Group #36448835 — subgroups

Subgroups — #36448835

Order 22784.

336 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 95 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	#26029358	C₂	1	1	yes	maximal, characteristic
2	#26019017	C₂	1	2	yes	maximal
3	#26018847	C₂	1	1	yes	maximal, characteristic
4	#26018145	C₂	1	2	yes	maximal
5	C₈₉×#1995	C₂	1	1	yes	maximal, characteristic
6	#19151729	—	2	2	no	—
7	#19151729	—	2	2	no	—
8	#19151659	—	2	2	no	—
9	#19151655	C₂²	1	2	yes	—
10	C₄×#13083558	C₂²	1	2	yes	—
11	#19151350	—	2	2	no	—
12	#19151348	—	2	2	no	—
13	#19151340	C₄	1	1	yes	characteristic, complemented
14	#19151340	C₄	1	2	yes	complemented
15	#19151340	C₄	1	1	yes	characteristic, complemented
16	#533×C₈₉	C₂²	1	1	yes	characteristic
17	#423×C₈₉	C₂²	1	1	yes	characteristic
18	#376×C₈₉	C₂²	1	1	yes	characteristic
19	#339×C₈₉	—	2	2	no	—
20	C₂×#13083558	—	2	2	no	—
21	C₄⋊#10623494	—	2	2	no	—
22	C₄⋊#10623494	—	2	2	no	—
23	C₄⋊#10623494	D₄	1	2	yes	—
24	C₄⋊#10623494	D₄	1	2	yes	—
25	C₂²⋊#10623494	—	2	2	no	—
26	#15667923	—	2	2	no	—
27	#15667923	—	2	2	no	—
28	#15667923	C₂×C₄	1	2	yes	—
29	#15667923	C₂×C₄	1	2	yes	—
30	C₄×#10623494	—	2	2	no	—
31	C₄×#10623494	—	2	2	no	—
32	C₂×M₁₆×C₈₉	—	2	1	no	—
33	C₄⋊Q₈×C₈₉	Q₈	1	2	yes	—
34	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
35	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
36	C₂²⋊Q₈×C₈₉	—	2	2	no	—
37	C₄×Q₈×C₈₉	—	2	2	no	—
38	#117×C₈₉	D₄	1	2	yes	—
39	C₂×C₄²×C₈₉	—	2	1	no	—
40	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₈₉	—	2	2	no	—
42	#95×C₈₉	—	2	2	no	—
43	#13083558	—	4	4	no	—
44	C₂×#10623494	—	2	2	no	—
45	C₂×#10623494	—	2	2	no	—
46	C₂×#10623494	—	2	2	no	—
47	C₂×#10623494	—	2	2	no	—
48	C₂×Q₈×C₈₉	—	2	2	no	—
49	C₂²×C₄×C₈₉	—	4	1	no	—
50	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₈₉	#41	1	2	yes	—
52	M₁₆×C₈₉	—	4	2	no	—
53	C₂×C₈×C₈₉	—	4	1	no	—
54	C₄⋊C₄×C₈₉	—	2	2	no	—
55	C₄⋊C₄×C₈₉	—	2	2	no	—
56	C₄⋊C₄×C₈₉	—	2	2	no	—
57	C₄⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
58	C₄⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
59	C₂²⋊C₄×C₈₉	—	2	2	no	—
60	C₄²×C₈₉	—	2	2	no	—
61	C₄²×C₈₉	—	2	2	no	—
62	C₄²×C₈₉	—	4	1	no	—
63	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₈₉	C₂×D₄	1	2	yes	—
65	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
66	C₂³×C₈₉	#123	1	1	yes	characteristic
67	Q₈×C₈₉	—	8	2	no	—
68	C₂×C₄×C₈₉	—	2	1	no	—
69	C₂×C₄×C₈₉	—	2	1	no	—
70	C₂×C₄×C₈₉	—	2	2	no	—
71	C₂×C₄×C₈₉	—	2	2	no	—
72	C₂×C₄×C₈₉	—	4	2	no	—
73	C₂×C₄×C₈₉	—	4	2	no	—
74	C₂×C₄×C₈₉	—	8	2	no	—
75	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
77	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
78	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
79	C₈×C₈₉	—	8	1	no	—
80	#10623494	—	2	4	no	—
81	#10623494	—	4	2	no	—
82	#10623494	—	4	2	no	—
83	#10623494	—	4	2	no	—
84	C₂²×C₈₉	—	2	1	no	—
85	C₂²×C₈₉	—	2	2	no	—
86	C₂²×C₈₉	#385	1	1	yes	characteristic
87	C₄×C₈₉	—	2	1	no	—
88	C₄×C₈₉	—	2	2	no	—
