Group #36562806 — subgroups

Subgroups — #36562806

Order 22784.

1350 conjugacy classes of subgroups; only the 367 normal subgroups are shown.

normal subgroups only

This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 367 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×#19151663	C₂	1	6	yes	maximal, complemented
2	C₄×#15668009	C₂	1	1	yes	maximal, characteristic
3	#26021045	C₂	1	6	yes	maximal, complemented
4	C₄²×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₈₉	C₂²	1	4	yes	—
7	C₂×#15668009	C₄	1	1	yes	characteristic
8	C₂×C₄×D₃₅₆	C₂²	1	6	yes	—
9	#19151663	—	2	24	no	—
10	C₂×#15667924	C₂²	1	12	yes	—
11	C₂×C₄×#10623494	C₂²	1	3	yes	—
12	C₂×C₄×#10623494	C₂²	1	3	yes	—
13	#19151500	C₄	1	6	yes	—
14	#19151468	C₄	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₈₉	C₂²	1	6	yes	—
16	C₄³×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×D₃₅₆	C₂×C₄	1	6	yes	—
18	C₂²×C₄×D₈₉	C₂³	1	4	yes	—
19	C₂²×#10623494	C₂³	1	3	yes	—
20	C₂²×#10623494	C₂³	1	1	yes	characteristic
21	C₂×C₈×D₈₉	—	2	24	no	—
22	#15668009	C₈	1	8	yes	complemented
23	C₄×D₃₅₆	—	2	12	no	—
24	C₄×D₃₅₆	—	2	12	no	—
25	C₂×C₄⋊Dic₈₉	C₂×C₄	1	6	yes	—
26	C₂×#13083551	C₂×C₄	1	12	yes	—
27	#15667924	—	2	24	no	—
28	C₄×#10623494	—	2	6	no	—
29	C₄×#10623494	D₄	1	12	yes	complemented
30	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
31	C₂×C₄²×C₈₉	C₂×C₄	1	3	yes	—
32	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
34	C₄⋊C₈×C₈₉	—	2	12	no	—
35	C₂³×D₈₉	C₂²×C₄	1	4	yes	—
36	C₂×D₃₅₆	—	2	12	no	—
37	C₂×D₃₅₆	—	2	12	no	—
38	C₂×D₃₅₆	C₂×C₈	1	24	yes	complemented
39	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
40	C₂×C₄×D₈₉	—	2	12	no	—
41	C₂×C₄×D₈₉	—	2	12	no	—
42	C₂×#10623494	—	2	6	no	—
43	C₂×#10623494	C₂×D₄	1	6	yes	—
44	C₂×#10623494	C₂×D₄	1	6	yes	—
45	C₈×D₈₉	—	4	16	no	—
46	C₄⋊Dic₈₉	—	2	12	no	—
47	#13083551	—	2	24	no	—
48	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
49	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
50	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
51	C₂×C₈×C₈₉	—	2	12	no	—
52	C₄²×C₈₉	—	2	6	no	—
53	C₄²×C₈₉	C₂×C₈	1	4	yes	complemented
54	C₄²×C₈₉	C₂×D₄	1	6	yes	—
55	C₄²×C₈₉	#41	1	6	yes	—
56	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
57	C₂²×D₈₉	—	2	12	no	—
58	C₂²×D₈₉	—	2	12	no	—
59	C₂²×D₈₉	C₂²×C₈	1	8	yes	—
60	C₂×C₄×C₈₉	—	2	6	no	—
61	C₂×C₄×C₈₉	C₄×D₄	1	6	yes	—
62	C₂×C₄×C₈₉	C₄×D₄	1	6	yes	—
63	C₂×C₄×C₈₉	C₂²×C₈	1	6	yes	—
64	C₂×C₄×C₈₉	#131	1	6	yes	—
65	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
66	C₂×C₄×C₈₉	C₂×#41	1	3	yes	—
67	C₂×Dic₈₉	—	2	12	no	—
68	D₃₅₆	—	2	48	no	—
69	C₄×D₈₉	—	4	4	no	—
70	C₄×D₈₉	—	4	12	no	—
71	C₈×C₈₉	—	4	4	no	—
72	#10623494	—	2	6	no	—
73	#10623494	#127	1	4	yes	complemented
74	C₂²×C₈₉	C₂×C₄×D₄	1	3	yes	—
75	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
76	C₂²×C₈₉	C₂×#131	1	3	yes	—
77	C₂×D₈₉	—	2	24	no	—
78	C₂×D₈₉	—	4	4	no	—
