Group #11781790 — subgroups

Subgroups — #11781790

Order 1152.

228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 76 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×#494	C₂	1	1	yes	maximal, characteristic
2	#10588767	C₂	1	2	yes	maximal
3	#10588359	C₂	1	1	yes	maximal, characteristic
4	#10588224	C₂	1	2	yes	maximal
5	#10588134	C₂	1	1	yes	maximal, characteristic
6	#71309	—	3	1	no	maximal
7	C₂×C₉×Q₁₆	—	2	1	no	—
8	C₂×C₉×Q₁₆	—	2	1	no	—
9	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₄×Dic₁₈	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	#63375	—	2	1	no	—
13	Dic₉⋊C₈	—	2	1	no	—
14	#63368	—	2	2	no	—
15	#63367	—	2	2	no	—
16	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₄⋊(C₉⋊C₈)	C₂²	1	2	yes	—
18	C₃×#494	D₃	1	1	yes	characteristic
19	#5094	—	3	2	no	—
20	#4679	—	3	1	no	—
21	#4547	—	3	2	no	—
22	#4457	—	3	1	no	—
23	C₂×Q₈×C₉	—	2	2	no	—
24	C₂×Dic₁₈	D₄	1	1	yes	characteristic
25	C₉×Q₁₆	—	4	2	no	—
26	C₉×Q₁₆	—	4	2	no	—
27	C₂×C₈×C₉	D₄	1	1	yes	characteristic
28	C₂×C₈×C₉	D₄	1	1	yes	characteristic
29	C₉×C₄⋊C₄	—	2	2	no	—
30	C₉×C₄⋊C₄	—	2	2	no	—
31	C₄²×C₉	C₂³	1	1	yes	characteristic
32	C₄⋊Dic₉	D₄	1	1	yes	characteristic
33	Dic₉⋊C₄	—	2	1	no	—
34	C₄×Dic₉	—	2	1	no	—
35	C₂×C₉⋊C₈	—	2	2	no	—
36	C₂×C₉⋊C₈	—	2	1	no	—
37	#1690	—	9	1	no	Sylow
38	C₂×C₃×Q₁₆	—	2	1	no	—
39	C₂×C₃×Q₁₆	—	2	1	no	—
40	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	—
41	C₄×Dic₆	—	3	1	no	—
42	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
43	#815	—	6	1	no	—
44	Dic₃⋊C₈	—	6	1	no	—
45	#810	—	6	2	no	—
46	#808	—	6	2	no	—
47	C₄⋊(C₃⋊C₈)	—	3	1	no	—
48	C₄⋊(C₃⋊C₈)	—	3	2	no	—
49	Q₈×C₉	—	4	2	no	—
50	Q₈×C₉	—	4	2	no	—
51	C₂×C₄×C₉	—	4	2	no	—
52	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₉	#41	1	1	yes	characteristic
55	C₂×Dic₉	—	2	1	no	—
56	C₂×Dic₉	—	2	1	no	—
57	Dic₁₈	—	2	2	no	—
58	C₈×C₉	—	2	1	no	—
59	C₈×C₉	SD₁₆	1	2	yes	—
60	C₉⋊C₈	—	4	1	no	—
61	C₉⋊C₈	—	4	2	no	—
62	#494	D₉	1	1	yes	characteristic
63	#475	—	9	2	no	—
64	#446	—	9	1	no	—
65	#334	—	9	1	no	—
66	#332	—	9	2	no	—
67	C₂×C₃×Q₈	—	2	2	no	—
68	C₂×Dic₆	—	3	1	no	—
69	C₃×Q₁₆	—	4	2	no	—
70	C₃×Q₁₆	—	4	2	no	—
71	C₂×C₃×C₈	#67	1	1	yes	characteristic
72	C₂×C₃×C₈	#67	1	1	yes	characteristic
73	C₃×C₄⋊C₄	—	2	2	no	—
74	C₃×C₄⋊C₄	—	2	2	no	—
75	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
76	C₄⋊Dic₃	—	3	1	no	—
77	Dic₃⋊C₄	—	6	1	no	—
78	C₄×Dic₃	—	6	1	no	—
79	C₂×C₃⋊C₈	—	6	2	no	—
80	C₂×C₃⋊C₈	—	6	1	no	—
81	C₂²×C₉	#121	1	1	yes	characteristic
