Group #11766748 — subgroups

Subgroups — C₉×#2027 #11766748

Order 1152.

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

normal subgroups only

This group has 423 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	C₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#418	C₂	1	2	yes	maximal
3	C₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#339	C₂	1	2	yes	maximal, complemented
6	C₃×#2027	C₃	1	1	yes	maximal, characteristic
7	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	C₉×C₄⋊Q₈	—	2	2	no	—
10	C₉×#125	—	2	2	no	—
11	C₉×C₂²⋊Q₈	—	2	2	no	—
12	C₉×#117	C₂²	1	2	yes	—
13	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₉×C₂²⋊C₄	—	2	2	no	—
15	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
16	C₉×#102	—	2	2	no	—
17	C₉×#102	—	2	2	no	—
18	C₃×#544	C₂×C₃	1	1	yes	characteristic
19	C₃×#418	C₂×C₃	1	2	yes	—
20	C₃×#390	C₂×C₃	1	1	yes	characteristic
21	C₃×#343	C₂×C₃	1	1	yes	characteristic
22	C₃×#339	C₂×C₃	1	2	yes	—
23	C₂⁴×C₉	—	2	1	no	—
24	C₂×Q₈×C₉	—	2	2	no	—
25	C₂×D₄×C₉	—	2	2	no	—
26	C₂×D₄×C₉	—	2	2	no	—
27	C₂×D₄×C₉	—	2	1	no	—
28	C₂×D₄×C₉	Q₈	1	2	yes	complemented
29	C₂²×C₄×C₉	—	2	1	no	—
30	C₂²×C₄×C₉	D₄	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₉×M₁₆	—	2	2	no	—
33	C₉×M₁₆	—	2	2	no	—
34	C₂×C₈×C₉	—	2	2	no	—
35	C₉×C₄⋊C₄	—	2	2	no	—
36	C₉×C₄⋊C₄	—	2	4	no	—
37	C₉×C₄⋊C₄	—	2	2	no	—
38	C₉×C₄⋊C₄	D₄	1	2	yes	—
39	C₉×C₄⋊C₄	D₄	1	2	yes	—
40	C₉×C₂²⋊C₄	—	2	2	no	—
41	C₉×C₂²⋊C₄	—	4	4	no	—
42	C₄²×C₉	—	2	2	no	—
43	C₄²×C₉	—	2	2	no	—
44	#2027	C₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
47	C₃×C₄⋊Q₈	—	2	2	no	—
48	C₃×#125	—	2	2	no	—
49	C₃×C₂²⋊Q₈	—	2	2	no	—
50	C₃×#117	C₂²×C₃	1	2	yes	—
51	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
54	C₃×#102	—	2	2	no	—
55	C₃×#102	—	2	2	no	—
56	C₂³×C₉	—	2	2	no	—
57	C₂³×C₉	—	4	2	no	—
58	C₂³×C₉	—	4	2	no	—
59	C₂³×C₉	—	4	1	no	—
60	C₂³×C₉	—	4	1	no	—
61	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
62	Q₈×C₉	—	8	2	no	—
63	D₄×C₉	—	2	4	no	—
64	D₄×C₉	—	4	2	no	—
65	C₂×C₄×C₉	—	2	2	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	—	4	1	no	—
70	C₂×C₄×C₉	—	4	1	no	—
71	C₂×C₄×C₉	—	4	2	no	—
72	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₉	#41	1	2	yes	—
75	C₂×C₄×C₉	#41	1	1	yes	characteristic
76	C₈×C₉	—	4	2	no	—
77	#544	C₂×C₉	1	1	yes	characteristic, complemented
78	#418	C₂×C₉	1	2	yes	—
79	#390	C₂×C₉	1	1	yes	characteristic
