Group #36447449 — subgroups

Subgroups — #36447449

Order 22784.

336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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	#26029182	C₂	1	1	yes	maximal, characteristic
2	#26019007	C₂	1	2	yes	maximal
3	#26018989	C₂	1	2	yes	maximal
4	#26018165	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1309	C₂	1	1	yes	maximal, characteristic
6	#19152155	C₂²	1	1	yes	characteristic
7	#19151725	—	2	2	no	—
8	#19151722	—	2	2	no	—
9	#19151626	C₄	1	2	yes	—
10	#19151622	C₂²	1	2	yes	—
11	#19151556	C₄	1	2	yes	—
12	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
13	#19151348	—	2	2	no	—
14	#19151348	—	2	2	no	—
15	#19151345	—	2	2	no	—
16	#19151343	—	2	2	no	—
17	#423×C₈₉	C₂²	1	2	yes	—
18	#423×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#13083558	—	2	2	no	—
20	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
21	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
22	#15668012	D₄	1	2	yes	—
23	#15668004	Q₈	1	2	yes	—
24	#15667991	—	2	2	no	—
25	C₄×Dic₁₇₈	—	2	2	no	—
26	#15667971	C₂×C₄	1	2	yes	—
27	C₄⋊#10623494	—	2	2	no	—
28	C₄⋊#10623494	—	2	2	no	—
29	#15667941	—	2	4	no	—
30	#15667922	—	2	2	no	—
31	C₄×#10623494	D₄	1	2	yes	—
32	C₄×#10623494	D₄	1	2	yes	—
33	C₈×Dic₈₉	—	2	2	no	—
34	C₂×M₁₆×C₈₉	—	2	2	no	—
35	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₈₉	—	2	2	no	—
38	C₄⋊C₈×C₈₉	—	2	2	no	—
39	C₄⋊C₈×C₈₉	—	2	2	no	—
40	C₂×Dic₁₇₈	—	2	2	no	—
41	#13083558	—	8	2	no	—
42	C₂×#10623494	—	2	2	no	—
43	C₂×#10623494	—	4	1	no	—
44	C₂×#10623494	—	4	2	no	—
45	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
47	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
48	C₄⋊Dic₈₉	—	2	2	no	—
49	C₄⋊Dic₈₉	C₄⋊C₄	1	4	yes	—
50	#13083553	—	2	4	no	—
51	C₂²⋊Dic₈₉	—	2	2	no	—
52	C₄×Dic₈₉	—	2	2	no	—
53	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₈₉	#41	1	2	yes	—
55	M₁₆×C₈₉	—	4	2	no	—
56	M₁₆×C₈₉	—	8	2	no	—
57	C₂×C₈×C₈₉	—	2	2	no	—
58	C₂×C₈×C₈₉	—	4	2	no	—
59	C₄²×C₈₉	C₂×D₄	1	2	yes	—
60	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
62	C₂³×C₈₉	#117	1	1	yes	characteristic
63	C₂×C₄×C₈₉	—	2	1	no	—
64	C₂×C₄×C₈₉	—	2	1	no	—
65	C₂×C₄×C₈₉	—	2	2	no	—
66	C₂×C₄×C₈₉	—	2	2	no	—
67	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₈₉	#121	1	2	yes	—
70	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
71	C₂×Dic₈₉	—	2	4	no	—
72	Dic₁₇₈	—	4	2	no	—
73	Dic₁₇₈	—	4	2	no	—
74	C₈×C₈₉	—	4	2	no	—
75	C₈×C₈₉	—	8	2	no	—
76	#10623494	—	2	1	no	—
77	#10623494	—	2	2	no	—
78	#10623494	—	8	2	no	—
79	#10623494	#101	1	2	yes	—
80	C₂²×C₈₉	—	2	1	no	—
81	C₂²×C₈₉	—	2	2	no	—
82	C₂²×C₈₉	#380	1	1	yes	characteristic
83	C₄×C₈₉	—	2	1	no	—
84	C₄×C₈₉	—	2	2	no	—
85	C₄×C₈₉	C₂×#101	1	1	yes	characteristic
