Group #20247677 — subgroups

Subgroups — #20247677

Order 6016.

512 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13093983	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#15689063	C₂	1	2	yes	maximal, complemented
4	#15689055	C₂	1	2	yes	maximal, complemented
5	#15689008	C₂	1	4	yes	maximal, complemented
6	#15688998	C₂	1	2	yes	maximal
7	#15688984	C₂	1	2	yes	maximal
8	C₄₇×#381	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
11	#13093983	—	2	4	no	—
12	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
13	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇⋊C₄	—	2	4	no	—
16	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
19	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
20	C₄₇⋊#95	C₂²	1	4	yes	—
21	C₄₇⋊#95	C₂²	1	4	yes	—
22	C₄₇⋊#95	C₂²	1	4	yes	—
23	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
25	#95×C₄₇	C₂²	1	2	yes	—
26	#95×C₄₇	C₂²	1	2	yes	—
27	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₄₇	—	2	4	no	—
29	C₂²×C₄×C₄₇	D₄	1	4	yes	—
30	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
31	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
33	C₂²×Dic₄₇	—	2	2	no	—
34	C₂²×Dic₄₇	—	2	4	no	—
35	C₂²×Dic₄₇	—	2	2	no	—
36	C₂²×Dic₄₇	—	2	4	no	—
37	C₂²×Dic₄₇	C₂³	1	2	yes	—
38	C₂²×Dic₄₇	C₂³	1	2	yes	—
39	C₂²×Dic₄₇	C₂³	1	2	yes	—
40	C₂²×Dic₄₇	C₂³	1	2	yes	—
41	C₂²⋊C₄×C₄₇	—	2	4	no	—
42	C₂²⋊Dic₄₇	—	2	4	no	—
43	C₄⋊Dic₄₇	—	2	2	no	—
44	C₄⋊Dic₄₇	—	2	2	no	—
45	C₄⋊Dic₄₇	—	2	8	no	—
46	Dic₄₇⋊C₄	—	2	4	no	—
47	Dic₄₇⋊C₄	—	2	4	no	—
48	C₄×Dic₄₇	—	2	4	no	—
49	C₂³×C₄₇	—	2	2	no	—
50	C₂³×C₄₇	—	2	2	no	—
51	C₂³×C₄₇	C₂×D₄	1	2	yes	—
52	C₂³×C₄₇	#41	1	4	yes	—
53	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
54	C₂×C₄×C₄₇	—	2	8	no	—
55	C₂×C₄×C₄₇	—	2	2	no	—
56	C₂×C₄×C₄₇	—	2	2	no	—
57	C₂×C₄×C₄₇	—	2	4	no	—
58	C₂×C₄×C₄₇	—	2	4	no	—
59	C₂×C₄×C₄₇	—	2	4	no	—
60	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
62	C₂×Dic₄₇	—	2	8	no	—
63	C₂×Dic₄₇	—	2	2	no	—
64	C₂×Dic₄₇	—	2	2	no	—
65	C₂×Dic₄₇	—	2	2	no	—
66	C₂×Dic₄₇	—	2	2	no	—
67	C₂×Dic₄₇	—	2	2	no	—
68	C₂×Dic₄₇	—	2	4	no	—
69	C₂×Dic₄₇	—	2	4	no	—
70	C₂×Dic₄₇	—	2	4	no	—
71	C₂×Dic₄₇	—	4	4	no	—
72	C₂×Dic₄₇	#41	1	4	yes	—
73	C₂²×C₄₇	—	2	2	no	—
74	C₂²×C₄₇	—	2	2	no	—
75	C₂²×C₄₇	—	2	8	no	—
76	C₂²×C₄₇	#123	1	4	yes	—
77	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
78	C₂²×C₄₇	C₂×#41	1	2	yes	—
79	C₂²×C₄₇	C₂×#41	1	2	yes	—
80	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
81	C₄×C₄₇	—	2	2	no	—
82	C₄×C₄₇	—	2	2	no	—
83	C₄×C₄₇	—	4	4	no	—
84	Dic₄₇	—	2	4	no	—
85	Dic₄₇	—	4	2	no	—
86	Dic₄₇	—	4	2	no	—
87	Dic₄₇	—	4	2	no	—
88	#2484	—	47	1	no	maximal, Sylow
89	C₂×C₄₇	—	2	4	no	—
90	C₂×C₄₇	C₂×#123	1	1	yes	characteristic
91	C₂×C₄₇	#525	1	1	yes	characteristic
92	C₂×C₄₇	#536	1	1	yes	characteristic
93	C₂×C₄₇	#552	1	4	yes	—
94	C₂×#117	—	47	1	no	—
95	C₂²×C₄⋊C₄	—	47	1	no	—
96	#400	—	47	2	no	—
97	#398	—	47	2	no	—
98	#387	—	47	4	no	—
99	#385	—	47	2	no	—
100	#381	—	47	2	no	—
101	#381	D₄₇	1	1	yes	characteristic
102	C₄₇	#2484	1	1	yes	characteristic, complemented, Sylow
103	C₂³×C₄	—	47	1	no	—
104	C₂³×C₄	—	47	1	no	—
105	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
106	#117	—	94	4	no	—
107	C₂×C₄⋊C₄	—	47	2	no	—
108	C₂×C₄⋊C₄	—	47	2	no	—
109	C₂×C₄⋊C₄	—	47	1	no	—
110	C₂×C₄⋊C₄	—	47	1	no	—
111	C₂×C₄⋊C₄	—	47	4	no	—
112	C₂×C₄⋊C₄	—	94	4	no	—
113	C₂×C₂²⋊C₄	—	47	2	no	—
114	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
115	C₂×C₄²	—	47	2	no	—
116	#95	—	47	4	no	—
117	#95	—	47	4	no	—
118	#95	—	47	4	no	—
119	#95	C₂×D₄₇	1	2	yes	—
120	#95	C₂×D₄₇	1	2	yes	—
121	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
122	C₂²×C₄	—	2	4	no	—
123	C₂²×C₄	—	47	2	no	—
124	C₂²×C₄	—	47	2	no	—
125	C₂²×C₄	—	47	2	no	—
126	C₂²×C₄	—	47	2	no	—
127	C₂²×C₄	—	94	4	no	—
128	C₂²×C₄	—	94	2	no	—
129	C₂²×C₄	—	94	2	no	—
130	C₂²×C₄	—	94	4	no	—
131	C₂²×C₄	D₁₈₈	1	4	yes	—
132	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
133	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
135	C₄⋊C₄	—	94	8	no	—
136	C₄⋊C₄	—	94	4	no	—
137	C₄⋊C₄	—	94	4	no	—
138	C₄⋊C₄	—	94	2	no	—
139	C₄⋊C₄	—	94	2	no	—
140	C₂²⋊C₄	—	2	4	no	—
141	C₂²⋊C₄	—	94	4	no	—
142	C₄²	—	94	4	no	—
143	C₂³	—	2	2	no	—
144	C₂³	—	2	2	no	—
145	C₂³	C₂×D₁₈₈	1	2	yes	—
146	C₂³	#10625352	1	4	yes	—
147	C₂³	C₂³×D₄₇	1	1	yes	characteristic
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	47	4	no	—
155	C₂×C₄	—	94	8	no	—
156	C₂×C₄	—	94	2	no	—
157	C₂×C₄	—	94	2	no	—
158	C₂×C₄	—	94	2	no	—
159	C₂×C₄	—	94	2	no	—
160	C₂×C₄	—	94	2	no	—
161	C₂×C₄	—	94	4	no	—
162	C₂×C₄	—	94	4	no	—
163	C₂×C₄	—	94	4	no	—
164	C₂×C₄	—	188	4	no	—
165	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
166	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
167	C₂²	—	2	8	no	—
168	C₂²	—	2	2	no	—
169	C₂²	—	2	2	no	—
170	C₂²	#13094008	1	4	yes	—
171	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
172	C₂²	#41×D₄₇	1	2	yes	—
173	C₂²	C₂×#10625352	1	2	yes	—
174	C₂²	#13094071	1	2	yes	—
175	C₄	—	2	2	no	—
176	C₄	—	2	2	no	—
177	C₄	—	4	4	no	—
178	C₄	—	94	4	no	—
179	C₄	—	188	2	no	—
180	C₄	—	188	2	no	—
181	C₄	—	188	2	no	—
182	C₂	—	2	4	no	—
183	C₂	C₂×#13094008	1	1	yes	characteristic
184	C₂	#15689635	1	1	yes	characteristic
185	C₂	#15689699	1	1	yes	characteristic
186	C₂	#15689810	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093983

