Group #20241655 — subgroups

Subgroups — #20241655

Order 6016.

520 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 193 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	C₂²×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇⋊#95	C₂	1	4	yes	maximal
3	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₇	C₂²	1	2	yes	—
6	C₂³×Dic₄₇	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₇	—	2	2	no	—
8	C₂×C₄⋊Dic₄₇	—	2	2	no	—
9	C₂×C₄⋊Dic₄₇	C₄	1	4	yes	complemented
10	C₄₇⋊#95	—	2	8	no	—
11	C₄₇⋊#95	—	2	2	no	—
12	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
13	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	#95×C₄₇	—	2	2	no	—
15	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	—	2	4	no	—
17	C₂²×C₄×C₄₇	—	2	2	no	—
18	C₂²×C₄×C₄₇	—	2	2	no	—
19	C₂²×C₄×C₄₇	—	2	4	no	—
20	C₂²×C₄×C₄₇	—	2	4	no	—
21	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₄₇	D₄	1	4	yes	—
23	C₂²×C₄×C₄₇	D₄	1	2	yes	—
24	C₂²×C₄×C₄₇	D₄	1	2	yes	—
25	C₂²×Dic₄₇	—	2	4	no	—
26	C₂²×Dic₄₇	—	2	2	no	—
27	C₂²×Dic₄₇	—	2	4	no	—
28	C₂²×Dic₄₇	—	2	2	no	—
29	C₂²×Dic₄₇	—	2	2	no	—
30	C₂²×Dic₄₇	—	2	4	no	—
31	C₂²×Dic₄₇	—	2	4	no	—
32	C₂²×Dic₄₇	—	2	2	no	—
33	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
34	C₂²×Dic₄₇	Q₈	1	4	yes	—
35	C₄⋊Dic₄₇	—	2	8	no	—
36	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂³×C₄₇	C₂×D₄	1	2	yes	—
39	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
40	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
41	C₂³×C₄₇	#41	1	2	yes	—
42	C₂³×C₄₇	#41	1	4	yes	—
43	C₂³×C₄₇	#41	1	2	yes	—
44	C₂×C₄×C₄₇	—	2	4	no	—
45	C₂×C₄×C₄₇	—	2	4	no	—
46	C₂×C₄×C₄₇	—	2	4	no	—
47	C₂×C₄×C₄₇	—	2	4	no	—
48	C₂×C₄×C₄₇	—	2	8	no	—
49	C₂×C₄×C₄₇	—	4	2	no	—
50	C₂×C₄×C₄₇	—	4	2	no	—
51	C₂×C₄×C₄₇	—	4	4	no	—
52	C₂×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
53	C₂×Dic₄₇	—	2	4	no	—
54	C₂×Dic₄₇	—	2	8	no	—
55	C₂×Dic₄₇	—	2	8	no	—
56	C₂×Dic₄₇	—	2	4	no	—
57	C₂×Dic₄₇	—	4	4	no	—
58	C₂×Dic₄₇	—	4	2	no	—
59	C₂×Dic₄₇	—	4	4	no	—
60	C₂×Dic₄₇	—	4	2	no	—
61	C₂×Dic₄₇	—	4	2	no	—
62	C₂×Dic₄₇	—	4	2	no	—
63	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄₇	#117	1	2	yes	—
65	C₂²×C₄₇	C₄×D₄	1	2	yes	—
66	C₂²×C₄₇	C₄×Q₈	1	2	yes	—
67	C₂²×C₄₇	#121	1	2	yes	—
68	C₂²×C₄₇	C₂²⋊Q₈	1	4	yes	—
69	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
70	C₂²×C₄₇	#123	1	2	yes	—
71	C₂²×C₄₇	#123	1	2	yes	—
72	C₂²×C₄₇	#123	1	4	yes	—
73	C₂²×C₄₇	#124	1	1	yes	characteristic
74	C₂²×C₄₇	#124	1	1	yes	characteristic
75	C₂²×C₄₇	#125	1	4	yes	—
76	C₂²×C₄₇	#126	1	4	yes	—
77	C₂²×C₄₇	#127	1	1	yes	characteristic
78	C₂²×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
79	C₄×C₄₇	—	2	4	no	—
80	C₄×C₄₇	—	4	4	no	—
81	Dic₄₇	—	4	4	no	—
82	Dic₄₇	—	4	4	no	—
83	#1445	—	47	1	no	maximal, Sylow
84	C₂×C₄₇	#381	1	1	yes	characteristic
85	C₂×C₄₇	#387	1	4	yes	—
86	C₂×C₄₇	#390	1	1	yes	characteristic
