Group #11790726 — subgroups

Subgroups — #11790726

Order 1152.

462 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 154 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	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×#63376	C₂	1	4	yes	maximal
4	#10588616	C₂	1	1	yes	maximal, characteristic
5	#69822	—	3	1	no	maximal
6	C₂²×Dic₁₈	C₂²	1	2	yes	—
7	C₂²×C₈×C₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₉	—	2	2	no	—
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	#63431	—	2	2	no	—
12	#63431	C₄	1	4	yes	complemented
13	C₉×#97	—	2	2	no	—
14	C₉⋊#95	—	2	2	no	—
15	#63376	—	2	8	no	—
16	C₂×#869	—	3	1	no	—
17	C₂×C₃×#97	D₃	1	1	yes	characteristic
18	C₂×#816	—	3	4	no	—
19	#4936	—	3	1	no	—
20	C₂²×C₄×C₉	D₄	1	2	yes	—
21	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₉	—	2	2	no	—
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	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	—	2	2	no	—
30	C₂×C₈×C₉	D₄	1	4	yes	—
31	C₄²×C₉	C₂×C₄	1	2	yes	—
32	C₄²×C₉	D₄	1	2	yes	—
33	C₄⋊Dic₉	—	2	8	no	—
34	C₄⋊Dic₉	—	2	4	no	—
35	#1960	—	9	1	no	Sylow
36	C₂²×Dic₆	—	3	2	no	—
37	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
38	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
39	C₂×C₄⋊Dic₃	—	3	2	no	—
40	C₂×C₄⋊Dic₃	—	6	2	no	—
41	#869	—	3	4	no	—
42	#869	—	6	2	no	—
43	C₃×#97	—	2	2	no	—
44	C₃⋊#95	—	6	2	no	—
45	#816	—	6	8	no	—
46	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₉	—	2	4	no	—
48	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
49	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₉	#41	1	2	yes	—
53	C₂×Dic₉	—	2	4	no	—
54	C₂×Dic₉	—	4	2	no	—
55	C₂×Dic₉	—	4	2	no	—
56	C₂×Dic₉	—	4	2	no	—
57	C₂×Dic₉	—	4	4	no	—
58	Dic₁₈	—	2	8	no	—
59	Dic₁₈	—	4	4	no	—
60	C₈×C₉	—	2	4	no	—
61	C₂×C₄⋊Q₈	—	9	1	no	—
62	C₂×#103	—	9	4	no	—
63	C₂×#97	D₉	1	1	yes	characteristic
64	#382	—	9	1	no	—
65	C₂²×C₃×C₄	D₁₂	1	2	yes	—
66	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
67	C₂²×Dic₃	—	6	2	no	—
68	C₂²×Dic₃	—	6	2	no	—
69	C₂×Dic₆	—	3	4	no	—
70	C₂×Dic₆	—	6	4	no	—
71	C₂×Dic₆	—	6	4	no	—
72	C₂×Dic₆	—	6	2	no	—
73	C₂×C₃×C₈	—	2	2	no	—
74	C₂×C₃×C₈	—	2	2	no	—
75	C₂×C₃×C₈	D₁₂	1	4	yes	—
76	C₃×C₄²	C₄×D₃	1	2	yes	—
77	C₃×C₄²	#67	1	2	yes	—
78	C₄⋊Dic₃	—	6	8	no	—
79	C₄⋊Dic₃	—	6	4	no	—
80	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₉	#124	1	1	yes	characteristic
82	C₂²×C₉	#127	1	1	yes	characteristic
83	C₂²×C₉	#137	1	4	yes	—
84	C₄×C₉	—	2	4	no	—
85	C₄×C₉	C₄×D₄	1	2	yes	—
86	C₄×C₉	#121	1	2	yes	—
87	Dic₉	—	4	4	no	—
88	Dic₉	—	8	2	no	—
89	C₂²×Q₈	—	9	2	no	—
90	C₂²×C₈	C₂×D₉	1	2	yes	—
91	C₄⋊Q₈	—	9	4	no	—
92	C₄⋊Q₈	—	18	2	no	—
