Group #11790607 — subgroups

Subgroups — #11790607

Order 1152.

498 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 194 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×#63431	C₂	1	1	yes	maximal, characteristic
2	C₉×#384	C₂	1	1	yes	maximal, characteristic
3	C₂×#63368	C₂	1	4	yes	maximal
4	C₂×C₄×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#69579	—	3	1	no	maximal
6	C₂²×Dic₁₈	C₂²	1	2	yes	—
7	C₂×C₉×C₄⋊C₄	—	2	2	no	—
8	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	—	2	2	no	—
11	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
12	#63431	—	2	2	no	—
13	#63431	C₄	1	4	yes	complemented
14	#63368	—	2	8	no	—
15	C₄×C₉⋊C₈	—	2	2	no	—
16	C₂×#869	—	3	1	no	—
17	C₃×#384	D₃	1	1	yes	characteristic
18	C₂×#810	—	3	4	no	—
19	C₂×C₄×C₃⋊C₈	—	3	1	no	—
20	C₂²×C₄×C₉	—	2	2	no	—
21	C₂²×C₄×C₉	D₄	1	2	yes	—
22	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₉	—	2	2	no	—
24	C₂×Dic₁₈	—	2	4	no	—
25	C₂×Dic₁₈	—	2	4	no	—
26	C₂×Dic₁₈	—	2	2	no	—
27	C₂×Dic₁₈	C₂×C₄	1	4	yes	—
28	C₉×C₄⋊C₄	—	2	4	no	—
29	C₉×C₄⋊C₄	—	4	4	no	—
30	C₄²×C₉	C₂×C₄	1	2	yes	—
31	C₄²×C₉	D₄	1	2	yes	—
32	C₄⋊Dic₉	—	2	8	no	—
33	C₂×C₉⋊C₈	—	2	2	no	—
34	C₂×C₉⋊C₈	—	2	2	no	—
35	C₂×C₉⋊C₈	D₄	1	4	yes	—
36	#1956	—	9	1	no	Sylow
37	C₂²×Dic₆	—	3	2	no	—
38	C₂×C₃×C₄⋊C₄	—	2	2	no	—
39	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
40	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₂×C₄⋊Dic₃	—	6	2	no	—
42	C₂²×C₃⋊C₈	—	3	2	no	—
43	#869	—	3	4	no	—
44	#869	—	6	2	no	—
45	#810	—	6	8	no	—
46	C₄×C₃⋊C₈	—	6	2	no	—
47	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	—	4	2	no	—
49	C₂×C₄×C₉	—	4	4	no	—
50	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
51	C₂×C₄×C₉	SD₁₆	1	4	yes	—
52	C₂×C₄×C₉	Q₁₆	1	4	yes	—
53	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₉	#41	1	2	yes	—
57	C₂×Dic₉	—	2	4	no	—
58	C₂×Dic₉	—	4	2	no	—
59	C₂×Dic₉	—	4	2	no	—
60	Dic₁₈	—	2	8	no	—
61	Dic₁₈	—	4	4	no	—
62	C₉⋊C₈	—	2	4	no	—
63	C₂×C₄⋊Q₈	—	9	1	no	—
64	C₂×#103	—	9	4	no	—
65	C₂×C₄×C₈	—	9	1	no	—
66	#384	D₉	1	1	yes	characteristic
67	C₂²×C₃×C₄	—	2	2	no	—
68	C₂²×C₃×C₄	#67	1	2	yes	—
69	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
70	C₂²×Dic₃	—	6	2	no	—
71	C₂×Dic₆	—	3	4	no	—
72	C₂×Dic₆	—	6	4	no	—
73	C₂×Dic₆	—	6	4	no	—
74	C₂×Dic₆	—	6	2	no	—
75	C₃×C₄⋊C₄	—	2	4	no	—
76	C₃×C₄⋊C₄	—	4	4	no	—
77	C₃×C₄²	C₄×D₃	1	2	yes	—
78	C₃×C₄²	D₁₂	1	2	yes	—
79	C₄⋊Dic₃	—	6	8	no	—
80	C₂×C₃⋊C₈	—	3	4	no	—
81	C₂×C₃⋊C₈	—	6	2	no	—
82	C₂×C₃⋊C₈	—	6	2	no	—
83	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₉	#124	1	1	yes	characteristic
85	C₂²×C₉	#127	1	1	yes	characteristic
86	C₂²×C₉	C₂×SD₁₆	1	2	yes	—
87	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
88	C₄×C₉	—	8	2	no	—
89	C₄×C₉	#103	1	8	yes	complemented
90	C₄×C₉	C₄×D₄	1	2	yes	—
91	C₄×C₉	#121	1	2	yes	—
92	Dic₉	—	4	4	no	—
93	C₂²×Q₈	—	9	2	no	—
94	C₂²×C₈	—	9	2	no	—
95	C₄⋊Q₈	—	9	4	no	—
96	C₄⋊Q₈	—	18	2	no	—
97	C₂×C₄⋊C₄	—	2	2	no	—
98	C₂×C₄⋊C₄	—	18	2	no	—
