Group #11766609 — subgroups

Subgroups — C₉×#1888 #11766609

Order 1152.

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

normal subgroups only

This group has 516 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×#124	C₂	1	1	yes	maximal, characteristic
2	C₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#418	C₂	1	2	yes	maximal
4	C₂×C₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#339	C₂	1	2	yes	maximal, complemented
6	C₃×#1888	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×M₁₆	C₂²	1	2	yes	—
10	C₉×#124	—	2	2	no	—
11	C₉×#124	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×C₂²⋊C₄	—	2	2	no	—
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₉×#102	—	2	4	no	—
18	C₉×#101	—	2	2	no	—
19	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
20	C₃×#519	C₂×C₃	1	1	yes	characteristic
21	C₃×#418	C₂×C₃	1	2	yes	—
22	C₂×C₃×#101	C₂×C₃	1	1	yes	characteristic
23	C₃×#339	C₂×C₃	1	2	yes	—
24	C₂⁴×C₉	—	2	1	no	—
25	C₂×Q₈×C₉	—	2	2	no	—
26	C₂×Q₈×C₉	—	2	2	no	—
27	C₂×Q₈×C₉	C₂×C₄	1	2	yes	—
28	C₂×Q₈×C₉	D₄	1	2	yes	—
29	C₂×D₄×C₉	—	2	2	no	—
30	C₂×D₄×C₉	—	2	1	no	—
31	C₂×D₄×C₉	—	2	2	no	—
32	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
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	D₄	1	4	yes	—
41	C₉×C₂²⋊C₄	—	2	2	no	—
42	C₉×C₂²⋊C₄	—	2	8	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	#1888	C₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
50	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
51	C₃×#124	—	2	2	no	—
52	C₃×#124	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×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
58	C₃×#102	—	2	4	no	—
59	C₃×#101	—	2	2	no	—
60	C₂³×C₉	—	2	2	no	—
61	C₂³×C₉	—	4	4	no	—
62	C₂³×C₉	—	4	1	no	—
63	C₂³×C₉	—	4	1	no	—
64	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
65	Q₈×C₉	—	2	4	no	—
66	Q₈×C₉	—	2	4	no	—
67	D₄×C₉	—	2	4	no	—
68	D₄×C₉	—	4	2	no	—
69	C₂×C₄×C₉	—	2	2	no	—
70	C₂×C₄×C₉	—	2	2	no	—
71	C₂×C₄×C₉	—	2	2	no	—
72	C₂×C₄×C₉	—	2	4	no	—
73	C₂×C₄×C₉	—	4	2	no	—
74	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
75	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₉	#41	1	2	yes	—
79	C₈×C₉	—	4	2	no	—
80	C₂×#124	C₂×C₉	1	1	yes	characteristic
81	#519	C₂×C₉	1	1	yes	characteristic, complemented
82	#418	C₂×C₉	1	2	yes	—
83	C₂×#101	C₂×C₉	1	1	yes	characteristic, complemented
84	#339	C₂×C₉	1	2	yes	complemented
85	C₂⁴×C₃	—	2	1	no	—
86	C₂×C₃×Q₈	—	2	2	no	—
87	C₂×C₃×Q₈	—	2	2	no	—
88	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
89	C₂×C₃×Q₈	C₃×D₄	1	2	yes	—
90	C₂×C₃×D₄	—	2	2	no	—
91	C₂×C₃×D₄	—	2	1	no	—
92	C₂×C₃×D₄	—	2	2	no	—
93	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
94	C₂²×C₃×C₄	—	2	1	no	—
95	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
96	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
97	C₃×M₁₆	—	2	2	no	—
98	C₃×M₁₆	—	2	2	no	—
99	C₂×C₃×C₈	—	2	2	no	—
100	C₃×C₄⋊C₄	—	2	4	no	—
101	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
102	C₃×C₂²⋊C₄	—	2	2	no	—
103	C₃×C₂²⋊C₄	—	2	8	no	—
104	C₃×C₄²	—	2	4	no	—
105	C₃×C₄²	—	2	1	no	—
106	C₃×C₄²	—	2	2	no	—
107	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
108	C₂²×C₉	—	2	2	no	—
109	C₂²×C₉	—	4	4	no	—
110	C₂²×C₉	—	4	2	no	—
111	C₂²×C₉	—	8	2	no	—
112	C₂²×C₉	—	8	2	no	—
113	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₉	#120	1	1	yes	characteristic
115	C₂²×C₉	#123	1	1	yes	characteristic
116	C₄×C₉	—	2	4	no	—
117	C₄×C₉	—	4	2	no	—
118	C₄×C₉	—	4	4	no	—
