Group #20246618 — subgroups

Subgroups — C₂×#15689053 #20246618

Order 6016.

692 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 261 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	C₂²×Dic₄₇⋊C₄	C₂	1	2	yes	maximal
3	#15689053	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄₇⋊#95	C₂	1	2	yes	maximal
5	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₄₇	C₂²	1	2	yes	—
8	C₂³×Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₇	—	2	4	no	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂×Dic₄₇⋊C₄	—	2	8	no	—
12	C₂×Dic₄₇⋊C₄	C₂²	1	8	yes	—
13	C₄₇⋊#95	C₂²	1	8	yes	—
14	C₄₇⋊#95	C₂²	1	4	yes	—
15	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
19	C₂×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
20	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	—	2	2	no	—
22	C₂²×C₄×C₄₇	—	2	2	no	—
23	C₂²×C₄×C₄₇	—	2	4	no	—
24	C₂²×C₄×C₄₇	—	2	2	no	—
25	C₂²×C₄×C₄₇	—	2	4	no	—
26	C₂²×C₄×C₄₇	D₄	1	4	yes	—
27	C₂²×C₄×C₄₇	D₄	1	4	yes	—
28	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
29	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
30	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
31	C₂²×Dic₄₇	—	2	4	no	—
32	C₂²×Dic₄₇	—	2	4	no	—
33	C₂²×Dic₄₇	—	2	4	no	—
34	C₂²×Dic₄₇	—	2	4	no	—
35	C₂²×Dic₄₇	—	2	4	no	—
36	C₂²×Dic₄₇	Q₈	1	8	yes	—
37	C₂²×Dic₄₇	C₂³	1	4	yes	—
38	C₂²×Dic₄₇	C₂³	1	4	yes	—
39	C₄⋊C₄×C₄₇	—	2	8	no	—
40	C₄⋊Dic₄₇	—	2	8	no	—
41	Dic₄₇⋊C₄	—	2	16	no	—
42	C₂³×C₄₇	C₂×D₄	1	2	yes	—
43	C₂³×C₄₇	C₂×D₄	1	2	yes	—
44	C₂³×C₄₇	C₂×Q₈	1	4	yes	—
45	C₂³×C₄₇	#41	1	2	yes	—
46	C₂³×C₄₇	#41	1	4	yes	—
47	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
48	C₂×C₄×C₄₇	—	2	8	no	—
49	C₂×C₄×C₄₇	—	2	8	no	—
50	C₂×C₄×C₄₇	—	2	2	no	—
51	C₂×C₄×C₄₇	—	2	4	no	—
52	C₂×C₄×C₄₇	—	2	2	no	—
53	C₂×C₄×C₄₇	—	2	2	no	—
54	C₂×C₄×C₄₇	—	2	4	no	—
55	C₂×C₄×C₄₇	—	4	4	no	—
56	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
57	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
58	C₂×Dic₄₇	—	2	16	no	—
59	C₂×Dic₄₇	—	2	4	no	—
60	C₂×Dic₄₇	—	2	4	no	—
61	C₂×Dic₄₇	—	2	4	no	—
62	C₂×Dic₄₇	—	2	4	no	—
63	C₂×Dic₄₇	—	2	4	no	—
64	C₂×Dic₄₇	—	4	8	no	—
65	C₂×Dic₄₇	C₂×Q₈	1	8	yes	—
66	C₂²×C₄₇	#121	1	4	yes	—
67	C₂²×C₄₇	C₂²⋊Q₈	1	8	yes	—
68	C₂²×C₄₇	#123	1	4	yes	—
69	C₂²×C₄₇	#125	1	8	yes	—
70	C₂²×C₄₇	C₄⋊Q₈	1	4	yes	—
71	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
72	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
73	C₂²×C₄₇	C₂²×Q₈	1	2	yes	—
74	C₂²×C₄₇	C₂×#41	1	2	yes	—
75	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
76	C₄×C₄₇	—	2	4	no	—
77	C₄×C₄₇	—	2	4	no	—
78	C₄×C₄₇	—	4	2	no	—
79	Dic₄₇	—	2	8	no	—
80	Dic₄₇	—	4	4	no	—
81	C₂×#398	—	47	1	no	maximal, Sylow
82	C₂×C₄₇	#398	1	8	yes	complemented
83	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
84	C₂×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄₇	C₂×#123	1	1	yes	characteristic
86	C₂×C₄₇	C₂×#125	1	2	yes	—
87	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
88	C₂²×C₄⋊C₄	—	47	2	no	—
89	C₂²×C₄⋊C₄	—	47	1	no	—
90	C₂²×C₄⋊C₄	D₄₇	1	1	yes	characteristic
91	#398	—	47	8	no	—
92	C₂×#95	—	47	1	no	—
93	C₂×#95	—	47	2	no	—
94	C₄₇	C₂×#398	1	1	yes	characteristic, complemented, Sylow
95	C₂³×C₄	—	47	2	no	—
96	C₂³×C₄	—	47	2	no	—
97	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
98	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
99	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
100	C₂×C₄⋊C₄	—	2	4	no	—
101	C₂×C₄⋊C₄	—	47	8	no	—
102	C₂×C₄⋊C₄	—	47	4	no	—
103	C₂×C₄⋊C₄	—	94	8	no	—
104	C₂×C₄⋊C₄	—	94	4	no	—
105	C₂×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
106	#95	—	47	4	no	—
107	#95	—	47	8	no	—
108	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
109	C₂²×C₄	—	2	2	no	—
110	C₂²×C₄	—	2	4	no	—
111	C₂²×C₄	—	2	2	no	—
112	C₂²×C₄	—	2	4	no	—
113	C₂²×C₄	—	2	2	no	—
114	C₂²×C₄	—	47	8	no	—
115	C₂²×C₄	—	47	4	no	—
116	C₂²×C₄	—	47	4	no	—
117	C₂²×C₄	—	94	4	no	—
118	C₂²×C₄	—	94	4	no	—
119	C₂²×C₄	—	94	4	no	—
120	C₂²×C₄	—	94	4	no	—
121	C₂²×C₄	—	94	4	no	—
122	C₂²×C₄	D₁₈₈	1	4	yes	—
123	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
124	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
125	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
126	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
127	C₄⋊C₄	—	2	8	no	—
128	C₄⋊C₄	—	94	16	no	—
129	C₄⋊C₄	—	94	8	no	—
130	C₂³	C₂×D₁₈₈	1	2	yes	—
131	C₂³	#10625350	1	2	yes	—
132	C₂³	#10625352	1	4	yes	—
133	C₂³	Q₈×D₄₇	1	4	yes	—
134	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
135	C₂³	C₂³×D₄₇	1	1	yes	characteristic
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	—	2	8	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	4	no	—
143	C₂×C₄	—	4	4	no	—
144	C₂×C₄	—	47	8	no	—
145	C₂×C₄	—	94	16	no	—
146	C₂×C₄	—	94	4	no	—
147	C₂×C₄	—	94	4	no	—
148	C₂×C₄	—	94	4	no	—
149	C₂×C₄	—	94	4	no	—
150	C₂×C₄	—	94	4	no	—
151	C₂×C₄	—	188	8	no	—
152	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
153	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
154	C₂²	#13093998	1	4	yes	—
155	C₂²	#13094004	1	8	yes	—
156	C₂²	#13094005	1	4	yes	—
157	C₂²	#13094014	1	8	yes	—
158	C₂²	#13094022	1	4	yes	—
159	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
160	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
161	C₂²	C₂×Q₈×D₄₇	1	2	yes	—
162	C₂²	C₂×#10625352	1	2	yes	—
163	C₂²	C₂×#10625350	1	1	yes	characteristic
164	C₄	—	2	4	no	—
165	C₄	—	2	4	no	—
166	C₄	—	4	2	no	—
167	C₄	—	94	8	no	—
168	C₄	—	188	4	no	—
169	C₂	#15689053	1	8	yes	direct product factor
170	C₂	C₂×#13093998	1	1	yes	characteristic
171	C₂	C₂×#13094004	1	2	yes	—
172	C₂	C₂×#13094005	1	1	yes	characteristic
173	C₂	C₂×#13094014	1	2	yes	—
174	C₂	C₂×#13094022	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₄₇⋊C₄