80	#343	C₂×C₉	1	1	yes	characteristic, complemented
81	#339	C₂×C₉	1	2	yes	complemented
82	C₂⁴×C₃	—	2	1	no	—
83	C₂×C₃×Q₈	—	2	2	no	—
84	C₂×C₃×D₄	—	2	2	no	—
85	C₂×C₃×D₄	—	2	2	no	—
86	C₂×C₃×D₄	—	2	1	no	—
87	C₂×C₃×D₄	C₃×Q₈	1	2	yes	—
88	C₂²×C₃×C₄	—	2	1	no	—
89	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
90	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
91	C₃×M₁₆	—	2	2	no	—
92	C₃×M₁₆	—	2	2	no	—
93	C₂×C₃×C₈	—	2	2	no	—
94	C₃×C₄⋊C₄	—	2	2	no	—
95	C₃×C₄⋊C₄	—	2	4	no	—
96	C₃×C₄⋊C₄	—	2	2	no	—
97	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
98	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
99	C₃×C₂²⋊C₄	—	2	2	no	—
100	C₃×C₂²⋊C₄	—	4	4	no	—
101	C₃×C₄²	—	2	2	no	—
102	C₃×C₄²	—	2	2	no	—
103	C₂²×C₉	—	2	1	no	—
104	C₂²×C₉	—	2	1	no	—
105	C₂²×C₉	—	4	4	no	—
106	C₂²×C₉	—	4	2	no	—
107	C₂²×C₉	—	8	2	no	—
108	C₂²×C₉	—	8	1	no	—
109	C₂²×C₉	—	8	1	no	—
110	C₂²×C₉	#120	1	1	yes	characteristic
111	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
112	C₂²×C₉	#124	1	1	yes	characteristic
113	C₄×C₉	—	4	2	no	—
114	C₄×C₉	—	4	2	no	—
115	C₄×C₉	—	4	2	no	—
116	C₄×C₉	—	4	2	no	—
117	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
118	C₄×C₉	#124	1	2	yes	—
119	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
120	C₂×M₁₆	C₂²×C₉	1	2	yes	—
121	C₄⋊Q₈	—	2	2	no	—
122	#125	—	2	2	no	—
123	C₂²⋊Q₈	—	2	2	no	—
124	#117	C₂²×C₉	1	2	yes	—
125	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
126	C₂×C₂²⋊C₄	—	2	2	no	—
127	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
128	#102	—	2	2	no	—
129	#102	—	2	2	no	—
130	C₂³×C₃	—	2	2	no	—
131	C₂³×C₃	—	4	2	no	—
132	C₂³×C₃	—	4	2	no	—
133	C₂³×C₃	—	4	1	no	—
134	C₂³×C₃	—	4	1	no	—
135	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
136	C₃×Q₈	—	8	2	no	—
137	C₃×D₄	—	2	4	no	—
138	C₃×D₄	—	4	2	no	—
139	C₂×C₃×C₄	—	2	2	no	—
140	C₂×C₃×C₄	—	2	2	no	—
141	C₂×C₃×C₄	—	2	2	no	—
142	C₂×C₃×C₄	—	2	2	no	—
143	C₂×C₃×C₄	—	4	1	no	—
144	C₂×C₃×C₄	—	4	1	no	—
145	C₂×C₃×C₄	—	4	2	no	—
146	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
147	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
148	C₂×C₃×C₄	C₃×#41	1	2	yes	—
149	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
150	C₃×C₈	—	4	2	no	—
151	C₂×C₉	—	2	1	no	—
152	C₂×C₉	—	2	1	no	—
153	C₂×C₉	—	8	2	no	—
154	C₂×C₉	#393	1	1	yes	characteristic
155	C₂×C₉	#453	1	1	yes	characteristic