99	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
100	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
101	#103	—	18	8	no	—
102	C₄×C₈	—	18	2	no	—
103	C₂³×C₃	C₂×#67	1	1	yes	characteristic
104	C₂×C₃×C₄	—	4	4	no	—
105	C₂×C₃×C₄	—	4	2	no	—
106	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
107	C₂×C₃×C₄	#214	1	4	yes	—
108	C₂×C₃×C₄	#216	1	4	yes	—
109	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
110	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
111	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
112	C₂×C₃×C₄	#239	1	2	yes	—
113	C₂×Dic₃	—	6	4	no	—
114	C₂×Dic₃	—	12	2	no	—
115	C₂×Dic₃	—	12	2	no	—
116	Dic₆	—	6	8	no	—
117	Dic₆	—	12	4	no	—
118	C₃⋊C₈	—	6	4	no	—
119	C₂×C₉	#390	1	1	yes	characteristic
120	C₂×C₉	C₂×#103	1	2	yes	—
121	C₂×C₉	#487	1	2	yes	—
122	C₂×C₉	#492	1	1	yes	characteristic
123	C₂×C₉	#494	1	1	yes	characteristic
124	C₂×Q₈	—	9	4	no	—
125	C₂×Q₈	—	18	2	no	—
126	C₂×Q₈	—	18	4	no	—
127	C₂×Q₈	—	18	4	no	—
128	C₂²×C₄	—	2	2	no	—
129	C₂²×C₄	—	18	2	no	—
130	C₂²×C₄	#611	1	2	yes	—
131	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
132	C₂×C₈	—	9	4	no	—
133	C₂×C₈	—	18	2	no	—
134	C₂×C₈	—	18	2	no	—
135	C₄⋊C₄	—	2	4	no	—
136	C₄⋊C₄	—	4	4	no	—
137	C₄⋊C₄	—	18	8	no	—
138	C₄²	C₄×D₉	1	2	yes	—
139	C₄²	D₃₆	1	2	yes	—
140	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
141	C₂²×C₃	C₂×#214	1	2	yes	—
142	C₂²×C₃	#940	1	1	yes	characteristic
143	C₂²×C₃	C₂×#216	1	2	yes	—
144	C₂²×C₃	#947	1	1	yes	characteristic
145	C₃×C₄	—	8	2	no	—
146	C₃×C₄	#810	1	8	yes	—
147	C₃×C₄	#893	1	2	yes	—
148	C₃×C₄	#895	1	2	yes	—
149	Dic₃	—	12	4	no	—
150	C₉	#1956	1	1	yes	characteristic, complemented, Sylow
151	C₂³	C₂×#611	1	1	yes	characteristic
152	Q₈	—	18	8	no	—
153	Q₈	—	36	4	no	—
154	C₂×C₄	—	4	4	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	—	18	4	no	—
157	C₂×C₄	—	36	2	no	—
158	C₂×C₄	—	36	2	no	—
159	C₂×C₄	(C₂×D₉)⋊C₄	1	4	yes	—
160	C₂×C₄	#3672	1	4	yes	—
161	C₂×C₄	#3674	1	4	yes	—
162	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
163	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
164	C₂×C₄	D₄×D₉	1	2	yes	—
165	C₂×C₄	#3701	1	2	yes	—
166	C₈	—	18	4	no	—
167	C₂×C₃	C₂×#810	1	2	yes	—
168	C₂×C₃	#4988	1	1	yes	characteristic
169	C₂×C₃	#5076	1	1	yes	characteristic
170	C₂×C₃	#5092	1	1	yes	characteristic
171	C₂×C₃	#5093	1	2	yes	—
172	C₂²	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
173	C₂²	C₂×#3672	1	2	yes	—
174	C₂²	#63502	1	1	yes	characteristic
175	C₂²	C₂×#3674	1	2	yes	—
176	C₂²	#63509	1	1	yes	characteristic
177	C₄	—	8	2	no	—
178	C₄	—	36	4	no	—
179	C₄	#63368	1	8	yes	complemented
180	C₄	#63455	1	2	yes	—
181	C₄	#63457	1	2	yes	—
182	C₃	#69579	1	1	yes	characteristic
183	C₂	C₂×#63368	1	2	yes	—
184	C₂	#10588668	1	1	yes	characteristic
185	C₂	#10588753	1	1	yes	characteristic
186	C₂	#10588765	1	1	yes	characteristic
187	C₂	#10588766	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63431