79	C₂×D₈₉	—	4	12	no	—
80	C₄×C₈₉	—	2	6	no	—
81	C₄×C₈₉	C₈×D₄	1	12	yes	complemented
82	C₄×C₈₉	C₂×#127	1	1	yes	characteristic
83	C₄×C₈₉	#532	1	3	yes	—
84	Dic₈₉	—	4	4	no	—
85	C₈×#127	—	89	1	no	maximal, Sylow
86	C₂×C₈₉	C₄×#127	1	1	yes	characteristic
87	C₂×C₈₉	C₂×C₈×D₄	1	3	yes	—
88	C₂×C₈₉	#2931	1	3	yes	—
89	D₈₉	—	4	8	no	—
90	C₂×C₈×D₄	—	89	6	no	—
91	C₄×#127	—	89	1	no	—
92	#1954	—	89	6	no	—
93	#1842	D₈₉	1	1	yes	characteristic, complemented
94	C₄²×C₈	—	89	1	no	—
95	C₈₉	C₈×#127	1	1	yes	characteristic, complemented, Sylow
96	C₂³×C₈	—	89	4	no	—
97	C₂×#127	—	89	1	no	—
98	C₂×C₄×D₄	—	89	6	no	—
99	C₈×D₄	—	178	24	no	—
100	C₂×C₄⋊C₈	C₂×D₈₉	1	6	yes	—
101	C₂×C₂²⋊C₈	—	89	12	no	—
102	C₂×C₄×C₈	—	89	3	no	—
103	C₂×C₄×C₈	—	89	3	no	—
104	#390	—	89	6	no	—
105	#384	—	89	1	no	—
106	C₄³	C₂×D₈₉	1	1	yes	characteristic
107	C₂²×D₄	—	89	6	no	—
108	C₂³×C₄	—	89	4	no	—
109	C₂²×C₈	—	89	1	no	—
110	C₂²×C₈	—	89	3	no	—
111	C₂²×C₈	—	178	24	no	—
112	C₂²×C₈	C₂²×D₈₉	1	4	yes	—
113	#127	—	89	8	no	—
114	C₄×D₄	—	178	12	no	—
115	C₄×D₄	—	178	12	no	—
116	C₂×C₄⋊C₄	—	89	6	no	—
117	C₂×C₂²⋊C₄	—	89	12	no	—
118	C₂×C₄²	C₄×D₈₉	1	3	yes	—
119	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
120	C₂×C₄²	C₂²×D₈₉	1	3	yes	—
121	C₄⋊C₈	—	2	12	no	—
122	C₂²⋊C₈	—	178	24	no	—
123	C₄×C₈	—	89	12	no	—
124	C₄×C₈	—	178	6	no	—
125	C₂⁴	—	89	4	no	—
126	C₂×D₄	—	89	24	no	—
127	C₂×D₄	—	178	12	no	—
128	C₂×D₄	—	178	12	no	—
129	C₂²×C₄	—	89	4	no	—
130	C₂²×C₄	—	178	12	no	—
131	C₂²×C₄	—	178	12	no	—
132	C₂²×C₄	C₂×C₄×D₈₉	1	3	yes	—
133	C₂²×C₄	C₂×C₄×D₈₉	1	3	yes	—
134	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
135	C₂×C₈	—	2	12	no	—
136	C₂×C₈	—	89	6	no	—
137	C₂×C₈	—	89	6	no	—
138	C₂×C₈	—	356	16	no	—
139	C₂×C₈	—	178	6	no	—
140	C₄⋊C₄	—	178	12	no	—
141	C₂²⋊C₄	—	178	24	no	—
142	C₄²	—	2	6	no	—
143	C₄²	C₈×D₈₉	1	4	yes	complemented
144	C₄²	D₄×D₈₉	1	6	yes	—
145	C₄²	#13083575	1	6	yes	—
146	C₂³	—	89	8	no	—
147	C₂³	—	178	12	no	—
148	C₂³	—	178	12	no	—
149	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
150	D₄	—	178	48	no	—
151	C₂×C₄	—	2	6	no	—
152	C₂×C₄	—	356	4	no	—
153	C₂×C₄	—	356	12	no	—
154	C₂×C₄	—	178	12	no	—
155	C₂×C₄	#15667974	1	6	yes	—
156	C₂×C₄	#15667974	1	6	yes	—
157	C₂×C₄	C₂×C₈×D₈₉	1	6	yes	—
158	C₂×C₄	#15668020	1	6	yes	—
159	C₂×C₄	C₂×D₄×D₈₉	1	3	yes	—
160	C₂×C₄	C₂×#13083575	1	3	yes	—
161	C₈	—	4	4	no	—
162	C₈	—	89	4	no	—
163	C₈	—	178	6	no	—
164	C₂²	—	356	4	no	—
165	C₂²	—	356	12	no	—
166	C₂²	—	178	24	no	—
167	C₂²	C₂×#15667974	1	3	yes	—
168	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
169	C₂²	C₂×#15668020	1	3	yes	—
170	C₄	—	2	6	no	—
171	C₄	—	356	4	no	—
172	C₄	#19151663	1	12	yes	complemented
173	C₄	#127×D₈₉	1	1	yes	characteristic
174	C₄	#19152149	1	3	yes	—
175	C₂	—	356	8	no	—
176	C₂	#26022814	1	1	yes	characteristic
177	C₂	C₂×#19151663	1	3	yes	—
178	C₂	#26028963	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151663

