Group #11795329 — subgroups

Subgroups — C₃×#70573 #11795329

Order 1152.

417 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 417 conjugacy classes of subgroups — too many to draw. Only its 134 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×C₃²×#106	C₂	1	1	yes	maximal, characteristic
2	C₃×#5102	C₂	1	1	yes	maximal, characteristic
3	C₃×#4964	C₂	1	2	yes	maximal
4	C₃×#4552	C₂	1	1	yes	maximal, characteristic
5	C₃×#4530	C₂	1	2	yes	maximal
6	C₃×#2090	—	3	1	no	maximal
7	#70573	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
10	C₃×#926	C₂²	1	1	yes	characteristic
11	C₂×C₃×#208	C₂²	1	1	yes	characteristic
12	C₂×C₃×#208	C₂²	1	2	yes	—
13	C₃²×#106	—	2	2	no	—
14	C₃×Dic₃⋊C₈	—	2	2	no	—
15	C₃×#808	—	2	2	no	—
16	C₃×#807	—	2	2	no	—
17	C₃×#428	—	3	2	no	—
18	C₂×C₃×#106	—	2	1	no	—
19	C₂×C₃×#106	D₃	1	1	yes	characteristic
20	C₂×C₃×#106	C₂×C₃	1	1	yes	characteristic
21	C₃×#424	—	3	1	no	—
22	#5102	C₂×C₃	1	1	yes	characteristic
23	#4964	C₂×C₃	1	2	yes	—
24	C₃×#343	—	3	2	no	—
25	C₃×#341	—	3	1	no	—
26	#4552	C₂×C₃	1	1	yes	characteristic
27	#4530	C₂×C₃	1	2	yes	—
28	C₂²×C₃²×C₄	—	2	2	no	—
29	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
30	C₂×C₃²×C₈	—	2	2	no	—
31	C₂×C₃²×C₈	D₄	1	2	yes	—
32	C₃²×C₄⋊C₄	—	2	2	no	—
33	C₃²×C₄⋊C₄	—	2	2	no	—
34	C₃×#217	—	2	1	no	—
35	C₃×C₄⋊Dic₃	D₄	1	2	yes	—
36	C₃×C₄×Dic₃	—	2	1	no	—
37	C₃×#208	—	2	2	no	—
38	C₃×#208	—	2	2	no	—
39	C₃×#208	Q₈	1	4	yes	—
40	C₂×C₃×C₃⋊C₈	—	2	2	no	—
41	C₂×C₃×C₃⋊C₈	—	2	1	no	—
42	#2090	—	3	1	no	Sylow
43	C₂×C₃×M₁₆	—	3	2	no	—
44	C₂×C₃×M₁₆	—	3	1	no	—
45	C₂²×C₃×C₈	—	2	1	no	—
46	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
47	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
48	C₃×#117	—	3	1	no	—
49	C₂×C₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
51	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
52	#926	C₂²×C₃	1	1	yes	characteristic
53	C₂×#208	C₂²×C₃	1	1	yes	characteristic
54	C₂×#208	C₂²×C₃	1	2	yes	—
55	C₃×#107	—	6	2	no	—
56	C₃×#106	—	2	4	no	—
57	C₃×#106	—	2	2	no	—
58	C₃×#106	—	2	2	no	—
59	C₃×#106	—	6	2	no	—
60	C₃×C₄⋊C₈	—	6	2	no	—
61	Dic₃⋊C₈	—	2	2	no	—
62	#808	—	2	2	no	—
63	#807	—	2	2	no	—
64	C₂³×C₃²	#41	1	1	yes	characteristic
65	C₂×C₃²×C₄	—	4	2	no	—
66	C₂×C₃²×C₄	—	8	2	no	—
67	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
68	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
69	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