93	C₂×C₄⋊C₄	—	9	2	no	—
94	C₂×C₄⋊C₄	—	18	2	no	—
95	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
96	#103	—	18	8	no	—
97	#97	—	2	2	no	—
98	#95	—	18	2	no	—
99	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
100	C₂×C₃×C₄	—	2	4	no	—
101	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
102	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
103	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
104	C₂×C₃×C₄	#235	1	2	yes	—
105	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
106	C₂×Dic₃	—	6	4	no	—
107	C₂×Dic₃	—	12	2	no	—
108	C₂×Dic₃	—	12	2	no	—
109	C₂×Dic₃	—	12	2	no	—
110	C₂×Dic₃	—	12	4	no	—
111	Dic₆	—	6	8	no	—
112	Dic₆	—	12	4	no	—
113	C₃×C₈	—	2	4	no	—
114	C₂×C₉	#390	1	1	yes	characteristic
115	C₂×C₉	#419	1	2	yes	—
116	C₂×C₉	#491	1	2	yes	—
117	C₂×C₉	#497	1	2	yes	—
118	C₂×Q₈	—	9	4	no	—
119	C₂×Q₈	—	18	2	no	—
120	C₂×Q₈	—	18	4	no	—
121	C₂×Q₈	—	18	4	no	—
122	C₂²×C₄	—	18	2	no	—
123	C₂²×C₄	—	18	2	no	—
124	C₂²×C₄	D₃₆	1	2	yes	—
125	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
126	C₂×C₈	—	2	2	no	—
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	D₃₆	1	4	yes	—
129	C₄⋊C₄	—	18	8	no	—
130	C₄⋊C₄	—	18	4	no	—
131	C₄²	C₄×D₉	1	2	yes	—
132	C₄²	#611	1	2	yes	—
133	C₂²×C₃	#874	1	1	yes	characteristic
134	C₂²×C₃	#875	1	1	yes	characteristic
135	C₂²×C₃	#909	1	4	yes	—
136	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
137	C₃×C₄	—	2	4	no	—
138	C₃×C₄	C₄×D₁₂	1	2	yes	—
139	C₃×C₄	#930	1	2	yes	—
140	Dic₃	—	12	4	no	—
141	Dic₃	—	24	2	no	—
142	C₉	#1960	1	1	yes	characteristic, complemented, Sylow
143	C₂³	C₂×D₃₆	1	1	yes	characteristic
144	Q₈	—	18	8	no	—
145	Q₈	—	36	4	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	18	4	no	—
148	C₂×C₄	—	36	2	no	—
149	C₂×C₄	—	36	2	no	—
150	C₂×C₄	—	36	2	no	—
151	C₂×C₄	—	36	4	no	—
152	C₂×C₄	(C₂×D₉)⋊C₄	1	4	yes	—
153	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
154	C₂×C₄	C₂×D₃₆	1	2	yes	—
155	C₂×C₄	#3697	1	2	yes	—
156	C₂×C₄	C₂×#611	1	1	yes	characteristic
157	C₈	—	2	4	no	—
158	C₂×C₃	#4703	1	2	yes	—
159	C₂×C₃	#4715	1	2	yes	—
160	C₂×C₃	#4939	1	1	yes	characteristic
161	C₂×C₃	#5120	1	2	yes	—
162	C₂²	#63436	1	1	yes	characteristic
163	C₂²	#63437	1	1	yes	characteristic
164	C₂²	#63471	1	4	yes	—
165	C₂²	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
166	C₄	—	2	4	no	—
167	C₄	—	36	4	no	—
168	C₄	—	72	2	no	—
169	C₄	C₄×D₃₆	1	2	yes	—
170	C₄	#63492	1	2	yes	—
171	C₃	#69822	1	1	yes	characteristic
172	C₂	#10588383	1	2	yes	—
173	C₂	#10588396	1	2	yes	—
174	C₂	#10588619	1	1	yes	characteristic
175	C₂	#10588804	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63431