C₂

yes

maximal, characteristic

C₉×#384

C₂

yes

maximal, characteristic

C₂×#63368

C₂

yes

maximal

C₂×C₄×C₉⋊C₈

C₂

yes

maximal, characteristic

#69579

—

maximal

C₂²×Dic₁₈

C₂²

yes

—

C₂×C₉×C₄⋊C₄

—

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

—

C₂²×C₉⋊C₈

C₂²

yes

—

#63431

—

#63431

C₄

yes

complemented

#63368

—

C₄×C₉⋊C₈

—

C₂×#869

—

C₃×#384

D₃

yes

characteristic

C₂×#810

—

C₂×C₄×C₃⋊C₈

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₂×Dic₁₈

—

C₂×Dic₁₈

—

C₂×Dic₁₈

—

C₂×Dic₁₈

C₂×C₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

D₄

yes

—

C₄⋊Dic₉

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

D₄

yes

—

#1956

—

Sylow

C₂²×Dic₆

—

C₂×C₃×C₄⋊C₄

—

C₂×C₃×C₄⋊C₄

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

C₂²×C₃⋊C₈

—

#869

—

#869

—

#810

—

C₄×C₃⋊C₈

—

C₂³×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

SD₁₆

yes

—

C₂×C₄×C₉

Q₁₆

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

Dic₁₈

—

Dic₁₈

—

C₉⋊C₈

—

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×C₄×C₈

—

#384

D₉

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

#67

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×Dic₆

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₄×D₃

yes

—

C₃×C₄²

D₁₂

yes

—

C₄⋊Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

C₂²×C₉

yes

C₂²×C₉

yes

C₂²×C₉

C₂×SD₁₆

yes

—

C₂²×C₉

C₂×Q₁₆

yes

—

C₄×C₉

—

C₄×C₉

#103

yes

complemented

C₄×C₉

C₄×D₄

yes

—

C₄×C₉

#121

yes

—

Dic₉

—

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₉

yes

—

100

C₂×C₄²

C₂×D₉

yes

characteristic

101

#103

—

102

C₄×C₈

—

103

C₂³×C₃

C₂×#67

yes

characteristic

104

C₂×C₃×C₄

—

105

C₂×C₃×C₄

—

106

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

107

C₂×C₃×C₄

#214

yes

—

108

C₂×C₃×C₄

#216

yes

—

109

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

110

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

111

C₂×C₃×C₄

D₃×D₄

yes

—

112

C₂×C₃×C₄

#239

yes

—

113

C₂×Dic₃

—

114

C₂×Dic₃

—

115

C₂×Dic₃

—

116

Dic₆

—

117

Dic₆

—

118

C₃⋊C₈

—

119

C₂×C₉

#390

yes

characteristic

120

C₂×C₉

C₂×#103

yes

—

121

C₂×C₉

#487

yes

—

122

C₂×C₉

#492

yes

characteristic

123

C₂×C₉

#494

yes

characteristic

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

#611

yes

—

131