70	C₂×C₃²×C₄	#41	1	2	yes	—
71	C₂×C₃×Dic₃	—	2	2	no	—
72	C₃²×C₈	—	2	2	no	—
73	C₃×C₃⋊C₈	—	2	4	no	—
74	C₃×C₃⋊C₈	—	4	1	no	—
75	#428	—	3	2	no	—
76	C₂×#106	C₃×D₃	1	1	yes	characteristic
77	#424	—	3	1	no	—
78	#343	—	3	2	no	—
79	#341	—	3	1	no	—
80	C₂²×C₃×C₄	—	2	2	no	—
81	C₂²×C₃×C₄	—	2	2	no	—
82	C₂²×C₃×C₄	—	2	1	no	—
83	C₂²×C₃×C₄	—	4	2	no	—
84	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
85	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
86	C₃×M₁₆	—	3	4	no	—
87	C₃×M₁₆	—	6	2	no	—
88	C₃×M₁₆	—	6	2	no	—
89	C₂×C₃×C₈	—	2	4	no	—
90	C₂×C₃×C₈	—	2	2	no	—
91	C₂×C₃×C₈	—	2	2	no	—
92	C₂×C₃×C₈	—	2	2	no	—
93	C₂×C₃×C₈	—	6	2	no	—
94	C₂×C₃×C₈	—	6	1	no	—
95	C₂×C₃×C₈	#67	1	2	yes	—
96	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
97	C₃×C₄⋊C₄	—	2	4	no	—
98	C₃×C₄⋊C₄	—	2	2	no	—
99	C₃×C₄⋊C₄	—	2	2	no	—
100	C₃×C₄⋊C₄	—	2	2	no	—
101	C₃×C₄⋊C₄	—	2	2	no	—
102	C₃×C₄⋊C₄	—	3	2	no	—
103	C₃×C₄⋊C₄	—	4	2	no	—
104	C₃×C₂²⋊C₄	—	6	1	no	—
105	C₃×C₄²	—	6	1	no	—
106	#217	—	2	1	no	—
107	C₄⋊Dic₃	C₃×D₄	1	2	yes	—
108	C₄×Dic₃	—	2	1	no	—
109	#208	—	2	2	no	—
110	#208	—	2	2	no	—
111	#208	C₃×Q₈	1	4	yes	—
112	C₂×C₃⋊C₈	—	2	2	no	—
113	C₂×C₃⋊C₈	—	2	1	no	—
114	C₂²×C₃²	—	2	2	no	—
115	C₂²×C₃²	#121	1	1	yes	characteristic
116	C₂²×C₃²	#125	1	2	yes	—
117	C₃²×C₄	—	8	2	no	—
118	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
119	C₃²×C₄	#123	1	1	yes	characteristic
120	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
121	C₃×Dic₃	—	4	2	no	—
122	C₂×M₁₆	—	3	2	no	—
123	C₂×M₁₆	—	3	1	no	—
124	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
125	#117	—	3	1	no	—
126	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
127	#107	—	6	2	no	—
128	#106	—	2	2	no	—
129	#106	—	6	2	no	—
130	C₄⋊C₈	—	6	2	no	—
131	C₂³×C₃	—	2	1	no	—
132	C₂³×C₃	#237	1	1	yes	characteristic
133	C₂³×C₃	C₃×#41	1	1	yes	characteristic
134	C₂×C₃×C₄	—	2	2	no	—
135	C₂×C₃×C₄	—	2	1	no	—
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	—	2	1	no	—
138	C₂×C₃×C₄	—	4	4	no	—
139	C₂×C₃×C₄	—	4	2	no	—
140	C₂×C₃×C₄	—	4	2	no	—
141	C₂×C₃×C₄	—	6	2	no	—
142	C₂×C₃×C₄	—	8	4	no	—
143	C₂×C₃×C₄	—	8	2	no	—
144	C₂×C₃×C₄	—	8	2	no	—
145	C₂×C₃×C₄	#235	1	2	yes	—
146	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
148	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
149	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
152	C₂×C₃×C₄	C₃×#41	1	2	yes	—
153	C₂×Dic₃	—	2	2	no	—
154	C₃×C₈	—	2	4	no	—
155	C₃×C₈	—	2	2	no	—