C₂

yes

maximal, characteristic

C₂×C₉×#97

C₂

yes

maximal, characteristic

C₂×#63376

C₂

yes

maximal

#10588616

C₂

yes

maximal, characteristic

#69822

—

maximal

C₂²×Dic₁₈

C₂²

yes

—

C₂²×C₈×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

—

C₂×C₄⋊Dic₉

C₂²

yes

—

#63431

—

#63431

C₄

yes

complemented

C₉×#97

—

C₉⋊#95

—

#63376

—

C₂×#869

—

C₂×C₃×#97

D₃

yes

characteristic

C₂×#816

—

#4936

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₂²×Dic₉

—

C₂×Dic₁₈

—

C₂×Dic₁₈

—

C₂×Dic₁₈

—

C₂×Dic₁₈

C₂×C₄

yes

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

D₄

yes

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

#1960

—

Sylow

C₂²×Dic₆

—

C₂²×C₃×C₈

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

C₂×C₄⋊Dic₃

—

#869

—

#869

—

C₃×#97

—

C₃⋊#95

—

#816

—

C₂³×C₉

C₂×D₄

yes

characteristic

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

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

Dic₁₈

—

Dic₁₈

—

C₈×C₉

—

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×#97

D₉

yes

characteristic

#382

—

C₂²×C₃×C₄

D₁₂

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

D₁₂

yes

—

C₃×C₄²

C₄×D₃

yes

—

C₃×C₄²

#67

yes

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

C₂²×C₉

yes

C₂²×C₉

yes

C₂²×C₉

yes

—

C₄×C₉

—

C₄×C₉

C₄×D₄

yes

—

C₄×C₉

#121

yes

—

Dic₉

—

Dic₉

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₉

yes

—

—

—

C₂³×C₃

C₂×D₁₂

yes

characteristic

100

C₂×C₃×C₄

—

101

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

102

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

103

C₂×C₃×C₄

C₂×D₁₂

yes

—

104

C₂×C₃×C₄

#235

yes

—

105

C₂×C₃×C₄

C₂×#67

yes

characteristic

106

C₂×Dic₃

—

107

C₂×Dic₃

—

108

C₂×Dic₃

—

109

C₂×Dic₃

—

110

C₂×Dic₃

—

111

Dic₆

—

112

Dic₆

—

113

C₃×C₈

—

114

C₂×C₉

#390

yes

characteristic

115

C₂×C₉

#419

yes

—

116

C₂×C₉

#491

yes

—

117

C₂×C₉

#497

yes

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

D₃₆

yes

—

125

C₂²×C₄

C₂²×D₉

yes

characteristic

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

D₃₆

yes

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄²

C₄×D₉

yes

—

132

C₄²

#611

yes

—

133

C₂²×C₃

#874

yes

characteristic

134

C₂²×C₃

#875

yes

characteristic

135

C₂²×C₃

#909

yes

—

136

C₂²×C₃

C₂×(C₂×D₃)⋊C₄

yes

characteristic

137

C₃×C₄

—

138

C₃×C₄

C₄×D₁₂

yes

—

139

C₃×C₄

#930

yes

—

140

Dic₃

—

141

Dic₃

—

142

C₉

#1960

yes

characteristic, complemented, Sylow

143

C₂³

C₂×D₃₆

yes

characteristic

144

Q₈

—

145

Q₈

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

(C₂×D₉)⋊C₄

yes

—

153

C₂×C₄

C₂×C₄×D₉

yes

characteristic

154

C₂×C₄

C₂×D₃₆

yes

—

155

C₂×C₄

#3697

yes

—

156

C₂×C₄

C₂×#611

yes

characteristic

157

C₈

—

158

C₂×C₃

#4703

yes

—

159

C₂×C₃

#4715

yes

—

160

C₂×C₃

#4939

yes

characteristic

161

C₂×C₃

#5120

yes

—

162

C₂²

#63436

yes

characteristic

163

C₂²

#63437

yes

characteristic

164

C₂²

#63471

yes

—

165

C₂²

C₂×(C₂×D₉)⋊C₄

yes

characteristic

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

C₄×D₃₆

yes

—

170

C₄

#63492

yes

—

171

C₃

#69822

yes

characteristic

172

C₂

#10588383

yes

—

173

C₂

#10588396

yes

—

174

C₂

#10588619

yes

characteristic

175

C₂

#10588804

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#97	C₂
socle, prime radical	C₂³×C₃	C₂×D₁₂
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#97	D₉
hypocenter	C₉	#1960
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₃₆

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#97

C₂

socle, prime radical

C₂³×C₃

C₂×D₁₂

cosocle

C₂²×C₄×C₉

C₂³

hypercenter

C₂×#97

D₉

hypocenter

C₉

#1960

LCS

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
12. #63431	C₄	semidirect
142. C₉	#1960	semidirect

H ≅ G/N

type

12. #63431

C₄

semidirect

142. C₉

#1960

semidirect

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

subgroup	index
C₂×#63431	2
C₂×C₉×#97	2
C₂×#63376	2
#10588616	2
#69822	3

subgroup

index

C₂×C₉×#97

Subgroups — #11790726

Conjugacy classes of subgroups

Complements

Maximal subgroups