no	—
131	C₃×Q₈	—	2	4	no	—
132	C₃×Q₈	—	2	4	no	—
133	C₃×Q₈	—	4	2	no	—
134	C₂×C₃×C₄	—	2	4	no	—
135	C₂×C₃×C₄	—	2	2	no	—
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	—	2	2	no	—
138	C₂×C₃×C₄	—	2	2	no	—
139	C₂×C₃×C₄	—	2	4	no	—
140	C₂×C₃×C₄	—	4	1	no	—
141	C₂×C₃×C₄	—	4	1	no	—
142	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
143	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
144	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
145	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄	C₃×#41	1	2	yes	—
147	C₃×C₈	—	4	2	no	—
148	C₂×C₉	—	2	1	no	—
149	C₂×C₉	—	2	1	no	—
150	C₂×C₉	#386	1	1	yes	characteristic
151	C₂×C₉	#456	1	2	yes	—
152	C₂×Q₈	—	2	2	no	—
153	C₂×Q₈	—	2	1	no	—
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	2	2	no	—
156	C₂×Q₈	—	2	2	no	—
157	C₂×Q₈	C₂×C₄×C₉	1	2	yes	—
158	C₂×Q₈	C₂×C₄×C₉	1	2	yes	—
159	C₂×Q₈	D₄×C₉	1	2	yes	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	D₄×C₉	1	2	yes	—
163	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
164	M₁₆	—	2	2	no	—
165	M₁₆	—	2	2	no	—
166	C₂×C₈	—	2	2	no	—
167	C₄⋊C₄	—	2	4	no	—
168	C₄⋊C₄	—	2	8	no	—
169	C₄⋊C₄	D₄×C₉	1	4	yes	—
170	C₂²⋊C₄	—	2	2	no	—
171	C₄²	—	2	4	no	—
172	C₄²	—	2	1	no	—
173	C₄²	—	2	2	no	—
174	C₄²	C₂×C₄×C₉	1	2	yes	—
175	C₂²×C₃	—	2	2	no	—
176	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₃	C₃×#120	1	1	yes	characteristic
178	C₂²×C₃	C₃×#123	1	1	yes	characteristic
179	C₃×C₄	—	2	4	no	—
180	C₃×C₄	—	2	4	no	—
181	C₃×C₄	—	4	2	no	—
182	C₃×C₄	—	4	4	no	—
183	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
184	C₃×C₄	C₃×#121	1	2	yes	—
185	C₉	#1886	1	1	yes	characteristic, direct product factor, Sylow
186	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
187	Q₈	—	2	4	no	—
188	Q₈	—	2	4	no	—
189	Q₈	—	2	4	no	—
190	Q₈	—	4	2	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	C₉×C₂²⋊C₄	1	4	yes	—
200	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
201	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
202	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
203	C₂×C₄	C₉×#41	1	2	yes	—
204	C₈	—	4	2	no	—
205	C₂×C₃	—	2	1	no	—
206	C₂×C₃	—	2	1	no	—
207	C₂×C₃	C₃×#386	1	1	yes	characteristic
208	C₂×C₃	C₃×#456	1	2	yes	—
209	C₂²	—	2	2	no	—
210	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²	C₉×#120	1	1	yes	characteristic
212	C₂²	C₉×#123	1	1	yes	characteristic
213	C₄	—	2	4	no	—
214	C₄	—	2	4	no	—
215	C₄	—	4	2	no	—
216	C₄	—	4	4	no	—
217	C₄	C₄×D₄×C₉	1	2	yes	—
218	C₄	C₉×#121	1	2	yes	—
219	C₃	C₃×#1886	1	1	yes	characteristic
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	C₉×#386	1	1	yes	characteristic
223	C₂	C₉×#456	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₉×#519