156	C₂×C₉	#454	1	1	yes	characteristic
157	C₂⁴	—	2	1	no	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×D₄	—	2	2	no	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	—	2	1	no	—
162	C₂×D₄	Q₈×C₉	1	2	yes	complemented
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	D₄×C₉	1	2	yes	—
165	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
166	M₁₆	—	2	2	no	—
167	M₁₆	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	D₄×C₉	1	2	yes	—
173	C₄⋊C₄	D₄×C₉	1	2	yes	—
174	C₂²⋊C₄	—	2	2	no	—
175	C₂²⋊C₄	—	4	4	no	—
176	C₄²	—	2	2	no	—
177	C₄²	—	2	2	no	—
178	C₂²×C₃	—	2	1	no	—
179	C₂²×C₃	—	2	1	no	—
180	C₂²×C₃	—	4	4	no	—
181	C₂²×C₃	—	4	2	no	—
182	C₂²×C₃	—	8	2	no	—
183	C₂²×C₃	—	8	1	no	—
184	C₂²×C₃	—	8	1	no	—
185	C₂²×C₃	C₃×#120	1	1	yes	characteristic
186	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
187	C₂²×C₃	C₃×#124	1	1	yes	characteristic
188	C₃×C₄	—	4	2	no	—
189	C₃×C₄	—	4	2	no	—
190	C₃×C₄	—	4	2	no	—
191	C₃×C₄	—	4	2	no	—
192	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
193	C₃×C₄	C₃×#124	1	2	yes	—
194	C₉	#2027	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³	—	2	2	no	—
196	C₂³	—	4	2	no	—
197	C₂³	—	4	2	no	—
198	C₂³	—	4	1	no	—
199	C₂³	—	4	1	no	—
200	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
201	Q₈	—	8	2	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	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
212	C₂×C₄	C₂×Q₈×C₉	1	1	yes	characteristic
213	C₂×C₄	C₉×#41	1	2	yes	—
214	C₂×C₄	C₉×#41	1	1	yes	characteristic
215	C₈	—	4	2	no	—
216	C₂×C₃	—	2	1	no	—
217	C₂×C₃	—	2	1	no	—
218	C₂×C₃	—	8	2	no	—
219	C₂×C₃	C₃×#393	1	1	yes	characteristic
220	C₂×C₃	C₃×#453	1	1	yes	characteristic
221	C₂×C₃	C₃×#454	1	1	yes	characteristic
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	4	4	no	—
225	C₂²	—	4	2	no	—
226	C₂²	—	8	2	no	—
227	C₂²	—	8	1	no	—
228	C₂²	—	8	1	no	—
229	C₂²	C₉×#120	1	1	yes	characteristic
230	C₂²	C₉×C₂²⋊Q₈	1	1	yes	characteristic
231	C₂²	C₉×#124	1	1	yes	characteristic
232	C₄	—	4	2	no	—
233	C₄	—	4	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	4	2	no	—
236	C₄	C₉×C₂²⋊Q₈	1	2	yes	—
237	C₄	C₉×#124	1	2	yes	—
238	C₃	C₃×#2027	1	1	yes	characteristic
239	C₂	—	2	1	no	—
240	C₂	—	2	1	no	—
241	C₂	—	8	2	no	—
242	C₂	C₉×#393	1	1	yes	characteristic
243	C₂	C₉×#453	1	1	yes	characteristic
244	C₂	C₉×#454	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#544