C₂

yes

maximal

#15689053

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂×C₄₇⋊#95

C₂

yes

maximal, characteristic

C₂²×C₄⋊C₄×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂³×Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

Q₈

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

#41

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×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×Q₈

yes

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#125

yes

—

C₂²×C₄₇

C₄⋊Q₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₂²⋊Q₈

yes

—

C₂×C₄₇

C₂×#123

yes

characteristic

C₂×C₄₇

C₂×#125

yes

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

D₄₇

yes

characteristic

#398

—

C₂×#95

—

C₂×#95

—

C₄₇

C₂×#398

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂³×C₄

C₂×D₄₇

yes

characteristic

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

106

#95

—

107

#95

—

108

C₂⁴

C₂²×D₄₇

yes

characteristic

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

D₁₈₈

yes

—

123

C₂²×C₄

C₂²⋊D₄₇

yes

—

124

C₂²×C₄

C₂²×D₄₇

yes

—

125

C₂²×C₄

C₂²×D₄₇

yes

—

126

C₂²×C₄

C₂²×D₄₇

yes

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₂³

C₂×D₁₈₈

yes

—

131

C₂³

#10625350

yes

—

132

C₂³

#10625352

yes

—

133

C₂³

Q₈×D₄₇

yes

—

134

C₂³

C₂×C₂²⋊D₄₇

yes

—

135

C₂³

C₂³×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

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

188

—

152

C₂×C₄

C₂×D₁₈₈

yes

—

153

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

154

C₂²

#13093998

yes

—

155

C₂²

#13094004

yes

—

156

C₂²

#13094005

yes

—

157

C₂²

#13094014

yes

—

158

C₂²

#13094022

yes

—

159

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

160

C₂²

C₂²×D₁₈₈

yes

characteristic

161

C₂²

C₂×Q₈×D₄₇

yes

—

162

C₂²

C₂×#10625352

yes

—

163

C₂²

C₂×#10625350

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

—

188

—

169

C₂

#15689053

yes

direct product factor

170

C₂

C₂×#13093998

yes

characteristic

171

C₂

C₂×#13094004

yes

—

172

C₂

C₂×#13094005

yes

characteristic

173

C₂

C₂×#13094014

yes

—

174

C₂

C₂×#13094022

yes

characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂²×C₄⋊C₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂²×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂×#398
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

subgroup

G/H

center

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂²×C₄⋊C₄×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂²×C₄⋊C₄

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

N	H ≅ G/N	type
3. #15689053	C₂	direct (N × H)
82. C₂×C₄₇	#398	semidirect
94. C₄₇	C₂×#398	semidirect
169. C₂	#15689053	direct (N × H)

H ≅ G/N

type

3. #15689053

C₂

direct (N × H)

82. C₂×C₄₇

#398

semidirect

94. C₄₇

C₂×#398

semidirect

169. C₂

#15689053

direct (N × H)

Subgroups — C₂×#15689053 #20246618

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689053 #20246618

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689053 #20246618