C₂

yes

maximal, characteristic

C₉×#419

C₂

yes

maximal

C₂×C₉×#101

C₂

yes

maximal, characteristic

C₉×#339

C₂

yes

maximal

C₃×#1886

C₃

yes

maximal, characteristic

C₂²×Q₈×C₉

C₂²

yes

characteristic

C₂²×Q₈×C₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₉×C₄⋊Q₈

—

C₉×C₄⋊Q₈

C₄

yes

complemented

C₄×Q₈×C₉

—

C₉×#117

—

C₉×#117

C₂²

yes

—

C₂×C₉×C₄⋊C₄

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₉×#103

—

C₉×#101

—

C₂×C₃×C₄⋊Q₈

C₂×C₃

yes

characteristic

C₃×#519

C₂×C₃

yes

characteristic

C₃×#419

C₂×C₃

yes

—

C₂×C₃×#101

C₂×C₃

yes

characteristic

C₃×#339

C₂×C₃

yes

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

C₂×C₄

yes

—

C₂×Q₈×C₉

C₂×C₄

yes

—

C₂×Q₈×C₉

D₄

yes

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

D₄

yes

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

C₄²×C₉

—

C₄²×C₉

—

C₄²×C₉

C₂×C₄

yes

—

#1886

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×Q₈

C₂²×C₃

yes

characteristic

C₂²×C₃×Q₈

C₂²×C₃

yes

characteristic

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₃×C₄⋊Q₈

—

C₃×C₄⋊Q₈

C₃×C₄

yes

—

C₃×C₄×Q₈

—

C₃×#117

—

C₃×#117

C₂²×C₃

yes

—

C₂×C₃×C₄⋊C₄

—

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×#103

—

C₃×#101

—

C₂³×C₉

C₂×D₄

yes

characteristic

Q₈×C₉

—

Q₈×C₉

—

Q₈×C₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₈×C₉

—

C₂×C₄⋊Q₈

C₂×C₉

yes

characteristic

#519

C₂×C₉

yes

characteristic

#419

C₂×C₉

yes

—

C₂×#101

C₂×C₉

yes

characteristic

#339

C₂×C₉

yes

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

C₂×C₃×C₄

yes

—

C₂×C₃×Q₈

C₂×C₃×C₄

yes

—

C₂×C₃×Q₈

C₃×D₄

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₃×D₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₃×C₄⋊C₄