119	C₄×C₉	C₄×D₄	1	2	yes	—
120	C₄×C₉	#121	1	2	yes	—
121	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
122	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
123	C₂×M₁₆	C₂²×C₉	1	2	yes	—
124	#124	—	2	2	no	—
125	#124	C₄×C₉	1	4	yes	complemented
126	C₄×Q₈	—	2	4	no	—
127	#117	—	2	2	no	—
128	#117	C₂²×C₉	1	2	yes	—
129	C₂×C₂²⋊C₄	—	2	2	no	—
130	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
131	#102	—	2	4	no	—
132	#101	—	2	2	no	—
133	C₂³×C₃	—	2	2	no	—
134	C₂³×C₃	—	4	4	no	—
135	C₂³×C₃	—	4	1	no	—
136	C₂³×C₃	—	4	1	no	—
137	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
138	C₃×Q₈	—	2	4	no	—
139	C₃×Q₈	—	2	4	no	—
140	C₃×D₄	—	2	4	no	—
141	C₃×D₄	—	4	2	no	—
142	C₂×C₃×C₄	—	2	2	no	—
143	C₂×C₃×C₄	—	2	2	no	—
144	C₂×C₃×C₄	—	2	2	no	—
145	C₂×C₃×C₄	—	2	4	no	—
146	C₂×C₃×C₄	—	4	2	no	—
147	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	4	yes	—
148	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
150	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄	C₃×#41	1	2	yes	—
152	C₃×C₈	—	4	2	no	—
153	C₂×C₉	—	2	1	no	—
154	C₂×C₉	—	2	1	no	—
155	C₂×C₉	—	8	2	no	—
156	C₂×C₉	#386	1	1	yes	characteristic
157	C₂×C₉	#454	1	2	yes	—
158	C₂⁴	—	2	1	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	C₂×C₄×C₉	1	2	yes	—
162	C₂×Q₈	D₄×C₉	1	2	yes	—
163	C₂×D₄	—	2	2	no	—
164	C₂×D₄	—	2	1	no	—
165	C₂×D₄	—	2	2	no	—
166	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	D₄×C₉	1	2	yes	—
169	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
170	M₁₆	—	2	2	no	—
171	M₁₆	—	2	2	no	—
172	C₂×C₈	—	2	2	no	—
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	D₄×C₉	1	4	yes	—
175	C₂²⋊C₄	—	2	2	no	—
176	C₂²⋊C₄	—	2	8	no	—
177	C₄²	—	2	4	no	—
178	C₄²	—	2	1	no	—
179	C₄²	—	2	2	no	—
180	C₄²	C₂×C₄×C₉	1	2	yes	—
181	C₂²×C₃	—	2	2	no	—
182	C₂²×C₃	—	4	4	no	—
183	C₂²×C₃	—	4	2	no	—
184	C₂²×C₃	—	8	2	no	—
185	C₂²×C₃	—	8	2	no	—
186	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₃	C₃×#120	1	1	yes	characteristic
188	C₂²×C₃	C₃×#123	1	1	yes	characteristic
189	C₃×C₄	—	2	4	no	—
190	C₃×C₄	—	4	2	no	—
191	C₃×C₄	—	4	4	no	—
192	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
193	C₃×C₄	C₃×#121	1	2	yes	—
194	C₉	#1888	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³	—	2	2	no	—
196	C₂³	—	4	4	no	—
197	C₂³	—	4	1	no	—
198	C₂³	—	4	1	no	—
199	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
200	Q₈	—	2	4	no	—
201	Q₈	—	2	4	no	—
202	D₄	—	2	4	no	—
203	D₄	—	4	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	C₉×C₂²⋊C₄	1	4	yes	—
210	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
211	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
212	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
213	C₂×C₄	C₉×#41	1	2	yes	—
214	C₈	—	4	2	no	—
215	C₂×C₃	—	2	1	no	—
216	C₂×C₃	—	2	1	no	—
217	C₂×C₃	—	8	2	no	—
218	C₂×C₃	C₃×#386	1	1	yes	characteristic
219	C₂×C₃	C₃×#454	1	2	yes	—
220	C₂²	—	2	2	no	—
221	C₂²	—	4	4	no	—
222	C₂²	—	4	2	no	—
223	C₂²	—	8	2	no	—
224	C₂²	—	8	2	no	—
225	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
226	C₂²	C₉×#120	1	1	yes	characteristic
227	C₂²	C₉×#123	1	1	yes	characteristic
228	C₄	—	2	4	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	4	no	—
231	C₄	C₄×D₄×C₉	1	2	yes	—
232	C₄	C₉×#121	1	2	yes	—
233	C₃	C₃×#1888	1	1	yes	characteristic
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	—	8	2	no	—
237	C₂	C₉×#386	1	1	yes	characteristic
238	C₂	C₉×#454	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#124