89	C₄×C₈₉	—	2	2	no	—
90	C₄×C₈₉	—	4	2	no	—
91	C₄×C₈₉	—	4	2	no	—
92	C₄×C₈₉	—	8	2	no	—
93	C₄×C₈₉	#454	1	1	yes	characteristic
94	C₄×C₈₉	#456	1	1	yes	characteristic
95	#8919	—	89	1	no	maximal, Sylow
96	C₂×C₈₉	—	4	1	no	—
97	C₂×C₈₉	#1857	1	1	yes	characteristic
98	C₂×C₈₉	#1861	1	2	yes	—
99	#2987	—	89	1	no	—
100	#1995	D₈₉	1	1	yes	characteristic
101	#1569	—	89	2	no	—
102	#1526	—	89	1	no	—
103	#1300	—	89	2	no	—
104	C₈₉	#8919	1	1	yes	characteristic, complemented, Sylow
105	#533	C₂×D₈₉	1	1	yes	characteristic
106	#446	—	178	2	no	—
107	#446	—	178	2	no	—
108	#433	—	178	2	no	—
109	#432	—	89	2	no	—
110	#423	C₂×D₈₉	1	1	yes	characteristic
111	C₄×M₁₆	—	89	2	no	—
112	#376	C₂×D₈₉	1	1	yes	characteristic
113	#339	—	2	2	no	—
114	#335	—	178	2	no	—
115	#334	—	178	2	no	—
116	#330	—	89	1	no	—
117	#330	—	89	2	no	—
118	#330	—	89	1	no	—
119	C₂×M₁₆	—	2	1	no	—
120	C₂×M₁₆	—	178	2	no	—
121	C₄⋊Q₈	Dic₁₇₈	1	2	yes	—
122	#125	C₄×D₈₉	1	1	yes	characteristic
123	#125	C₄×D₈₉	1	1	yes	characteristic
124	C₂²⋊Q₈	—	2	2	no	—
125	C₄×Q₈	—	2	2	no	—
126	#117	C₂²⋊D₈₉	1	2	yes	—
127	C₂×C₄²	—	2	1	no	—
128	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
129	C₄⋊C₈	—	2	2	no	—
130	C₄⋊C₈	—	89	2	no	—
131	C₄⋊C₈	—	89	2	no	—
132	C₄⋊C₈	—	178	2	no	—
133	C₄⋊C₈	—	178	2	no	—
134	C₂²⋊C₈	—	178	2	no	—
135	#97	—	89	2	no	—
136	#97	—	89	2	no	—
137	#97	—	178	2	no	—
138	#97	—	178	2	no	—
139	C₄×C₈	—	178	2	no	—
140	C₄×C₈	—	178	2	no	—
141	#95	—	2	2	no	—
142	C₂×Q₈	—	2	2	no	—
143	C₂²×C₄	—	4	1	no	—
144	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
145	C₂²×C₄	#13083573	1	2	yes	—
146	M₁₆	—	4	2	no	—
147	M₁₆	—	356	4	no	—
148	C₂×C₈	—	4	1	no	—
149	C₂×C₈	—	178	2	no	—
150	C₂×C₈	—	178	2	no	—
151	C₂×C₈	—	178	2	no	—
152	C₂×C₈	—	178	2	no	—
153	C₄⋊C₄	—	2	2	no	—
154	C₄⋊C₄	—	2	2	no	—
155	C₄⋊C₄	—	2	2	no	—
156	C₄⋊C₄	#13083553	1	2	yes	—
157	C₄⋊C₄	#13083553	1	2	yes	—
158	C₂²⋊C₄	—	2	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	4	1	no	—
162	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
163	C₄²	D₄×D₈₉	1	2	yes	—
164	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
165	C₂³	#15667993	1	1	yes	characteristic
166	Q₈	—	8	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	4	2	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	—	8	2	no	—
174	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
175	C₂×C₄	#15667972	1	2	yes	—
176	C₂×C₄	#15667980	1	1	yes	characteristic
177	C₂×C₄	#15667989	1	2	yes	—
178	C₈	—	8	1	no	—
179	C₈	—	356	2	no	—
180	C₈	—	356	2	no	—
181	C₈	—	356	2	no	—
182	C₈	—	178	4	no	—
183	C₂²	—	2	1	no	—
184	C₂²	—	2	2	no	—
185	C₂²	#19151470	1	1	yes	characteristic
186	C₄	—	2	1	no	—
187	C₄	—	2	2	no	—
188	C₄	—	2	2	no	—
189	C₄	—	4	2	no	—
190	C₄	—	4	2	no	—
191	C₄	—	8	2	no	—
192	C₄	#19151770	1	1	yes	characteristic
193	C₄	#19151780	1	1	yes	characteristic
194	C₂	—	4	1	no	—
195	C₂	#26020466	1	1	yes	characteristic
196	C₂	#26020490	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26029358

