Group #11781802 — subgroups

Subgroups — #11781802

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	#10588515	C₂	1	2	yes	maximal
2	#10588365	C₂	1	1	yes	maximal, characteristic
3	#10588359	C₂	1	1	yes	maximal, characteristic
4	C₉×#334	C₂	1	1	yes	maximal, characteristic
5	#10588161	C₂	1	2	yes	maximal
6	#68551	—	3	1	no	maximal
7	C₂×Dic₃₆	—	2	1	no	—
8	C₂×Dic₃₆	—	2	1	no	—
9	#63431	C₂²	1	2	yes	—
10	C₄×Dic₁₈	C₂²	1	1	yes	characteristic
11	C₉×C₄⋊C₈	C₂²	1	2	yes	—
12	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
13	#63377	—	2	2	no	—
14	#63376	—	2	2	no	—
15	#63375	—	2	1	no	—
16	Dic₉⋊C₈	—	2	1	no	—
17	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
18	#4851	—	3	2	no	—
19	#4699	—	3	1	no	—
20	#4679	—	3	1	no	—
21	C₃×#334	D₃	1	1	yes	characteristic
22	#4486	—	3	2	no	—
23	C₂×Dic₁₈	—	2	2	no	—
24	C₂×Dic₁₈	D₄	1	1	yes	characteristic
25	C₂×C₈×C₉	—	2	2	no	—
26	C₂×C₈×C₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₉	D₄	1	1	yes	characteristic
28	C₄²×C₉	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₉	—	2	2	no	—
30	C₄⋊Dic₉	—	2	2	no	—
31	C₄⋊Dic₉	D₄	1	1	yes	characteristic
32	Dic₉⋊C₄	—	2	1	no	—
33	C₄×Dic₉	—	2	1	no	—
34	C₂×C₉⋊C₈	—	2	1	no	—
35	Dic₃₆	—	4	2	no	—
36	Dic₃₆	—	4	2	no	—
37	#1690	—	9	1	no	Sylow
38	C₂×Dic₁₂	—	6	1	no	—
39	C₂×Dic₁₂	—	6	1	no	—
40	#869	—	3	2	no	—
41	C₄×Dic₆	—	3	1	no	—
42	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
43	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
44	#817	—	6	2	no	—
45	#816	—	6	2	no	—
46	#815	—	6	1	no	—
47	Dic₃⋊C₈	—	6	1	no	—
48	C₄⋊(C₃⋊C₈)	—	3	1	no	—
49	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₉	#41	1	1	yes	characteristic
52	C₂×Dic₉	—	2	1	no	—
53	C₂×Dic₉	—	2	1	no	—
54	C₂×Dic₉	—	4	2	no	—
55	Dic₁₈	—	2	2	no	—
56	Dic₁₈	—	4	2	no	—
57	Dic₁₈	—	4	2	no	—
58	C₈×C₉	—	2	1	no	—
59	C₈×C₉	—	4	2	no	—
60	C₈×C₉	SD₁₆	1	2	yes	—
61	C₉⋊C₈	—	4	1	no	—
62	#494	—	9	1	no	—
63	#475	—	9	2	no	—
64	#446	—	9	1	no	—
65	#334	D₉	1	1	yes	characteristic
66	#332	—	9	2	no	—
67	C₂×Dic₆	—	3	1	no	—
68	C₂×Dic₆	—	6	2	no	—
69	C₂×C₃×C₈	—	2	2	no	—
70	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
71	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
72	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
73	C₄⋊Dic₃	—	3	1	no	—
74	C₄⋊Dic₃	—	6	2	no	—
75	C₄⋊Dic₃	—	6	2	no	—
76	Dic₃⋊C₄	—	6	1	no	—
77	C₄×Dic₃	—	6	1	no	—
78	C₂×C₃⋊C₈	—	6	1	no	—
79	Dic₁₂	—	12	2	no	—
80	Dic₁₂	—	12	2	no	—
81	C₂²×C₉	#121	1	1	yes	characteristic