C₂

yes

maximal, characteristic

C₉×#519

C₂

yes

maximal, characteristic, complemented

C₉×#418

C₂

yes

maximal

C₂×C₉×#101

C₂

yes

maximal, characteristic, complemented

C₉×#339

C₂

yes

maximal, complemented

C₃×#1888

C₃

yes

maximal, characteristic

C₂²×Q₈×C₉

C₂²

yes

characteristic

C₂²×D₄×C₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₉×#124

—

C₉×#124

C₄

yes

complemented

C₄×Q₈×C₉

—

C₉×#117

—

C₉×#117

C₂²

yes

—

C₂×C₉×C₂²⋊C₄

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₉×#102

—

C₉×#101

—

C₂×C₃×#124

C₂×C₃

yes

characteristic

C₃×#519

C₂×C₃

yes

characteristic

C₃×#418

C₂×C₃

yes

—

C₂×C₃×#101

C₂×C₃

yes

characteristic

C₃×#339

C₂×C₃

yes

—

C₂⁴×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

C₂×C₄

yes

—

C₂×Q₈×C₉

D₄

yes

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂×C₄

yes

—

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

D₄

yes

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

C₄²×C₉

—

C₄²×C₉

—

C₄²×C₉

C₂×C₄

yes

—

#1888

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×Q₈

C₂²×C₃

yes

characteristic

C₂²×C₃×D₄

C₂²×C₃

yes

characteristic

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₃×#124

—

C₃×#124

C₃×C₄

yes

—

C₃×C₄×Q₈

—

C₃×#117

—

C₃×#117

C₂²×C₃

yes

—

C₂×C₃×C₂²⋊C₄

—

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×#102

—

C₃×#101

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂×D₄

yes

characteristic

Q₈×C₉

—

Q₈×C₉

—

D₄×C₉

—

D₄×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×#124

C₂×C₉

yes

characteristic

#519

C₂×C₉

yes

characteristic, complemented

#418

C₂×C₉

yes

—

C₂×#101

C₂×C₉

yes

characteristic, complemented

#339

C₂×C₉

yes

complemented

C₂⁴×C₃

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

C₂×C₃×C₄

yes

—

C₂×C₃×Q₈

C₃×D₄

yes

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₃×D₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