82	C₄×C₉	—	2	1	no	—
83	C₄×C₉	—	8	2	no	—
84	C₄×C₉	C₂×SD₁₆	1	1	yes	characteristic
85	C₄×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₄×C₉	#137	1	2	yes	—
87	Dic₉	—	4	1	no	—
88	Dic₉	—	4	1	no	—
89	C₂×Q₁₆	—	2	1	no	—
90	C₂×Q₁₆	—	2	1	no	—
91	C₄⋊Q₈	C₂×D₉	1	2	yes	—
92	C₄×Q₈	—	9	1	no	—
93	#106	—	18	2	no	—
94	C₄⋊C₈	—	9	1	no	—
95	C₄⋊C₈	—	9	2	no	—
96	C₄⋊C₈	—	18	1	no	—
97	#103	—	18	2	no	—
98	#97	—	18	1	no	—
99	C₄×C₈	C₂×D₉	1	1	yes	characteristic
100	C₃×Q₈	—	4	2	no	—
101	C₃×Q₈	—	4	2	no	—
102	C₂×C₃×C₄	—	4	2	no	—
103	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄	#237	1	1	yes	characteristic
105	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
106	C₂×Dic₃	—	6	1	no	—
107	C₂×Dic₃	—	6	1	no	—
108	Dic₆	—	6	2	no	—
109	C₃×C₈	—	2	1	no	—
110	C₃×C₈	#214	1	2	yes	—
111	C₃⋊C₈	—	12	2	no	—
112	C₃⋊C₈	—	12	1	no	—
113	C₂×C₉	#460	1	1	yes	characteristic
114	C₂×C₉	#470	1	1	yes	characteristic
115	C₂×C₉	#473	1	1	yes	characteristic
116	C₂×Q₈	—	2	2	no	—
117	C₂×Q₈	—	9	1	no	—
118	Q₁₆	—	4	2	no	—
119	Q₁₆	—	4	2	no	—
120	C₂×C₈	—	18	2	no	—
121	C₂×C₈	—	18	1	no	—
122	C₂×C₈	#611	1	1	yes	characteristic
123	C₂×C₈	#611	1	1	yes	characteristic
124	C₄⋊C₄	—	2	2	no	—
125	C₄⋊C₄	—	2	2	no	—
126	C₄⋊C₄	—	9	1	no	—
127	C₄⋊C₄	—	18	1	no	—
128	C₄²	—	18	1	no	—
129	C₄²	C₂²×D₉	1	1	yes	characteristic
130	C₂²×C₃	#938	1	1	yes	characteristic
131	C₃×C₄	—	2	1	no	—
132	C₃×C₄	—	8	2	no	—
133	C₃×C₄	#918	1	2	yes	—
134	C₃×C₄	#932	1	1	yes	characteristic
135	C₃×C₄	C₂×#214	1	1	yes	characteristic
136	Dic₃	—	12	1	no	—
137	Dic₃	—	12	1	no	—
138	C₉	#1690	1	1	yes	characteristic, complemented, Sylow
139	Q₈	—	4	2	no	—
140	Q₈	—	4	2	no	—
141	Q₈	—	18	2	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	18	1	no	—
144	C₂×C₄	—	18	1	no	—
145	C₂×C₄	D₄×D₉	1	1	yes	characteristic
146	C₂×C₄	#3699	1	1	yes	characteristic
147	C₂×C₄	C₂×#611	1	1	yes	characteristic
148	C₈	—	2	1	no	—
149	C₈	—	36	1	no	—
150	C₈	—	36	2	no	—
151	C₈	#3672	1	2	yes	—
152	C₂×C₃	#5075	1	1	yes	characteristic
153	C₂×C₃	#5189	1	1	yes	characteristic
154	C₂×C₃	#5192	1	1	yes	characteristic
155	C₂²	#63500	1	1	yes	characteristic
156	C₄	—	2	1	no	—
157	C₄	—	8	2	no	—
158	C₄	—	36	1	no	—
159	C₄	—	36	1	no	—
160	C₄	#63480	1	2	yes	—
161	C₄	C₂×#3672	1	1	yes	characteristic
162	C₄	#63495	1	1	yes	characteristic
163	C₃	#71309	1	1	yes	characteristic
164	C₂	#10588752	1	1	yes	characteristic
165	C₂	#10588869	1	1	yes	characteristic
166	C₂	#10588872	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#494