156	C₃×C₈	—	2	2	no	—
157	C₃×C₈	—	6	4	no	—
158	C₃×C₈	—	12	1	no	—
159	C₃⋊C₈	—	2	4	no	—
160	C₃⋊C₈	—	4	1	no	—
161	C₂×C₃²	—	2	2	no	—
162	C₂×C₃²	#398	1	1	yes	characteristic
163	C₂×C₃²	#471	1	2	yes	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
166	M₁₆	—	3	4	no	—
167	M₁₆	—	6	2	no	—
168	M₁₆	—	6	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	6	2	no	—
171	C₂×C₈	—	6	1	no	—
172	C₂×C₈	C₃×#67	1	2	yes	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	3	2	no	—
176	C₂²⋊C₄	—	6	1	no	—
177	C₄²	—	6	1	no	—
178	C₂²×C₃	—	2	4	no	—
179	C₂²×C₃	—	2	2	no	—
180	C₂²×C₃	—	2	2	no	—
181	C₂²×C₃	—	2	2	no	—
182	C₂²×C₃	—	2	1	no	—
183	C₂²×C₃	#889	1	2	yes	—
184	C₂²×C₃	#938	1	1	yes	characteristic
185	C₂²×C₃	C₃×#121	1	1	yes	characteristic
186	C₂²×C₃	C₃×#125	1	2	yes	—
187	C₃×C₄	—	2	2	no	—
188	C₃×C₄	—	2	1	no	—
189	C₃×C₄	—	2	1	no	—
190	C₃×C₄	—	8	4	no	—
191	C₃×C₄	—	8	2	no	—
192	C₃×C₄	—	8	2	no	—
193	C₃×C₄	—	12	2	no	—
194	C₃×C₄	#896	1	2	yes	—
195	C₃×C₄	#929	1	1	yes	characteristic
196	C₃×C₄	#944	1	1	yes	characteristic
197	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
198	C₃×C₄	C₃×#123	1	1	yes	characteristic
199	C₃×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
200	Dic₃	—	4	2	no	—
201	C₃²	#2090	1	1	yes	characteristic, complemented, Sylow
202	C₂³	C₃×#237	1	1	yes	characteristic
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	6	2	no	—
205	C₂×C₄	—	8	2	no	—
206	C₂×C₄	C₃×#235	1	2	yes	—
207	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
208	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
209	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
210	C₈	—	2	2	no	—
211	C₈	—	6	4	no	—
212	C₈	—	12	1	no	—
213	C₂×C₃	—	2	4	no	—
214	C₂×C₃	—	2	2	no	—
215	C₂×C₃	—	2	2	no	—
216	C₂×C₃	—	2	2	no	—
217	C₂×C₃	—	2	1	no	—
218	C₂×C₃	#4983	1	1	yes	characteristic
219	C₂×C₃	#5177	1	2	yes	—
220	C₂×C₃	C₃×#398	1	1	yes	characteristic
221	C₂×C₃	C₃×#471	1	2	yes	—
222	C₂²	—	2	2	no	—
223	C₂²	C₃×#889	1	2	yes	—
224	C₂²	C₃×#938	1	1	yes	characteristic
225	C₄	—	8	2	no	—
226	C₄	—	12	2	no	—
227	C₄	C₃×#896	1	2	yes	—
228	C₄	C₃×#929	1	1	yes	characteristic
229	C₄	C₃×#944	1	1	yes	characteristic
230	C₃	—	2	1	no	—
231	C₃	#70573	1	1	yes	characteristic, direct product factor
232	C₃	C₃×#2090	1	1	yes	characteristic, complemented
233	C₂	—	2	2	no	—
234	C₂	C₃×#4983	1	1	yes	characteristic
235	C₂	C₃×#5177	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃²×#106