100

C₃×C₄⋊C₄

—

101

C₃×C₄⋊C₄

C₃×D₄

yes

—

102

C₃×C₂²⋊C₄

—

103

C₃×C₂²⋊C₄

—

104

C₃×C₄²

—

105

C₃×C₄²

—

106

C₃×C₄²

—

107

C₃×C₄²

C₂×C₃×C₄

yes

—

108

C₂²×C₉

—

109

C₂²×C₉

—

110

C₂²×C₉

—

111

C₂²×C₉

—

112

C₂²×C₉

—

113

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

114

C₂²×C₉

#120

yes

characteristic

115

C₂²×C₉

#123

yes

characteristic

116

C₄×C₉

—

117

C₄×C₉

—

118

C₄×C₉

—

119

C₄×C₉

C₄×D₄

yes

—

120

C₄×C₉

#121

yes

—

121

C₂²×Q₈

C₂²×C₉

yes

characteristic

122

C₂²×D₄

C₂²×C₉

yes

characteristic

123

C₂×M₁₆

C₂²×C₉

yes

—

124

#124

—

125

#124

C₄×C₉

yes

complemented

126

C₄×Q₈

—

127

#117

—

128

#117

C₂²×C₉

yes

—

129

C₂×C₂²⋊C₄

—

130

C₂×C₄²

C₂²×C₉

yes

characteristic

131

#102

—

132

#101

—

133

C₂³×C₃

—

134

C₂³×C₃

—

135

C₂³×C₃

—

136

C₂³×C₃

—

137

C₂³×C₃

C₂×C₃×D₄

yes

characteristic

138

C₃×Q₈

—

139

C₃×Q₈

—

140

C₃×D₄

—

141

C₃×D₄

—

142

C₂×C₃×C₄

—

143

C₂×C₃×C₄

—

144

C₂×C₃×C₄

—

145

C₂×C₃×C₄

—

146

C₂×C₃×C₄

—

147

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

148

C₂×C₃×C₄

C₂²×C₃×C₄

yes

characteristic

149

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

150

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

151

C₂×C₃×C₄

C₃×#41

yes

—

152

C₃×C₈

—

153

C₂×C₉

—

154

C₂×C₉

—

155

C₂×C₉

—

156

C₂×C₉

#386

yes

characteristic

157

C₂×C₉

#454

yes

—

158

C₂⁴

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₂×C₄×C₉

yes

—

162

C₂×Q₈

D₄×C₉

yes

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

C₂×C₄×C₉

yes

—

167

C₂²×C₄

—

168

C₂²×C₄

D₄×C₉

yes

—

169

C₂²×C₄

C₂³×C₉

yes

characteristic

170

M₁₆

—

171

M₁₆

—

172

C₂×C₈

—

173

C₄⋊C₄

—

174

C₄⋊C₄

D₄×C₉

yes

—

175

C₂²⋊C₄

—

176

C₂²⋊C₄

—

177

C₄²

—

178

C₄²

—

179

C₄²

—

180

C₄²

C₂×C₄×C₉

yes

—

181

C₂²×C₃

—

182

C₂²×C₃

—

183

C₂²×C₃

—

184

C₂²×C₃

—

185

C₂²×C₃

—

186

C₂²×C₃

C₂×C₃×C₂²⋊C₄

yes

characteristic

187

C₂²×C₃

C₃×#120

yes

characteristic

188

C₂²×C₃

C₃×#123

yes

characteristic

189

C₃×C₄

—

190

C₃×C₄

—

191

C₃×C₄

—

192

C₃×C₄

C₃×C₄×D₄

yes

—

193

C₃×C₄

C₃×#121

yes

—

194

C₉

#1888

yes

characteristic, direct product factor, Sylow

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

C₂×D₄×C₉

yes

characteristic

200

Q₈

—

201

Q₈

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₉×C₂²⋊C₄

yes

—

210

C₂×C₄

C₂²×C₄×C₉

yes

characteristic

211

C₂×C₄

C₂×D₄×C₉

yes

—

212

C₂×C₄

C₂×D₄×C₉

yes

characteristic

213

C₂×C₄

C₉×#41

yes

—

214

C₈

—

215

C₂×C₃

—

216

C₂×C₃

—

217

C₂×C₃

—

218

C₂×C₃

C₃×#386

yes

characteristic

219

C₂×C₃

C₃×#454

yes

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

C₂×C₉×C₂²⋊C₄

yes

characteristic

226

C₂²

C₉×#120

yes

characteristic

227

C₂²

C₉×#123

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

C₄×D₄×C₉

yes

—

232

C₄

C₉×#121

yes

—

233

C₃

C₃×#1888

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

—

237

C₂

C₉×#386

yes

characteristic

238

C₂

C₉×#454

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	C₂²×C₃×D₄	C₂²×C₃
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

C₂²×C₃×D₄

C₂²×C₃

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
2. C₉×#519	C₂	semidirect
4. C₂×C₉×#101	C₂	semidirect
5. C₉×#339	C₂	semidirect
11. C₉×#124	C₄	semidirect
47. #1888	C₉	direct (N × H)
81. #519	C₂×C₉	semidirect
83. C₂×#101	C₂×C₉	semidirect
84. #339	C₂×C₉	semidirect
125. #124	C₄×C₉	semidirect
194. C₉	#1888	direct (N × H)

H ≅ G/N

type

2. C₉×#519

C₂

semidirect

4. C₂×C₉×#101

C₂

semidirect

5. C₉×#339

C₂

semidirect

11. C₉×#124

C₄

semidirect

47. #1888

C₉

direct (N × H)

81. #519

C₂×C₉

semidirect

83. C₂×#101

C₂×C₉

semidirect

84. #339

C₂×C₉

semidirect

125. #124

C₄×C₉

semidirect

194. C₉

#1888

direct (N × H)

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

subgroup	index
C₂×C₉×#124	2
C₉×#519	2
C₉×#418	2
C₂×C₉×#101	2
C₉×#339	2
C₃×#1888	3

subgroup

index

C₂×C₉×#124

C₂×C₉×#101

Subgroups — C₉×#1888 #11766609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#1888 #11766609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1888 #11766609