—

100

C₃×C₄⋊C₄

—

101

C₃×C₄⋊C₄

C₃×D₄

yes

—

102

C₃×C₂²⋊C₄

—

103

C₃×C₄²

—

104

C₃×C₄²

—

105

C₃×C₄²

—

106

C₃×C₄²

C₂×C₃×C₄

yes

—

107

C₂²×C₉

—

108

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

109

C₂²×C₉

#120

yes

characteristic

110

C₂²×C₉

#123

yes

characteristic

111

C₄×C₉

—

112

C₄×C₉

—

113

C₄×C₉

—

114

C₄×C₉

—

115

C₄×C₉

C₄×D₄

yes

—

116

C₄×C₉

#121

yes

—

117

C₂²×Q₈

C₂²×C₉

yes

characteristic

118

C₂²×Q₈

C₂²×C₉

yes

characteristic

119

C₂×M₁₆

C₂²×C₉

yes

—

120

C₄⋊Q₈

—

121

C₄⋊Q₈

C₄×C₉

yes

complemented

122

C₄×Q₈

—

123

#117

—

124

#117

C₂²×C₉

yes

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄²

C₂²×C₉

yes

characteristic

127

#103

—

128

#101

—

129

C₂³×C₃

C₂×C₃×D₄

yes

characteristic

130

C₃×Q₈

—

131

C₃×Q₈

—

132

C₃×Q₈

—

133

C₃×Q₈

—

134

C₂×C₃×C₄

—

135

C₂×C₃×C₄

—

136

C₂×C₃×C₄

—

137

C₂×C₃×C₄

—

138

C₂×C₃×C₄

—

139

C₂×C₃×C₄

—

140

C₂×C₃×C₄

—

141

C₂×C₃×C₄

—

142

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

143

C₂×C₃×C₄

C₂²×C₃×C₄

yes

characteristic

144

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

145

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

146

C₂×C₃×C₄

C₃×#41

yes

—

147

C₃×C₈

—

148

C₂×C₉

—

149

C₂×C₉

—

150

C₂×C₉

#386

yes

characteristic

151

C₂×C₉

#456

yes

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

C₂×C₄×C₉

yes

—

158

C₂×Q₈

C₂×C₄×C₉

yes

—

159

C₂×Q₈

D₄×C₉

yes

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

D₄×C₉

yes

—

163

C₂²×C₄

C₂³×C₉

yes

characteristic

164

M₁₆

—

165

M₁₆

—

166

C₂×C₈

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

D₄×C₉

yes

—

170

C₂²⋊C₄

—

171

C₄²

—

172

C₄²

—

173

C₄²

—

174

C₄²

C₂×C₄×C₉

yes

—

175

C₂²×C₃

—

176

C₂²×C₃

C₂×C₃×C₂²⋊C₄

yes

characteristic

177

C₂²×C₃

C₃×#120

yes

characteristic

178

C₂²×C₃

C₃×#123

yes

characteristic

179

C₃×C₄

—

180

C₃×C₄

—

181

C₃×C₄

—

182

C₃×C₄

—

183

C₃×C₄

C₃×C₄×D₄

yes

—

184

C₃×C₄

C₃×#121

yes

—

185

C₉

#1886

yes

characteristic, direct product factor, Sylow

186

C₂³

C₂×D₄×C₉

yes

characteristic

187

Q₈

—

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

C₉×C₂²⋊C₄

yes

—

200

C₂×C₄

C₂²×C₄×C₉

yes

characteristic

201

C₂×C₄

C₂×D₄×C₉

yes

—

202

C₂×C₄

C₂×D₄×C₉

yes

characteristic

203

C₂×C₄

C₉×#41

yes

—

204

C₈

—

205

C₂×C₃

—

206

C₂×C₃

—

207

C₂×C₃

C₃×#386

yes

characteristic

208

C₂×C₃

C₃×#456

yes

—

209

C₂²

—

210

C₂²

C₂×C₉×C₂²⋊C₄

yes

characteristic

211

C₂²

C₉×#120

yes

characteristic

212

C₂²

C₉×#123

yes

characteristic

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

C₄×D₄×C₉

yes

—

218

C₄

C₉×#121

yes

—

219

C₃

C₃×#1886

yes

characteristic

220

C₂

—

221

C₂

—

222

C₂

C₉×#386

yes

characteristic

223

C₂

C₉×#456

yes

—

	subgroup	G/H
center	C₂²×C₉	#120
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₃×#120
prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

#120

commutator

C₂×C₄

C₂²×C₄×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle

C₂²×C₃

C₃×#120

prime radical

C₂³×C₃

C₂×C₃×D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
11. C₉×C₄⋊Q₈	C₄	semidirect
47. #1886	C₉	direct (N × H)
121. C₄⋊Q₈	C₄×C₉	semidirect
185. C₉	#1886	direct (N × H)

H ≅ G/N

type

11. C₉×C₄⋊Q₈

C₄

semidirect

47. #1886

C₉

direct (N × H)

121. C₄⋊Q₈

C₄×C₉

semidirect

185. C₉

#1886

direct (N × H)

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

subgroup	index
C₂×C₉×C₄⋊Q₈	2
C₉×#519	2
C₉×#419	2
C₂×C₉×#101	2
C₉×#339	2
C₃×#1886	3

subgroup

index

C₂×C₉×C₄⋊Q₈

C₂×C₉×#101

Subgroups — C₉×#1886 #11766607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#1886 #11766607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1886 #11766607