C₂

yes

maximal, complemented

C₄×#15668009

C₂

yes

maximal, characteristic

#26021045

C₂

yes

maximal, complemented

C₄²×#10623494

C₂

yes

maximal, characteristic, complemented

C₈₉×#1842

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₈₉

C₂²

yes

—

C₂×#15668009

C₄

yes

characteristic

C₂×C₄×D₃₅₆

C₂²

yes

—

#19151663

—

C₂×#15667924

C₂²

yes

—

C₂×C₄×#10623494

C₂²

yes

—

C₂×C₄×#10623494

C₂²

yes

—

#19151500

C₄

yes

—

#19151468

C₄

yes

characteristic

C₂×C₄⋊C₈×C₈₉

C₂²

yes

—

C₄³×C₈₉

C₂²

yes

characteristic

C₂²×D₃₅₆

C₂×C₄

yes

—

C₂²×C₄×D₈₉

C₂³

yes

—

C₂²×#10623494

C₂³

yes

—

C₂²×#10623494

C₂³

yes

characteristic

C₂×C₈×D₈₉

—

#15668009

C₈

yes

complemented

C₄×D₃₅₆

—

C₄×D₃₅₆

—

C₂×C₄⋊Dic₈₉

C₂×C₄

yes

—

C₂×#13083551

C₂×C₄

yes

—

#15667924

—

C₄×#10623494

—

C₄×#10623494

D₄

yes

complemented

C₂²×C₈×C₈₉

C₂³

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₈₉

C₂³

yes

—

C₄⋊C₈×C₈₉

—

C₂³×D₈₉

C₂²×C₄

yes

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

C₂×C₈

yes

complemented

C₂²×Dic₈₉

C₂²×C₄

yes

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×#10623494

—

C₂×#10623494

C₂×D₄

yes

—

C₂×#10623494

C₂×D₄

yes

—

C₈×D₈₉

—

C₄⋊Dic₈₉

—

#13083551

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂²×C₄×C₈₉

C₂⁴

yes

characteristic

C₂×C₈×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×C₈

yes

complemented

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂³×C₄

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

C₂²×C₈

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₂²×C₈

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

C₂²×D₄

yes

—

C₂×C₄×C₈₉

C₂×#41

yes

—

C₂×Dic₈₉

—

D₃₅₆

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

—

yes

C₂²×C₈₉

C₂×C₄×D₄

yes

—

C₂²×C₈₉

C₂³×C₈

yes

characteristic

C₂²×C₈₉

C₂×#131

yes

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

C₄×C₈₉

C₈×D₄

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

C₂×C₈×D₄

yes

—

C₂×C₈₉

#2931

yes

—

D₈₉

—

C₂×C₈×D₄

—

C₄×#127

—

#1954

—

#1842

D₈₉

yes

characteristic, complemented

C₄²×C₈

—

C₈₉

C₈×#127

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂×#127

—

C₂×C₄×D₄

—

C₈×D₄

—

178

—

100

C₂×C₄⋊C₈

C₂×D₈₉

yes

—

101

C₂×C₂²⋊C₈

—

102

C₂×C₄×C₈

—

103

C₂×C₄×C₈

—

104

#390

—

105

#384

—

106

C₄³

C₂×D₈₉

yes

characteristic

107

C₂²×D₄

—

108

C₂³×C₄

—

109

C₂²×C₈

—

110

C₂²×C₈

—

111

C₂²×C₈

—

178

—

112

C₂²×C₈

C₂²×D₈₉

yes

—

113

#127

—

114

C₄×D₄

—

178

—

115

C₄×D₄

—

178

—

116

C₂×C₄⋊C₄

—

117

C₂×C₂²⋊C₄

—

118

C₂×C₄²

C₄×D₈₉

yes

—

119

C₂×C₄²

C₄×D₈₉

yes

characteristic

120

C₂×C₄²

C₂²×D₈₉

yes

—

121

C₄⋊C₈

—

122

C₂²⋊C₈

—

178

—

123

C₄×C₈

—

124

C₄×C₈

—

178

—

125

C₂⁴

—

126

C₂×D₄

—

127

C₂×D₄

—

178

—

128

C₂×D₄