C₂

yes

maximal, characteristic, complemented

C₉×#418

C₂

yes

maximal

C₉×#390

C₂

yes

maximal, characteristic

C₉×#343

C₂

yes

maximal, characteristic, complemented

C₉×#339

C₂

yes

maximal, complemented

C₃×#2027

C₃

yes

maximal, characteristic

C₂²×D₄×C₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₉×C₄⋊Q₈

—

C₉×#125

—

C₉×C₂²⋊Q₈

—

C₉×#117

C₂²

yes

—

C₂×C₉×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₉×C₂²⋊C₄

—

C₂×C₄²×C₉

C₂²

yes

—

—

C₂×C₃

yes

characteristic

C₃×#418

C₂×C₃

yes

—

C₃×#390

C₂×C₃

yes

characteristic

C₃×#343

C₂×C₃

yes

characteristic

C₃×#339

C₂×C₃

yes

—

C₂⁴×C₉

—

C₂×Q₈×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

Q₈

yes

complemented

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

—

C₉×C₄⋊C₄

D₄

yes

—

C₉×C₄⋊C₄

D₄

yes

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

C₄²×C₉

—

#2027

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×D₄

C₂²×C₃

yes

characteristic

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₃×C₄⋊Q₈

—

C₃×#125

—

C₃×C₂²⋊Q₈

—

C₃×#117

C₂²×C₃

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

characteristic

C₂×C₃×C₂²⋊C₄

—

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×#102

—

C₃×#102

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂×D₄

yes

characteristic

Q₈×C₉

—

D₄×C₉

—

D₄×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×D₄

yes

—

C₂×C₄×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

characteristic

C₈×C₉

—

#544

C₂×C₉

yes

characteristic, complemented

#418

C₂×C₉

yes

—

#390

C₂×C₉

yes

characteristic

#343

C₂×C₉

yes

characteristic, complemented

#339

C₂×C₉

yes

complemented

C₂⁴×C₃

—

C₂×C₃×Q₈

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

C₃×Q₈

yes

—

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

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

C₃×D₄

yes

—

C₃×C₄⋊C₄

C₃×D₄

yes

—

C₃×C₂²⋊C₄

—

100

C₃×C₂²⋊C₄

—

101

C₃×C₄²

—

102

C₃×C₄²

—

103

C₂²×C₉

—

104

C₂²×C₉

—

105

C₂²×C₉

—

106

C₂²×C₉

—

107

C₂²×C₉

—

108

C₂²×C₉

—

109

C₂²×C₉

—

110

C₂²×C₉

#120

yes

characteristic

111

C₂²×C₉

C₂²⋊Q₈

yes

characteristic

112

C₂²×C₉

#124

yes

characteristic

113

C₄×C₉

—

114

C₄×C₉

—

115

C₄×C₉

—

116

C₄×C₉

—

117

C₄×C₉

C₂²⋊Q₈

yes

—

118

C₄×C₉

#124

yes

—

119

C₂²×D₄

C₂²×C₉

yes

characteristic

120

C₂×M₁₆

C₂²×C₉

yes

—

121

C₄⋊Q₈

—

122

#125

—

123

C₂²⋊Q₈

—

124

#117

C₂²×C₉

yes

—

125

C₂×C₄⋊C₄

C₂²×C₉

yes

characteristic

126

C₂×C₂²⋊C₄

—

127

C₂×C₄²

C₂²×C₉

yes

characteristic

128

#102

—

129

#102

—

130

C₂³×C₃

—

131

C₂³×C₃

—

132

C₂³×C₃

—

133

C₂³×C₃

—

134

C₂³×C₃

—

135

C₂³×C₃

C₂×C₃×D₄

yes

characteristic

136

C₃×Q₈

—

137

C₃×D₄

—

138

C₃×D₄

—

139

C₂×C₃×C₄

—

140

C₂×C₃×C₄

—

141

C₂×C₃×C₄

—

142

C₂×C₃×C₄

—

143

C₂×C₃×C₄

—

144

C₂×C₃×C₄

—

145

C₂×C₃×C₄

—

146

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

147

C₂×C₃×C₄

C₂×C₃×Q₈

yes

characteristic

148

C₂×C₃×C₄

C₃×#41

yes

—

149

C₂×C₃×C₄

C₃×#41

yes

characteristic