82	C₄×C₉	—	2	1	no	—
83	C₄×C₉	C₂×SD₁₆	1	1	yes	characteristic
84	C₄×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
85	C₄×C₉	#137	1	2	yes	—
86	Dic₉	—	4	1	no	—
87	Dic₉	—	4	1	no	—
88	Dic₉	—	8	2	no	—
89	C₂×Q₁₆	—	18	1	no	—
90	C₂×Q₁₆	—	18	1	no	—
91	C₄⋊Q₈	—	9	2	no	—
92	C₄×Q₈	—	9	1	no	—
93	#106	—	18	2	no	—
94	C₄⋊C₈	—	9	1	no	—
95	C₄⋊C₈	—	18	1	no	—
96	C₄⋊C₈	C₂×D₉	1	2	yes	—
97	#103	—	18	2	no	—
98	#97	—	18	1	no	—
99	C₄×C₈	C₂×D₉	1	1	yes	characteristic
100	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
101	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄	#239	1	1	yes	characteristic
103	C₂×Dic₃	—	6	1	no	—
104	C₂×Dic₃	—	6	1	no	—
105	C₂×Dic₃	—	12	2	no	—
106	Dic₆	—	6	2	no	—
107	Dic₆	—	12	2	no	—
108	Dic₆	—	12	2	no	—
109	C₃×C₈	—	2	1	no	—
110	C₃×C₈	—	4	2	no	—
111	C₃×C₈	#204	1	2	yes	—
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	—	9	1	no	—
117	C₂×Q₈	—	18	2	no	—
118	Q₁₆	—	36	2	no	—
119	Q₁₆	—	36	2	no	—
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	18	1	no	—
122	C₂×C₈	D₃₆	1	1	yes	characteristic
123	C₂×C₈	D₃₆	1	1	yes	characteristic
124	C₄⋊C₄	—	9	1	no	—
125	C₄⋊C₄	—	18	1	no	—
126	C₄⋊C₄	—	18	2	no	—
127	C₄⋊C₄	—	18	2	no	—
128	C₄²	—	18	1	no	—
129	C₄²	C₂²×D₉	1	1	yes	characteristic
130	C₂²×C₃	#895	1	1	yes	characteristic
131	C₃×C₄	—	2	1	no	—
132	C₃×C₄	C₂×#204	1	1	yes	characteristic
133	C₃×C₄	#908	1	1	yes	characteristic
134	C₃×C₄	#915	1	2	yes	—
135	Dic₃	—	12	1	no	—
136	Dic₃	—	12	1	no	—
137	Dic₃	—	24	2	no	—
138	C₉	#1690	1	1	yes	characteristic, complemented, Sylow
139	Q₈	—	18	2	no	—
140	Q₈	—	36	2	no	—
141	Q₈	—	36	2	no	—
142	C₂×C₄	—	18	1	no	—
143	C₂×C₄	—	18	1	no	—
144	C₂×C₄	—	36	2	no	—
145	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
146	C₂×C₄	D₄×D₉	1	1	yes	characteristic
147	C₂×C₄	#3701	1	1	yes	characteristic
148	C₈	—	2	1	no	—
149	C₈	—	4	2	no	—
150	C₈	—	36	1	no	—
151	C₈	#3664	1	2	yes	—
152	C₂×C₃	#4848	1	1	yes	characteristic
153	C₂×C₃	#4867	1	1	yes	characteristic
154	C₂×C₃	#4896	1	1	yes	characteristic
155	C₂²	#63457	1	1	yes	characteristic
156	C₄	—	2	1	no	—
157	C₄	—	36	1	no	—
158	C₄	—	36	1	no	—
159	C₄	—	72	2	no	—
160	C₄	C₂×#3664	1	1	yes	characteristic
161	C₄	#63470	1	1	yes	characteristic
162	C₄	#63477	1	2	yes	—
163	C₃	#68551	1	1	yes	characteristic
164	C₂	#10588512	1	1	yes	characteristic
165	C₂	#10588547	1	1	yes	characteristic
166	C₂	#10588576	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588515