86	C₄×C₈₉	#413	1	1	yes	characteristic
87	C₄×C₈₉	#471	1	2	yes	—
88	C₄×C₈₉	#471	1	2	yes	—
89	Dic₈₉	—	4	4	no	—
90	#8637	—	89	1	no	maximal, Sylow
91	C₂×C₈₉	—	4	1	no	—
92	C₂×C₈₉	#1801	1	1	yes	characteristic
93	C₂×C₈₉	#1815	1	2	yes	—
94	#2960	—	89	1	no	—
95	#1566	—	89	2	no	—
96	#1561	—	89	2	no	—
97	#1309	—	89	1	no	—
98	#1309	D₈₉	1	1	yes	characteristic
99	C₈₉	#8637	1	1	yes	characteristic, complemented, Sylow
100	#533	—	89	1	no	—
101	#446	—	178	2	no	—
102	C₈×Q₈	—	178	2	no	—
103	#424	—	89	2	no	—
104	#423	—	89	2	no	—
105	#423	C₂×D₈₉	1	2	yes	—
106	#423	C₂×D₈₉	1	1	yes	characteristic
107	#405	—	89	2	no	—
108	C₂×C₄×C₈	—	89	1	no	—
109	#334	—	178	2	no	—
110	#334	—	178	2	no	—
111	#332	—	178	2	no	—
112	#332	—	178	2	no	—
113	C₂×M₁₆	—	2	2	no	—
114	C₂×M₁₆	—	178	2	no	—
115	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
116	C₂²×C₈	—	89	1	no	—
117	C₂²×C₈	—	89	1	no	—
118	C₄⋊Q₈	—	89	2	no	—
119	#125	—	89	2	no	—
120	C₂²⋊Q₈	—	178	2	no	—
121	C₄×Q₈	—	178	2	no	—
122	#117	—	89	2	no	—
123	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	—	2	2	no	—
126	C₄⋊C₈	—	2	2	no	—
127	C₄⋊C₈	—	178	4	no	—
128	C₄⋊C₈	—	178	2	no	—
129	C₄⋊C₈	—	178	2	no	—
130	#97	—	178	2	no	—
131	C₄×C₈	—	89	2	no	—
132	C₄×C₈	—	89	2	no	—
133	C₄×C₈	—	178	2	no	—
134	C₂×Q₈	—	178	2	no	—
135	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
136	C₂²×C₄	#13083574	1	2	yes	—
137	M₁₆	—	4	2	no	—
138	M₁₆	—	8	2	no	—
139	M₁₆	—	712	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	4	2	no	—
142	C₂×C₈	—	89	1	no	—
143	C₂×C₈	—	89	1	no	—
144	C₂×C₈	—	89	2	no	—
145	C₂×C₈	—	356	1	no	—
146	C₂×C₈	—	356	2	no	—
147	C₂×C₈	—	178	2	no	—
148	C₄⋊C₄	—	89	4	no	—
149	C₄⋊C₄	—	178	2	no	—
150	C₄⋊C₄	—	178	4	no	—
151	C₂²⋊C₄	—	178	2	no	—
152	C₄²	—	178	2	no	—
153	C₄²	D₄×D₈₉	1	1	yes	characteristic
154	C₄²	D₄×D₈₉	1	2	yes	—
155	C₄²	Q₈×D₈₉	1	1	yes	characteristic
156	C₂³	#15667969	1	1	yes	characteristic
157	Q₈	—	356	2	no	—
158	Q₈	—	356	2	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	178	4	no	—
164	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
165	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
166	C₂×C₄	#15667985	1	2	yes	—
167	C₂×C₄	#15667990	1	2	yes	—
168	C₈	—	4	2	no	—
169	C₈	—	8	2	no	—
170	C₈	—	89	2	no	—
171	C₈	—	178	1	no	—
172	C₈	—	178	2	no	—
173	C₈	—	712	2	no	—
174	C₂²	—	2	1	no	—
175	C₂²	—	2	2	no	—
176	C₂²	#19151457	1	1	yes	characteristic
177	C₄	—	2	1	no	—
178	C₄	—	2	2	no	—
179	C₄	—	356	4	no	—
180	C₄	#101×D₈₉	1	1	yes	characteristic
181	C₄	#19151579	1	1	yes	characteristic
182	C₄	#19151860	1	2	yes	—
183	C₄	#19151864	1	2	yes	—
184	C₂	—	4	1	no	—
185	C₂	#26020247	1	1	yes	characteristic
186	C₂	#26020310	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26029182