C₂

yes

maximal, characteristic

#26019017

C₂

yes

maximal

#26018847

C₂

yes

maximal, characteristic

#26018145

C₂

yes

maximal

C₈₉×#1995

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₄×#13083558

C₂²

yes

—

#19151350

—

#19151348

—

#19151340

C₄

yes

characteristic, complemented

#19151340

C₄

yes

complemented

#19151340

C₄

yes

characteristic, complemented

#533×C₈₉

C₂²

yes

characteristic

#423×C₈₉

C₂²

yes

characteristic

#376×C₈₉

C₂²

yes

characteristic

#339×C₈₉

—

—

—

—

D₄

yes

—

C₄⋊#10623494

D₄

yes

—

—

—

—

C₂×C₄

yes

—

#15667923

C₂×C₄

yes

—

C₄×#10623494

—

C₄×#10623494

—

C₂×M₁₆×C₈₉

—

C₄⋊Q₈×C₈₉

Q₈

yes

—

#125×C₈₉

C₂×C₄

yes

characteristic

#125×C₈₉

C₂×C₄

yes

characteristic

C₂²⋊Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

#117×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

#95×C₈₉

—

—

—

—

—

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

C₄⋊C₄

yes

—

C₄⋊C₄×C₈₉

C₄⋊C₄

yes

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₂³×C₈₉

#123

yes

characteristic

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

#120

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₈×C₈₉

—

—

—

—

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#385

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₂×C₈₉

—

C₂×C₈₉

#1857

yes

characteristic

C₂×C₈₉

#1861

yes

—

#2987

—

100

#1995

D₈₉

yes

characteristic

101

#1569

—

102

#1526

—

103

#1300

—

104

C₈₉

#8919

yes

characteristic, complemented, Sylow

105

#533

C₂×D₈₉

yes

characteristic

106

#446

—

178

—

107

#446

—

178

—

108

#433

—

178

—

109

#432

—

110

#423

C₂×D₈₉

yes

characteristic

111

C₄×M₁₆

—

112

#376

C₂×D₈₉

yes

characteristic

113

#339

—

114

#335

—

178

—

115

#334

—

178

—

116

#330

—

117

#330

—

118

#330

—

119

C₂×M₁₆

—

120

C₂×M₁₆

—

178

—

121

C₄⋊Q₈

Dic₁₇₈

yes

—

122

#125

C₄×D₈₉

yes

characteristic

123

#125

C₄×D₈₉

yes

characteristic

124

C₂²⋊Q₈

—

125

C₄×Q₈

—

126

#117

C₂²⋊D₈₉

yes

—

127

C₂×C₄²

—

128

C₂×C₄²

C₂²×D₈₉

yes

characteristic

129

C₄⋊C₈

—

130

C₄⋊C₈

—

131

C₄⋊C₈

—

132

C₄⋊C₈

—

178

—

133

C₄⋊C₈

—

178

—

134

C₂²⋊C₈

—

178

—

135

#97

—

136

#97

—

137

#97

—

178

—

138

#97

—

178

—

139

C₄×C₈

—

178

—

140

C₄×C₈

—

178

—

141

#95

—

142

C₂×Q₈

—

143

C₂²×C₄

—

144

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

145

C₂²×C₄

#13083573

yes

—

146

M₁₆

—

147

M₁₆

—

356

—

148

C₂×C₈

—

149

C₂×C₈

—

178

—

150

C₂×C₈

—

178

—

151

C₂×C₈

—

178

—

152

C₂×C₈

—

178

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

#13083553

yes

—

157

C₄⋊C₄

#13083553

yes

—

158

C₂²⋊C₄

—

159

C₄²

—

160

C₄²

—

161

C₄²

—

162

C₄²

C₂×C₄×D₈₉

yes

characteristic

163

C₄²

D₄×D₈₉

yes

—

164

C₄²

C₂×Dic₁₇₈

yes

characteristic

165

C₂³

#15667993

yes

characteristic

166

Q₈

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

C₂×#13083553

yes

characteristic

175

C₂×C₄

#15667972

yes

—

176

C₂×C₄

#15667980

yes

characteristic

177

C₂×C₄

#15667989

yes

—

178

C₈

—

179

C₈

—

356

—

180

C₈

—

356

—

181

C₈

—

356

—

182

C₈

—

178

—

183

C₂²

—

184

C₂²

—

185

C₂²

#19151470

yes

characteristic

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

#19151770

yes

characteristic

193

C₄

#19151780

yes

characteristic

194

C₂

—

195

C₂

#26020466

yes

characteristic

196

C₂

#26020490

yes

—

	subgroup	G/H
center	C₂×C₄	#15667980
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1995	C₂
socle	C₂²×C₈₉	#385
prime radical	C₂³×C₈₉	#123
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1995	D₈₉
hypocenter	C₈₉	#8919
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

subgroup

G/H

center

C₂×C₄

#15667980

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1995

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

N	H ≅ G/N	type
13. #19151340	C₄	semidirect
14. #19151340	C₄	semidirect
15. #19151340	C₄	semidirect
104. C₈₉	#8919	semidirect

H ≅ G/N

type

13. #19151340

C₄

semidirect

14. #19151340

C₄

semidirect

15. #19151340

C₄

semidirect

104. C₈₉

#8919

semidirect

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

subgroup	index
#26029358	2
#26019017	2
#26018847	2
#26018145	2
C₈₉×#1995	2
#8919	89

subgroup

index

C₈₉×#1995

Subgroups — #36448835

Conjugacy classes of subgroups

Complements

Maximal subgroups