C₂

yes

maximal, characteristic

C₂²×Dic₄₇⋊C₄

C₂

yes

maximal, characteristic

#15689063

C₂

yes

maximal, complemented

#15689055

C₂

yes

maximal, complemented

#15689008

C₂

yes

maximal, complemented

#15688998

C₂

yes

maximal

#15688984

C₂

yes

maximal

C₄₇×#381

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

#13093983

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2484

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×#117

—

C₂²×C₄⋊C₄

—

—

—

—

—

100

#381

—

101

#381

D₄₇

yes

characteristic

102

C₄₇

#2484

yes

characteristic, complemented, Sylow

103

C₂³×C₄

—

104

C₂³×C₄

—

105

C₂³×C₄

C₂×D₄₇

yes

characteristic

106

#117

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₂²⋊C₄

—

114

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

115

C₂×C₄²

—

116

#95

—

117

#95

—

118

#95

—

119

#95

C₂×D₄₇

yes

—

120

#95

C₂×D₄₇

yes

—

121

C₂⁴

C₂²×D₄₇

yes

characteristic

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

D₁₈₈

yes

—

132

C₂²×C₄

C₂²×D₄₇

yes

—

133

C₂²×C₄

C₂²×D₄₇

yes

characteristic

134

C₂²×C₄

C₂²×D₄₇

yes

characteristic

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₂²⋊C₄

—

141

C₂²⋊C₄

—

142

C₄²

—

143

C₂³

—

144

C₂³

—

145

C₂³

C₂×D₁₈₈

yes

—

146

C₂³

#10625352

yes

—

147

C₂³

C₂³×D₄₇

yes

characteristic

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

188

—

165

C₂×C₄

C₂×D₁₈₈

yes

—

166

C₂×C₄

C₂×D₁₈₈

yes

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

#13094008

yes

—

171

C₂²

C₂²×D₁₈₈

yes

characteristic

172

C₂²

#41×D₄₇

yes

—

173

C₂²

C₂×#10625352

yes

—

174

C₂²

#13094071

yes

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

188

—

180

C₄

—

188

—

181

C₄

—

188

—

182

C₂

—

183

C₂

C₂×#13094008

yes

characteristic

184

C₂

#15689635

yes

characteristic

185

C₂

#15689699

yes

characteristic

186

C₂

#15689810

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#381	C₂
hypercenter	#381	D₄₇
hypocenter	C₄₇	#2484
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#381

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
3. #15689063	C₂	semidirect
4. #15689055	C₂	semidirect
5. #15689008	C₂	semidirect
102. C₄₇	#2484	semidirect

H ≅ G/N

type

3. #15689063

C₂

semidirect

4. #15689055

C₂

semidirect

5. #15689008

C₂

semidirect

102. C₄₇

#2484

semidirect

Subgroups — #20247677

Conjugacy classes of subgroups

Complements