C₂

yes

maximal, characteristic

C₃×#5102

C₂

yes

maximal, characteristic

C₃×#4964

C₂

yes

maximal

C₃×#4552

C₂

yes

maximal, characteristic

C₃×#4530

C₂

yes

—

C₃

yes

maximal, characteristic, direct product factor

C₂²×C₃²×C₈

C₂²

yes

characteristic

C₂×C₃²×C₄⋊C₄

C₂²

yes

—

C₃×#926

C₂²

yes

characteristic

C₂×C₃×#208

C₂²

yes

characteristic

C₂×C₃×#208

C₂²

yes

—

C₃²×#106

—

C₃×Dic₃⋊C₈

—

C₃×#808

—

C₃×#807

—

C₃×#428

—

C₂×C₃×#106

—

C₂×C₃×#106

D₃

yes

characteristic

C₂×C₃×#106

C₂×C₃

yes

characteristic

C₃×#424

—

#5102

C₂×C₃

yes

characteristic

#4964

C₂×C₃

yes

—

C₃×#343

—

C₃×#341

—

#4552

C₂×C₃

yes

characteristic

#4530

C₂×C₃

yes

—

C₂²×C₃²×C₄

—

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₂×C₃²×C₈

—

C₂×C₃²×C₈

D₄

yes

—

C₃²×C₄⋊C₄

—

C₃²×C₄⋊C₄

—

C₃×#217

—

C₃×C₄⋊Dic₃

D₄

yes

—

C₃×C₄×Dic₃

—

C₃×#208

—

C₃×#208

—

C₃×#208

Q₈

yes

—

C₂×C₃×C₃⋊C₈

—

C₂×C₃×C₃⋊C₈

—

#2090

—

Sylow

C₂×C₃×M₁₆

—

C₂×C₃×M₁₆

—

C₂²×C₃×C₈

—

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₂²×C₃×C₈

C₂²×C₃

yes

characteristic

C₃×#117

—

C₂×C₃×C₄⋊C₄

—

C₂×C₃×C₄⋊C₄

C₂×D₃

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

#926

C₂²×C₃

yes

characteristic

C₂×#208

C₂²×C₃

yes

characteristic

C₂×#208

C₂²×C₃

yes

—

—

—

—

—

—

C₃×C₄⋊C₈

—

Dic₃⋊C₈

—

#808

—

#807

—

C₂³×C₃²

#41

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃²×C₄

C₂×Q₈

yes

—

C₂×C₃²×C₄

#41

yes

—

C₂×C₃×Dic₃

—

C₃²×C₈

—

C₃×C₃⋊C₈

—

C₃×C₃⋊C₈

—

#428

—

C₂×#106

C₃×D₃

yes

—

—

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

#67

yes

—

C₂×C₃×C₈

C₃×D₄

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

100

C₃×C₄⋊C₄

—

101

C₃×C₄⋊C₄

—

102

C₃×C₄⋊C₄

—

103

C₃×C₄⋊C₄

—

104

C₃×C₂²⋊C₄

—

105

C₃×C₄²

—

106

#217

—

107

C₄⋊Dic₃

C₃×D₄

yes

—

108

C₄×Dic₃

—

109

#208

—

110

#208

—

111

#208

C₃×Q₈

yes

—

112

C₂×C₃⋊C₈

—

113

C₂×C₃⋊C₈

—

114

C₂²×C₃²

—

115

C₂²×C₃²

#121

yes

characteristic

116

C₂²×C₃²

#125

yes

—

117

C₃²×C₄

—

118

C₃²×C₄

C₂²⋊Q₈

yes

—

119

C₃²×C₄

#123

yes

characteristic

120

C₃²×C₄

C₄⋊Q₈

yes

characteristic

121

C₃×Dic₃

—

122

C₂×M₁₆

—

123

C₂×M₁₆

—

124

C₂²×C₈

C₂×C₃×D₃

yes

characteristic

125

#117

—

126

C₂×C₄⋊C₄

C₂×C₃×D₃

yes

—

127

#107

—

128

#106

—

129

#106

—

130

C₄⋊C₈

—

131

C₂³×C₃

—

132

C₂³×C₃

#237

yes

characteristic

133

C₂³×C₃

C₃×#41

yes

characteristic

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

—

143

C₂×C₃×C₄

—

144

C₂×C₃×C₄

—

145

C₂×C₃×C₄

#235

yes

—

146

C₂×C₃×C₄

D₃×D₄

yes

characteristic

147

C₂×C₃×C₄

D₃×Q₈

yes

—

148

C₂×C₃×C₄

C₂×#67

yes

characteristic

149

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

150

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

151

C₂×C₃×C₄

C₂×C₃×Q₈

yes

—

152

C₂×C₃×C₄

C₃×#41

yes

—

153

C₂×Dic₃

—

154

C₃×C₈

—

155

C₃×C₈

—

156

C₃×C₈

—

157

C₃×C₈

—

158

C₃×C₈

—

159

C₃⋊C₈

—

160

C₃⋊C₈

—

161

C₂×C₃²

—

