Group #20243378 — subgroups

Subgroups — #20243378

Order 6016.

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	C₂×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#15689146	C₂	1	2	yes	maximal, complemented
3	C₂×#13093941	C₂	1	1	yes	maximal, characteristic
4	#15688891	C₂	1	2	yes	maximal, complemented
5	C₂×#100×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₄	1	2	yes	—
7	C₂×#10625329	C₂²	1	2	yes	—
8	D₄×Dic₄₇	—	2	2	no	—
9	D₄×Dic₄₇	—	2	2	no	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₄₇	C₄	1	2	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	Dic₄₇⋊C₈	—	2	2	no	—
14	Dic₄₇⋊C₈	—	2	2	no	—
15	#13093941	—	2	2	no	—
16	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
18	#100×C₄₇	—	2	2	no	—
19	C₂⁴×C₄₇	C₂×C₄	1	2	yes	—
20	C₂×D₄×C₄₇	—	2	2	no	—
21	C₂×D₄×C₄₇	—	2	2	no	—
22	C₂×D₄×C₄₇	D₄	1	2	yes	—
23	C₂×D₄×C₄₇	Q₈	1	2	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₇	—	2	2	no	—
26	C₂²×Dic₄₇	—	2	2	no	—
27	C₂²×Dic₄₇	—	4	4	no	—
28	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
30	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
31	M₁₆×C₄₇	—	2	2	no	—
32	M₁₆×C₄₇	—	2	2	no	—
33	C₂×C₈×C₄₇	—	2	2	no	—
34	C₂²⋊Dic₄₇	—	2	4	no	—
35	C₄⋊Dic₄₇	—	2	2	no	—
36	C₄×Dic₄₇	D₄	1	2	yes	—
37	C₄×Dic₄₇	D₄	1	2	yes	—
38	#10625329	—	2	2	no	—
39	#10625329	—	2	2	no	—
40	C₂×C₄₇⋊C₈	—	2	2	no	—
41	C₂³×C₄₇	—	2	2	no	—
42	C₂³×C₄₇	—	2	2	no	—
43	C₂³×C₄₇	—	4	2	no	—
44	C₂³×C₄₇	—	4	2	no	—
45	C₂³×C₄₇	C₄⋊C₄	1	4	yes	—
46	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
47	D₄×C₄₇	—	2	4	no	—
48	D₄×C₄₇	—	2	4	no	—
49	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₄₇	#41	1	2	yes	—
53	C₂×Dic₄₇	—	2	2	no	—
54	C₂×Dic₄₇	—	2	2	no	—
55	C₂×Dic₄₇	—	4	1	no	—
56	C₂×Dic₄₇	—	4	4	no	—
57	C₂×Dic₄₇	—	4	4	no	—
58	C₂×Dic₄₇	—	4	2	no	—
59	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
60	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₈×C₄₇	—	4	2	no	—
63	C₄₇⋊C₈	—	4	2	no	—
64	C₂²×C₄₇	—	2	1	no	—
65	C₂²×C₄₇	—	2	1	no	—
66	C₂²×C₄₇	—	2	4	no	—
67	C₂²×C₄₇	—	4	4	no	—
68	C₂²×C₄₇	—	4	4	no	—
69	C₂²×C₄₇	—	4	2	no	—
70	C₂²×C₄₇	—	4	2	no	—
71	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄₇	#117	1	1	yes	characteristic
74	C₄×C₄₇	#121	1	2	yes	—
75	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
76	Dic₄₇	—	2	1	no	—
77	Dic₄₇	—	2	2	no	—
78	Dic₄₇	—	4	2	no	—
79	Dic₄₇	#100	1	2	yes	complemented
80	#1800	—	47	1	no	maximal, Sylow
81	C₂×C₄₇	—	2	1	no	—
82	C₂×C₄₇	—	2	1	no	—
83	C₂×C₄₇	—	4	4	no	—
84	C₂×C₄₇	#380	1	1	yes	characteristic
85	C₂×C₄₇	C₂×#100	1	1	yes	characteristic
86	C₂×C₄₇	#413	1	1	yes	characteristic
87	C₂×C₄×D₄	—	47	1	no	—
88	#423	—	47	2	no	—
89	C₂×#100	—	47	1	no	—
90	C₂×#100	D₄₇	1	1	yes	characteristic
91	#343	—	47	2	no	—
92	C₄₇	#1800	1	1	yes	characteristic, complemented, Sylow
93	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
94	C₂³×C₄	—	47	2	no	—
95	C₂×M₁₆	—	47	2	no	—
96	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
97	C₄×D₄	—	94	2	no	—
98	C₄×D₄	—	94	2	no	—
99	C₂×C₄⋊C₄	—	47	1	no	—
100	C₂×C₂²⋊C₄	—	47	2	no	—
101	C₂×C₄²	—	47	1	no	—
102	C₄⋊C₈	—	94	2	no	—
103	C₄⋊C₈	—	94	2	no	—
104	#100	—	2	2	no	—
105	#100	—	94	2	no	—
106	C₂⁴	C₄×D₄₇	1	2	yes	—
107	C₂×D₄	—	2	2	no	—
108	C₂×D₄	—	2	2	no	—
109	C₂×D₄	Dic₉₄	1	2	yes	—
110	C₂×D₄	C₂²⋊D₄₇	1	2	yes	—
111	C₂²×C₄	—	47	1	no	—
112	C₂²×C₄	—	47	1	no	—
113	C₂²×C₄	—	47	2	no	—
114	C₂²×C₄	—	94	2	no	—
115	C₂²×C₄	—	94	2	no	—
116	C₂²×C₄	—	188	4	no	—
117	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
118	M₁₆	—	2	2	no	—
119	M₁₆	—	2	2	no	—
120	M₁₆	—	94	2	no	—
121	M₁₆	—	94	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	94	2	no	—
124	C₄⋊C₄	—	94	2	no	—
125	C₂²⋊C₄	—	94	4	no	—
126	C₄²	—	47	2	no	—
127	C₄²	—	47	2	no	—
128	C₂³	—	2	2	no	—
129	C₂³	—	2	2	no	—
130	C₂³	—	4	2	no	—
131	C₂³	—	4	2	no	—
132	C₂³	Dic₄₇⋊C₄	1	4	yes	—
133	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
134	D₄	—	2	4	no	—
135	D₄	—	2	4	no	—
136	C₂×C₄	—	47	1	no	—
137	C₂×C₄	—	47	2	no	—
138	C₂×C₄	—	47	1	no	—
139	C₂×C₄	—	94	2	no	—
140	C₂×C₄	—	94	2	no	—
141	C₂×C₄	—	188	4	no	—
142	C₂×C₄	—	188	1	no	—
143	C₂×C₄	—	188	4	no	—
144	C₂×C₄	—	188	2	no	—
145	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
146	C₂×C₄	D₄×D₄₇	1	2	yes	—
147	C₂×C₄	#10625352	1	2	yes	—
148	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
149	C₈	—	4	2	no	—
150	C₈	—	188	2	no	—
151	C₂²	—	2	1	no	—
152	C₂²	—	2	1	no	—
153	C₂²	—	2	4	no	—
154	C₂²	—	4	4	no	—
155	C₂²	—	4	4	no	—
156	C₂²	—	4	2	no	—
157	C₂²	—	4	2	no	—
158	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
159	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
160	C₂²	#13093980	1	1	yes	characteristic
161	C₄	—	47	2	no	—
162	C₄	—	94	1	no	—
163	C₄	—	94	2	no	—
164	C₄	—	188	2	no	—
165	C₄	#13093996	1	2	yes	—
166	C₄	#13094001	1	2	yes	—
167	C₂	—	2	1	no	—
168	C₂	—	2	1	no	—
169	C₂	—	4	4	no	—
170	C₂	#15688981	1	1	yes	characteristic
171	C₂	#100×D₄₇	1	1	yes	characteristic
172	C₂	#15689104	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×Dic₄₇