C₂²×C₄

C₂²×D₉

yes

characteristic

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄²

C₄×D₉

yes

—

139

C₄²

D₃₆

yes

—

140

C₂²×C₃

C₂×(C₂×D₃)⋊C₄

yes

characteristic

141

C₂²×C₃

C₂×#214

yes

—

142

C₂²×C₃

#940

yes

characteristic

143

C₂²×C₃

C₂×#216

yes

—

144

C₂²×C₃

#947

yes

characteristic

145

C₃×C₄

—

146

C₃×C₄

#810

yes

—

147

C₃×C₄

#893

yes

—

148

C₃×C₄

#895

yes

—

149

Dic₃

—

150

C₉

#1956

yes

characteristic, complemented, Sylow

151

C₂³

C₂×#611

yes

characteristic

152

Q₈

—

153

Q₈

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

160

C₂×C₄

#3672

yes

—

161

C₂×C₄

#3674

yes

—

162

C₂×C₄

C₂×C₄×D₉

yes

characteristic

163

C₂×C₄

C₂×D₃₆

yes

characteristic

164

C₂×C₄

D₄×D₉

yes

—

165

C₂×C₄

#3701

yes

—

166

C₈

—

167

C₂×C₃

C₂×#810

yes

—

168

C₂×C₃

#4988

yes

characteristic

169

C₂×C₃

#5076

yes

characteristic

170

C₂×C₃

#5092

yes

characteristic

171

C₂×C₃

#5093

yes

—

172

C₂²

C₂×(C₂×D₉)⋊C₄

yes

characteristic

173

C₂²

C₂×#3672

yes

—

174

C₂²

#63502

yes

characteristic

175

C₂²

C₂×#3674

yes

—

176

C₂²

#63509

yes

characteristic

177

C₄

—

178

C₄

—

179

C₄

#63368

yes

complemented

180

C₄

#63455

yes

—

181

C₄

#63457

yes

—

182

C₃

#69579

yes

characteristic

183

C₂

C₂×#63368

yes

—

184

C₂

#10588668

yes

characteristic

185

C₂

#10588753

yes

characteristic

186

C₂

#10588765

yes

characteristic

187

C₂

#10588766

yes

—

	subgroup	G/H
center	C₂³	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#384	C₂
socle, prime radical	C₂³×C₃	C₂×#67
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#384	D₉
hypocenter	C₉	#1956
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×#611

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₉×#384

C₂

socle, prime radical

C₂³×C₃

C₂×#67

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
13. #63431	C₄	semidirect
89. C₄×C₉	#103	semidirect
150. C₉	#1956	semidirect
179. C₄	#63368	semidirect

H ≅ G/N

type

13. #63431

C₄

semidirect

89. C₄×C₉

#103

semidirect

150. C₉

#1956

semidirect

179. C₄

#63368

semidirect

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

subgroup	index
C₂×#63431	2
C₉×#384	2
C₂×#63368	2
C₂×C₄×C₉⋊C₈	2
#69579	3

subgroup

index

C₂×C₄×C₉⋊C₈

Subgroups — #11790607

Conjugacy classes of subgroups

Complements

Maximal subgroups