—

178

—

129

C₂²×C₄

—

130

C₂²×C₄

—

178

—

131

C₂²×C₄

—

178

—

132

C₂²×C₄

C₂×C₄×D₈₉

yes

—

133

C₂²×C₄

C₂×C₄×D₈₉

yes

—

134

C₂²×C₄

C₂³×D₈₉

yes

characteristic

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

356

—

139

C₂×C₈

—

178

—

140

C₄⋊C₄

—

178

—

141

C₂²⋊C₄

—

178

—

142

C₄²

—

143

C₄²

C₈×D₈₉

yes

complemented

144

C₄²

D₄×D₈₉

yes

—

145

C₄²

#13083575

yes

—

146

C₂³

—

147

C₂³

—

178

—

148

C₂³

—

178

—

149

C₂³

C₂²×C₄×D₈₉

yes

characteristic

150

D₄

—

178

—

151

C₂×C₄

—

152

C₂×C₄

—

356

—

153

C₂×C₄

—

356

—

154

C₂×C₄

—

178

—

155

C₂×C₄

#15667974

yes

—

156

C₂×C₄

#15667974

yes

—

157

C₂×C₄

C₂×C₈×D₈₉

yes

—

158

C₂×C₄

#15668020

yes

—

159

C₂×C₄

C₂×D₄×D₈₉

yes

—

160

C₂×C₄

C₂×#13083575

yes

—

161

C₈

—

162

C₈

—

163

C₈

—

178

—

164

C₂²

—

356

—

165

C₂²

—

356

—

166

C₂²

—

178

—

167

C₂²

C₂×#15667974

yes

—

168

C₂²

C₂²×C₈×D₈₉

yes

characteristic

169

C₂²

C₂×#15668020

yes

—

170

C₄

—

171

C₄

—

356

—

172

C₄

#19151663

yes

complemented

173

C₄

#127×D₈₉

yes

characteristic

174

C₄

#19152149

yes

—

175

C₂

—

356

—

176

C₂

#26022814

yes

characteristic

177

C₂

C₂×#19151663

yes

—

178

C₂

#26028963

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#1842	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂×#15668009	C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1842	D₈₉
hypocenter	C₈₉	C₈×#127
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₈₉

commutator

C₂²×C₈₉

C₂³×C₈

Fitting

C₈₉×#1842

C₂

socle

C₂³×C₈₉

C₂³×C₄

prime radical

C₂×#15668009

C₄

cosocle

C₂²×C₄×C₈₉

C₂⁴

D₈₉

C₈₉

G ▷ C₂²×C₈₉ ▷ C₈₉

C₁ ◁ C₂²×C₄ ◁ #1842

N	H ≅ G/N	type
1. C₂×#19151663	C₂	semidirect
3. #26021045	C₂	semidirect
4. C₄²×#10623494	C₂	semidirect
5. C₈₉×#1842	C₂	semidirect
22. #15668009	C₈	semidirect
29. C₄×#10623494	D₄	semidirect
38. C₂×D₃₅₆	C₂×C₈	semidirect
53. C₄²×C₈₉	C₂×C₈	semidirect
73. #10623494	#127	semidirect
81. C₄×C₈₉	C₈×D₄	semidirect
93. #1842	D₈₉	semidirect
95. C₈₉	C₈×#127	semidirect
143. C₄²	C₈×D₈₉	semidirect
172. C₄	#19151663	semidirect

H ≅ G/N

type

1. C₂×#19151663

C₂

semidirect

3. #26021045

C₂

semidirect

4. C₄²×#10623494

C₂

semidirect

5. C₈₉×#1842

C₂

semidirect

22. #15668009

C₈

semidirect

29. C₄×#10623494

D₄

semidirect

38. C₂×D₃₅₆

C₂×C₈

semidirect

53. C₄²×C₈₉

C₂×C₈

semidirect

73. #10623494

#127

semidirect

81. C₄×C₈₉

C₈×D₄

semidirect

93. #1842

D₈₉

semidirect

95. C₈₉

C₈×#127

semidirect

143. C₄²

C₈×D₈₉

semidirect

172. C₄

#19151663

semidirect

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

subgroup	index
C₂×#19151663	2
C₄×#15668009	2
#26021045	2
C₄²×#10623494	2
C₈₉×#1842	2
C₈×#127	89

subgroup

index

C₈₉×#1842

Subgroups — #36562806

Conjugacy classes of subgroups

Complements

Maximal subgroups