C₂

yes

maximal

#10588365

C₂

yes

maximal, characteristic

#10588359

C₂

yes

maximal, characteristic

C₉×#334

C₂

yes

maximal, characteristic

#10588161

C₂

yes

maximal

#68551

—

maximal

C₂×Dic₃₆

—

C₂×Dic₃₆

—

#63431

C₂²

yes

—

C₄×Dic₁₈

C₂²

yes

characteristic

C₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

—

—

—

Dic₉⋊C₈

—

C₄⋊(C₉⋊C₈)

C₂²

yes

—

—

—

D₃

yes

characteristic

#4486

—

C₂×Dic₁₈

—

C₂×Dic₁₈

D₄

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

characteristic

C₂×C₈×C₉

D₄

yes

characteristic

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

D₄

yes

characteristic

Dic₉⋊C₄

—

C₄×Dic₉

—

C₂×C₉⋊C₈

—

Dic₃₆

—

Dic₃₆

—

#1690

—

Sylow

C₂×Dic₁₂

—

C₂×Dic₁₂

—

#869

—

C₄×Dic₆

—

C₃×C₄⋊C₈

C₂×D₃

yes

—

C₃×C₄×C₈

C₂×D₃

yes

—

—

—

Dic₃⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

Dic₁₈

—

Dic₁₈

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

SD₁₆

yes

—

C₉⋊C₈

—

—

—

—

D₉

yes

characteristic

#332

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

D₁₂

yes

characteristic

C₂×C₃×C₈

D₁₂

yes

characteristic

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

Dic₁₂

—

Dic₁₂

—

C₂²×C₉

#121

yes

characteristic

C₄×C₉

—

C₄×C₉

C₂×SD₁₆

yes

C₄×C₉

yes

C₄×C₉

yes

—

Dic₉

—

Dic₉

—

Dic₉

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₉

yes

—

#103

—

#97

—

C₄×C₈

C₂×D₉

yes

characteristic

100

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

101

C₂×C₃×C₄

D₃×D₄

yes

characteristic

102

C₂×C₃×C₄

#239

yes

characteristic

103

C₂×Dic₃

—

104

C₂×Dic₃

—

105

C₂×Dic₃

—

106

Dic₆

—

107

Dic₆

—

108

Dic₆

—

109

C₃×C₈

—

110

C₃×C₈

—

111

C₃×C₈

#204

yes

—

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

D₃₆

yes

characteristic

123

C₂×C₈

D₃₆

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

#895

yes

characteristic

131

C₃×C₄

—

132

C₃×C₄

C₂×#204

yes

characteristic

133

C₃×C₄

#908

yes

characteristic

134

C₃×C₄

#915

yes

—

135

Dic₃

—

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

C₂×D₃₆

yes

characteristic

146

C₂×C₄

D₄×D₉

yes

characteristic

147

C₂×C₄

#3701

yes

characteristic

148

C₈

—

149

C₈

—

150

C₈

—

151

C₈

#3664

yes

—

152

C₂×C₃

#4848

yes

characteristic

153

C₂×C₃

#4867

yes

characteristic

154

C₂×C₃

#4896

yes

characteristic

155

C₂²

#63457

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

C₂×#3664

yes

characteristic

161

C₄

#63470

yes

characteristic

162

C₄

#63477

yes

—

163

C₃

#68551

yes

characteristic

164

C₂

#10588512

yes

characteristic

165

C₂

#10588547

yes

characteristic

166

C₂

#10588576

yes

characteristic

	subgroup	G/H
center	C₂²	#63457
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#334	C₂
socle, prime radical	C₂²×C₃	#895
hypercenter	#334	D₉
hypocenter	C₉	#1690
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#63457

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 ◁ #334

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
#10588515	2
#10588365	2
#10588359	2
C₉×#334	2
#10588161	2
#68551	3

subgroup

index

Subgroups — #11781802

Conjugacy classes of subgroups

Complements

Maximal subgroups