150

C₃×C₈

—

151

C₂×C₉

—

152

C₂×C₉

—

153

C₂×C₉

—

154

C₂×C₉

#393

yes

characteristic

155

C₂×C₉

#453

yes

characteristic

156

C₂×C₉

#454

yes

characteristic

157

C₂⁴

—

158

C₂×Q₈

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

—

162

C₂×D₄

Q₈×C₉

yes

complemented

163

C₂²×C₄

—

164

C₂²×C₄

D₄×C₉

yes

—

165

C₂²×C₄

C₂³×C₉

yes

characteristic

166

M₁₆

—

167

M₁₆

—

168

C₂×C₈

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

D₄×C₉

yes

—

173

C₄⋊C₄

D₄×C₉

yes

—

174

C₂²⋊C₄

—

175

C₂²⋊C₄

—

176

C₄²

—

177

C₄²

—

178

C₂²×C₃

—

179

C₂²×C₃

—

180

C₂²×C₃

—

181

C₂²×C₃

—

182

C₂²×C₃

—

183

C₂²×C₃

—

184

C₂²×C₃

—

185

C₂²×C₃

C₃×#120

yes

characteristic

186

C₂²×C₃

C₃×C₂²⋊Q₈

yes

characteristic

187

C₂²×C₃

C₃×#124

yes

characteristic

188

C₃×C₄

—

189

C₃×C₄

—

190

C₃×C₄

—

191

C₃×C₄

—

192

C₃×C₄

C₃×C₂²⋊Q₈

yes

—

193

C₃×C₄

C₃×#124

yes

—

194

C₉

#2027

yes

characteristic, direct product factor, Sylow

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

C₂×D₄×C₉

yes

characteristic

201

Q₈

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

C₂×D₄×C₉

yes

—

212

C₂×C₄

C₂×Q₈×C₉

yes

characteristic

213

C₂×C₄

C₉×#41

yes

—

214

C₂×C₄

C₉×#41

yes

characteristic

215

C₈

—

216

C₂×C₃

—

217

C₂×C₃

—

218

C₂×C₃

—

219

C₂×C₃

C₃×#393

yes

characteristic

220

C₂×C₃

C₃×#453

yes

characteristic

221

C₂×C₃

C₃×#454

yes

characteristic

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

C₉×#120

yes

characteristic

230

C₂²

C₉×C₂²⋊Q₈

yes

characteristic

231

C₂²

C₉×#124

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

C₉×C₂²⋊Q₈

yes

—

237

C₄

C₉×#124

yes

—

238

C₃

C₃×#2027

yes

characteristic

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

C₉×#393

yes

characteristic

243

C₂

C₉×#453

yes

characteristic

244

C₂

C₉×#454

yes

characteristic

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

subgroup

G/H

center

C₂²×C₉

#120

commutator

C₂²×C₄

C₂³×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle

C₂²×C₃

C₃×#120

prime radical

C₂²×C₃×D₄

C₂²×C₃

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
1. C₉×#544	C₂	semidirect
4. C₉×#343	C₂	semidirect
5. C₉×#339	C₂	semidirect
28. C₂×D₄×C₉	Q₈	semidirect
44. #2027	C₉	direct (N × H)
77. #544	C₂×C₉	semidirect
80. #343	C₂×C₉	semidirect
81. #339	C₂×C₉	semidirect
162. C₂×D₄	Q₈×C₉	semidirect
194. C₉	#2027	direct (N × H)

H ≅ G/N

type

1. C₉×#544

C₂

semidirect

4. C₉×#343

C₂

semidirect

5. C₉×#339

C₂

semidirect

28. C₂×D₄×C₉

Q₈

semidirect

44. #2027

C₉

direct (N × H)

77. #544

C₂×C₉

semidirect

80. #343

C₂×C₉

semidirect

81. #339

C₂×C₉

semidirect

162. C₂×D₄

Q₈×C₉

semidirect

194. C₉

#2027

direct (N × H)

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

subgroup	index
C₉×#544	2
C₉×#418	2
C₉×#390	2
C₉×#343	2
C₉×#339	2
C₃×#2027	3

subgroup

index

Subgroups — C₉×#2027 #11766748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2027 #11766748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2027 #11766748