162

C₂×C₃²

#398

yes

characteristic

163

C₂×C₃²

#471

yes

—

164

C₂²×C₄

—

165

C₂²×C₄

C₂²×C₃×D₃

yes

characteristic

166

M₁₆

—

167

M₁₆

—

168

M₁₆

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

C₃×#67

yes

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₂²⋊C₄

—

177

C₄²

—

178

C₂²×C₃

—

179

C₂²×C₃

—

180

C₂²×C₃

—

181

C₂²×C₃

—

182

C₂²×C₃

—

183

C₂²×C₃

#889

yes

—

184

C₂²×C₃

#938

yes

characteristic

185

C₂²×C₃

C₃×#121

yes

characteristic

186

C₂²×C₃

C₃×#125

yes

—

187

C₃×C₄

—

188

C₃×C₄

—

189

C₃×C₄

—

190

C₃×C₄

—

191

C₃×C₄

—

192

C₃×C₄

—

193

C₃×C₄

—

194

C₃×C₄

#896

yes

—

195

C₃×C₄

#929

yes

characteristic

196

C₃×C₄

#944

yes

characteristic

197

C₃×C₄

C₃×C₂²⋊Q₈

yes

—

198

C₃×C₄

C₃×#123

yes

characteristic

199

C₃×C₄

C₃×C₄⋊Q₈

yes

characteristic

200

Dic₃

—

201

C₃²

#2090

yes

characteristic, complemented, Sylow

202

C₂³

C₃×#237

yes

characteristic

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₃×#235

yes

—

207

C₂×C₄

C₃×D₃×D₄

yes

characteristic

208

C₂×C₄

C₃×D₃×Q₈

yes

—

209

C₂×C₄

C₂×C₃×#67

yes

characteristic

210

C₈

—

211

C₈

—

212

C₈

—

213

C₂×C₃

—

214

C₂×C₃

—

215

C₂×C₃

—

216

C₂×C₃

—

217

C₂×C₃

—

218

C₂×C₃

#4983

yes

characteristic

219

C₂×C₃

#5177

yes

—

220

C₂×C₃

C₃×#398

yes

characteristic

221

C₂×C₃

C₃×#471

yes

—

222

C₂²

—

223

C₂²

C₃×#889

yes

—

224

C₂²

C₃×#938

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

C₃×#896

yes

—

228

C₄

C₃×#929

yes

characteristic

229

C₄

C₃×#944

yes

characteristic

230

C₃

—

231

C₃

#70573

yes

characteristic, direct product factor

232

C₃

C₃×#2090

yes

characteristic, complemented

233

C₂

—

234

C₂

C₃×#4983

yes

characteristic

235

C₂

C₃×#5177

yes

—

	subgroup	G/H
center	C₂²×C₃	#938
commutator, cosocle	C₂²×C₃×C₄	C₂³×C₃
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#106	C₂
socle	C₂²×C₃²	#121
prime radical	C₂³×C₃²	#41
hypercenter	C₂×C₃×#106	D₃
hypocenter	C₃	C₃×#2090
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#106

subgroup

G/H

center

C₂²×C₃

#938

commutator, cosocle

C₂²×C₃×C₄

C₂³×C₃

Frattini

C₂²×C₄

C₂²×C₃×D₃

Fitting

C₂×C₃²×#106

C₂

C₂²×C₃²

C₂³×C₃²

C₂×C₃×#106

D₃

hypocenter

C₃

C₃×#2090

LCS

G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃

UCS

C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#106

N	H ≅ G/N	type
7. #70573	C₃	direct (N × H)
201. C₃²	#2090	semidirect
231. C₃	#70573	direct (N × H)
232. C₃	C₃×#2090	semidirect

H ≅ G/N

type

7. #70573

C₃

direct (N × H)

201. C₃²

#2090

semidirect

231. C₃

#70573

direct (N × H)

232. C₃

C₃×#2090

semidirect

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

subgroup	index
C₂×C₃²×#106	2
C₃×#5102	2
C₃×#4964	2
C₃×#4552	2
C₃×#4530	2
C₃×#2090	3
#70573	3

subgroup

index

C₂×C₃²×#106

Subgroups — C₃×#70573 #11795329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#70573 #11795329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70573 #11795329