C₂

yes

maximal, characteristic

#10588767

C₂

yes

maximal

#10588359

C₂

yes

maximal, characteristic

#10588224

C₂

yes

maximal

#10588134

C₂

yes

maximal, characteristic

#71309

—

maximal

C₂×C₉×Q₁₆

—

C₂×C₉×Q₁₆

—

C₉×C₄⋊Q₈

C₂²

yes

—

C₄×Dic₁₈

C₂²

yes

characteristic

C₄×C₈×C₉

C₂²

yes

characteristic

#63375

—

Dic₉⋊C₈

—

#63368

—

#63367

—

C₄⋊(C₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₉⋊C₈)

C₂²

yes

—

C₃×#494

D₃

yes

—

—

—

—

C₂×Q₈×C₉

—

C₂×Dic₁₈

D₄

yes

characteristic

C₉×Q₁₆

—

C₉×Q₁₆

—

C₂×C₈×C₉

D₄

yes

characteristic

C₂×C₈×C₉

D₄

yes

characteristic

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

D₄

yes

characteristic

Dic₉⋊C₄

—

C₄×Dic₉

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

#1690

—

Sylow

C₂×C₃×Q₁₆

—

C₂×C₃×Q₁₆

—

C₃×C₄⋊Q₈

C₂×D₃

yes

—

C₄×Dic₆

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#815

—

Dic₃⋊C₈

—

#810

—

#808

—

C₄⋊(C₃⋊C₈)

—

C₄⋊(C₃⋊C₈)

—

Q₈×C₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

SD₁₆

yes

—

C₉⋊C₈

—

C₉⋊C₈

—

#494

D₉

yes

—

—

—

—

C₂×C₃×Q₈

—

C₂×Dic₆

—

C₃×Q₁₆

—

C₃×Q₁₆

—

C₂×C₃×C₈

yes

C₂×C₃×C₈

yes

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

#121

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

C₂×SD₁₆

yes

C₄×C₉

yes

C₄×C₉

yes

—

Dic₉

—

Dic₉

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

C₂×D₉

yes

—

C₄×Q₈

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

C₂×D₉

yes

characteristic

100

C₃×Q₈

—

101

C₃×Q₈

—

102

C₂×C₃×C₄

—

103

C₂×C₃×C₄

D₃×D₄

yes

characteristic

104

C₂×C₃×C₄

#237

yes

characteristic

105

C₂×C₃×C₄

C₂×#67

yes

characteristic

106

C₂×Dic₃

—

107

C₂×Dic₃

—

108

Dic₆

—

109

C₃×C₈

—

110

C₃×C₈

#214

yes

—

111

C₃⋊C₈

—

112

C₃⋊C₈

—

113

C₂×C₉

#460

yes

characteristic

114

C₂×C₉

#470

yes

characteristic

115

C₂×C₉

#473

yes

characteristic

116

C₂×Q₈

—

117

C₂×Q₈

—

118

Q₁₆

—

119

Q₁₆

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

#611

yes

characteristic

123

C₂×C₈

#611

yes

characteristic

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄²

—

129

C₄²

C₂²×D₉

yes

characteristic

130

C₂²×C₃

#938

yes

characteristic

131

C₃×C₄

—

132

C₃×C₄

—

133

C₃×C₄

#918

yes

—

134

C₃×C₄

#932

yes

characteristic

135

C₃×C₄

C₂×#214

yes

characteristic

136

Dic₃

—

137

Dic₃

—

138

C₉

#1690

yes

characteristic, complemented, Sylow

139

Q₈

—

140

Q₈

—

141

Q₈

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

D₄×D₉

yes

characteristic

146

C₂×C₄

#3699

yes

characteristic

147

C₂×C₄

C₂×#611

yes

characteristic

148

C₈

—

149

C₈

—

150

C₈

—

151

C₈

#3672

yes

—

152

C₂×C₃

#5075

yes

characteristic

153

C₂×C₃

#5189

yes

characteristic

154

C₂×C₃

#5192

yes

characteristic

155

C₂²

#63500

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

#63480

yes

—

161

C₄

C₂×#3672

yes

characteristic

162

C₄

#63495

yes

characteristic

163

C₃

#71309

yes

characteristic

164

C₂

#10588752

yes

characteristic

165

C₂

#10588869

yes

characteristic

166

C₂

#10588872

yes

characteristic

	subgroup	G/H
center	C₂²	#63500
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#494	C₂
socle, prime radical	C₂²×C₃	#938
hypercenter	#494	D₉
hypocenter	C₉	#1690
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#63500

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
138. C₉	#1690	semidirect

H ≅ G/N

type

138. C₉

#1690

semidirect

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

subgroup	index
C₉×#494	2
#10588767	2
#10588359	2
#10588224	2
#10588134	2
#71309	3

subgroup

index

Subgroups — #11781790

Conjugacy classes of subgroups

Complements

Maximal subgroups