87	C₂×C₄₇	#391	1	1	yes	characteristic
88	C₂×C₄₇	#397	1	2	yes	—
89	C₂×C₄₇	#398	1	2	yes	—
90	C₂×C₄₇	#399	1	2	yes	—
91	C₂×C₄₇	#400	1	2	yes	—
92	C₂²×C₄⋊C₄	—	47	1	no	—
93	C₂×#95	—	47	4	no	—
94	C₂×#95	—	47	1	no	—
95	C₂×#95	D₄₇	1	1	yes	characteristic
96	C₄₇	#1445	1	1	yes	characteristic, complemented, Sylow
97	C₂³×C₄	—	47	2	no	—
98	C₂³×C₄	—	47	2	no	—
99	C₂³×C₄	C₂×D₄₇	1	2	yes	—
100	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
101	C₂×C₄⋊C₄	—	47	4	no	—
102	C₂×C₄⋊C₄	—	94	2	no	—
103	C₂×C₄⋊C₄	—	94	2	no	—
104	#95	—	2	2	no	—
105	#95	—	94	8	no	—
106	#95	—	94	2	no	—
107	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
108	C₂²×C₄	—	2	4	no	—
109	C₂²×C₄	—	2	2	no	—
110	C₂²×C₄	—	2	4	no	—
111	C₂²×C₄	—	2	4	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	—	47	4	no	—
114	C₂²×C₄	—	47	4	no	—
115	C₂²×C₄	—	94	4	no	—
116	C₂²×C₄	—	94	2	no	—
117	C₂²×C₄	—	94	4	no	—
118	C₂²×C₄	—	94	2	no	—
119	C₂²×C₄	—	94	4	no	—
120	C₂²×C₄	—	94	4	no	—
121	C₂²×C₄	—	94	2	no	—
122	C₂²×C₄	—	94	2	no	—
123	C₂²×C₄	C₄×D₄₇	1	2	yes	—
124	C₂²×C₄	D₁₈₈	1	4	yes	—
125	C₂²×C₄	D₁₈₈	1	2	yes	—
126	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
127	C₄⋊C₄	—	94	8	no	—
128	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
129	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
130	C₂³	C₂×D₁₈₈	1	2	yes	—
131	C₂³	#10625350	1	2	yes	—
132	C₂³	#10625352	1	4	yes	—
133	C₂³	#10625352	1	2	yes	—
134	C₂³	Q₈×D₄₇	1	2	yes	—
135	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	8	no	—
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	4	4	no	—
144	C₂×C₄	—	94	4	no	—
145	C₂×C₄	—	94	8	no	—
146	C₂×C₄	—	94	8	no	—
147	C₂×C₄	—	94	4	no	—
148	C₂×C₄	—	188	4	no	—
149	C₂×C₄	—	188	2	no	—
150	C₂×C₄	—	188	4	no	—
151	C₂×C₄	—	188	2	no	—
152	C₂×C₄	—	188	2	no	—
153	C₂×C₄	—	188	2	no	—
154	C₂×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
155	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
156	C₂²	#13093980	1	2	yes	—
157	C₂²	C₄×D₁₈₈	1	2	yes	—
158	C₂²	#13093989	1	2	yes	—
159	C₂²	#13093998	1	2	yes	—
160	C₂²	#13094004	1	4	yes	—
161	C₂²	#13094004	1	2	yes	—
162	C₂²	#13094005	1	2	yes	—
163	C₂²	#13094008	1	2	yes	—
164	C₂²	#13094008	1	4	yes	—
165	C₂²	#13094011	1	1	yes	characteristic
166	C₂²	#13094012	1	1	yes	characteristic
167	C₂²	#13094014	1	4	yes	—
168	C₂²	#13094017	1	4	yes	—
169	C₂²	#13094021	1	1	yes	characteristic
170	C₂²	#13094022	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	4	4	no	—
173	C₄	—	188	4	no	—
174	C₄	—	188	4	no	—
175	C₂	#15688984	1	1	yes	characteristic
176	C₂	#15689008	1	4	yes	—
177	C₂	#15689025	1	1	yes	characteristic
178	C₂	#15689028	1	1	yes	characteristic
179	C₂	#15689048	1	2	yes	—
180	C₂	#15689053	1	2	yes	—
181	C₂	#15689060	1	2	yes	—
182	C₂	#15689063	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂×C₄₇⋊#95