C₂

yes

maximal, characteristic

#15689146

C₂

yes

maximal, complemented

C₂×#13093941

C₂

yes

maximal, characteristic

#15688891

C₂

yes

maximal, complemented

C₂×#100×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₄

yes

—

C₂×#10625329

C₂²

yes

—

D₄×Dic₄₇

—

D₄×Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×C₂²⋊Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

Dic₄₇⋊C₈

—

#13093941

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

—

#100×C₄₇

—

C₂⁴×C₄₇

C₂×C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂×D₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

D₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₄⋊C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

C₂×C₄⋊C₄

yes

C₂²×C₄₇

yes

C₄×C₄₇

yes

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄×D₄

—

#423

—

C₂×#100

—

C₂×#100

D₄₇

yes

characteristic

#343

—

C₄₇

#1800

yes

characteristic, complemented, Sylow

C₂²×D₄

C₂×D₄₇

yes

characteristic

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

—

100

C₂×C₂²⋊C₄

—

101

C₂×C₄²

—

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

#100

—

105

#100

—

106

C₂⁴

C₄×D₄₇

yes

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

Dic₉₄

yes

—

110

C₂×D₄

C₂²⋊D₄₇

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

188

—

117

C₂²×C₄

C₂²×D₄₇

yes

characteristic

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

M₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₄²

—

127

C₄²

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

Dic₄₇⋊C₄

yes

—

133

C₂³

C₂×C₄×D₄₇

yes

characteristic

134

D₄

—

135

D₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

188

—

142

C₂×C₄

—

188

—

143

C₂×C₄

—

188

—

144

C₂×C₄

—

188

—

145

C₂×C₄

C₂×Dic₉₄

yes

characteristic

146

C₂×C₄

D₄×D₄₇

yes

—

147

C₂×C₄

#10625352

yes

—

148

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

149

C₈

—

150

C₈

—

188

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

C₂²⋊C₄×D₄₇

yes

characteristic

159

C₂²

C₂×Dic₄₇⋊C₄

yes

characteristic

160

C₂²

#13093980

yes

characteristic

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

—

188

—

165

C₄

#13093996

yes

—

166

C₄

#13094001

yes

—

167

C₂

—

168

C₂

—

169

C₂

—

170

C₂

#15688981

yes

characteristic

171

C₂

#100×D₄₇

yes

characteristic

172

C₂

#15689104

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#100×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	C₂×#100	D₄₇
hypocenter	C₄₇	#1800
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₇

commutator

C₂³×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#100×C₄₇

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

N	H ≅ G/N	type
2. #15689146	C₂	semidirect
4. #15688891	C₂	semidirect
79. Dic₄₇	#100	semidirect
92. C₄₇	#1800	semidirect

H ≅ G/N

type

2. #15689146

C₂

semidirect

4. #15688891

C₂

semidirect

79. Dic₄₇

#100

semidirect

92. C₄₇

#1800

semidirect

Subgroups — #20243378

Conjugacy classes of subgroups

Complements