C₂

yes

maximal, characteristic

#26019007

C₂

yes

maximal

#26018989

C₂

yes

maximal

#26018165

C₂

yes

maximal, characteristic

C₈₉×#1309

C₂

yes

maximal, characteristic

#19152155

C₂²

yes

—

—

C₄

yes

—

#19151622

C₂²

yes

—

#19151556

C₄

yes

—

C₂×C₄×#10623494

C₂²

yes

—

—

—

—

#423×C₈₉

C₂²

yes

—

#423×C₈₉

C₂²

yes

characteristic

C₂×#13083558

—

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

characteristic

#15668012

D₄

yes

—

#15668004

Q₈

yes

—

#15667991

—

C₄×Dic₁₇₈

—

#15667971

C₂×C₄

yes

—

—

—

—

—

D₄

yes

—

C₄×#10623494

D₄

yes

—

C₈×Dic₈₉

—

C₂×M₁₆×C₈₉

—

C₂×M₁₆×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

—

C₂×Dic₁₇₈

—

—

—

—

—

C₂²⋊C₄

yes

characteristic

C₂×#10623494

C₂²⋊C₄

yes

—

C₂×#10623494

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₄⋊C₄

yes

—

#13083553

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

—

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₂³×C₈₉

#117

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₉

#121

yes

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

—

—

—

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#380

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₄×C₈₉

#471

yes

—

Dic₈₉

—

#8637

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

#1801

yes

characteristic

C₂×C₈₉

#1815

yes

—

—

—

—

—

D₈₉

yes

characteristic

C₈₉

#8637

yes

characteristic, complemented, Sylow

100

#533

—

101

#446

—

178

—

102

C₈×Q₈

—

178

—

103

#424

—

104

#423

—

105

#423

C₂×D₈₉

yes

—

106

#423

C₂×D₈₉

yes

characteristic

107

#405

—

108

C₂×C₄×C₈

—

109

#334

—

178

—

110

#334

—

178

—

111

#332

—

178

—

112

#332

—

178

—

113

C₂×M₁₆

—

114

C₂×M₁₆

—

178

—

115

C₂×M₁₆

C₄×D₈₉

yes

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

C₄⋊Q₈

—

119

#125

—

120

C₂²⋊Q₈

—

178

—

121

C₄×Q₈

—

178

—

122

#117

—

123

C₂×C₄²

C₂²×D₈₉

yes

characteristic

124

C₄⋊C₈

—

125

C₄⋊C₈

—

126

C₄⋊C₈

—

127

C₄⋊C₈

—

178

—

128

C₄⋊C₈

—

178

—

129

C₄⋊C₈

—

178

—

130

#97

—

178

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₄×C₈

—

178

—

134

C₂×Q₈

—

178

—

135

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

136

C₂²×C₄

#13083574

yes

—

137

M₁₆

—

138

M₁₆

—

139

M₁₆

—

712

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

356

—

146

C₂×C₈

—

356

—

147

C₂×C₈

—

178

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

178

—

150

C₄⋊C₄

—

178

—

151

C₂²⋊C₄

—

178

—

152

C₄²

—

178

—

153

C₄²

D₄×D₈₉

yes

characteristic

154

C₄²

D₄×D₈₉

yes

—

155

C₄²

Q₈×D₈₉

yes

characteristic

156

C₂³

#15667969

yes

characteristic

157

Q₈

—

356

—

158

Q₈

—

356

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

178

—

164

C₂×C₄

C₂²⋊C₄×D₈₉

yes

characteristic

165

C₂×C₄

C₄⋊C₄×D₈₉

yes

characteristic

166

C₂×C₄

#15667985

yes

—

167

C₂×C₄

#15667990

yes

—

168

C₈

—

169

C₈

—

170

C₈

—

171

C₈

—

178

—

172

C₈

—

178

—

173

C₈

—

712

—

174

C₂²

—

175

C₂²

—

176

C₂²

#19151457

yes

characteristic

177

C₄

—

178

C₄

—

179

C₄

—

356

—

180

C₄

#101×D₈₉

yes

characteristic

181

C₄

#19151579

yes

characteristic

182

C₄

#19151860

yes

—

183

C₄

#19151864

yes

—

184

C₂

—

185

C₂

#26020247

yes

characteristic

186

C₂

#26020310

yes

—

	subgroup	G/H
center	C₂²	#19151457
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1309	C₂
socle	C₂²×C₈₉	#380
prime radical	C₂³×C₈₉	#117
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1309	D₈₉
hypocenter	C₈₉	#8637
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#19151457

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1309

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
99. C₈₉	#8637	semidirect

H ≅ G/N

type

99. C₈₉

#8637

semidirect

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

subgroup	index
#26029182	2
#26019007	2
#26018989	2
#26018165	2
C₈₉×#1309	2
#8637	89

subgroup

index

C₈₉×#1309

Subgroups — #36447449

Conjugacy classes of subgroups

Complements

Maximal subgroups