C₂

yes

maximal, characteristic

C₂×#95×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂³×Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₄

yes

complemented

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#95×C₄₇

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

C₄×Q₈

yes

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#126

yes

—

C₂²×C₄₇

#127

yes

characteristic

C₂²×C₄₇

C₄⋊Q₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#398

yes

—

C₂×C₄₇

#399

yes

—

C₂×C₄₇

#400

yes

—

C₂²×C₄⋊C₄

—

C₂×#95

—

C₂×#95

—

C₂×#95

D₄₇

yes

characteristic

C₄₇

#1445

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

—

100

C₂³×C₄

C₂×D₄₇

yes

characteristic

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

#95

—

105

#95

—

106

#95

—

107

C₂⁴

C₂²×D₄₇

yes

characteristic

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

C₄×D₄₇

yes

—

124

C₂²×C₄

D₁₈₈

yes

—

125

C₂²×C₄

D₁₈₈

yes

—

126

C₂²×C₄

C₂²⋊D₄₇

yes

—

127

C₄⋊C₄

—

128

C₂³

C₂×C₄×D₄₇

yes

characteristic

129

C₂³

C₂×D₁₈₈

yes

characteristic

130

C₂³

C₂×D₁₈₈

yes

—

131

C₂³

#10625350

yes

—

132

C₂³

#10625352

yes

—

133

C₂³

#10625352

yes

—

134

C₂³

Q₈×D₄₇

yes

—

135

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

188

—

149

C₂×C₄

—

188

—

150

C₂×C₄

—

188

—

151

C₂×C₄

—

188

—

152

C₂×C₄

—

188

—

153

C₂×C₄

—

188

—

154

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

155

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

156

C₂²

#13093980

yes

—

157

C₂²

C₄×D₁₈₈

yes

—

158

C₂²

#13093989

yes

—

159

C₂²

#13093998

yes

—

160

C₂²

#13094004

yes

—

161

C₂²

#13094004

yes

—

162

C₂²

#13094005

yes

—

163

C₂²

#13094008

yes

—

164

C₂²

#13094008

yes

—

165

C₂²

#13094011

yes

characteristic

166

C₂²

#13094012

yes

characteristic

167

C₂²

#13094014

yes

—

168

C₂²

#13094017

yes

—

169

C₂²

#13094021

yes

characteristic

170

C₂²

#13094022

yes

characteristic

171

C₄

—

172

C₄

—

173

C₄

—

188

—

174

C₄

—

188

—

175

C₂

#15688984

yes

characteristic

176

C₂

#15689008

yes

—

177

C₂

#15689025

yes

characteristic

178

C₂

#15689028

yes

characteristic

179

C₂

#15689048

yes

—

180

C₂

#15689053

yes

—

181

C₂

#15689060

yes

—

182

C₂

#15689063

yes

—

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Fitting	C₂×#95×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	#1445
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂²×C₄

Fitting

C₂×#95×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂×#95

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂×#95

N	H ≅ G/N	type
9. C₂×C₄⋊Dic₄₇	C₄	semidirect
96. C₄₇	#1445	semidirect

H ≅ G/N

type

9. C₂×C₄⋊Dic₄₇

C₄

semidirect

96. C₄₇

#1445

semidirect

Subgroups — #20241655

Conjugacy classes of subgroups

Complements