Group #19135759 — subgroups

Subgroups — #19135759

Order 5504.

466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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	#14583525	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582755	C₂	1	2	yes	maximal
3	#14582666	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582665	C₂	1	2	yes	maximal, complemented
5	C₄₃×#379	C₂	1	1	yes	maximal, characteristic
6	#13063304	—	2	2	no	—
7	#13063302	—	2	4	no	—
8	C₂×C₂²⋊Dic₄₃	—	2	4	no	—
9	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
11	C₂⁵×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
13	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄₃	—	2	1	no	—
16	C₂⁴×C₄₃	—	2	2	no	—
17	C₂⁴×C₄₃	—	2	1	no	—
18	C₂⁴×C₄₃	—	2	2	no	—
19	C₂⁴×C₄₃	—	4	4	no	—
20	C₂⁴×C₄₃	Q₈	1	2	yes	complemented
21	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	—	2	1	no	—
23	C₂²×C₄×C₄₃	D₄	1	2	yes	—
24	C₂²×Dic₄₃	—	2	2	no	—
25	C₂²×Dic₄₃	D₄	1	4	yes	—
26	C₂×Dic₈₆	—	2	2	no	—
27	C₂²⋊C₄×C₄₃	—	2	2	no	—
28	C₂²⋊C₄×C₄₃	—	2	2	no	—
29	C₂²⋊C₄×C₄₃	—	4	4	no	—
30	C₂²⋊Dic₄₃	—	2	2	no	—
31	C₂²⋊Dic₄₃	—	2	2	no	—
32	C₂²⋊Dic₄₃	—	2	2	no	—
33	C₂²⋊Dic₄₃	—	2	2	no	—
34	C₂²⋊Dic₄₃	—	4	8	no	—
35	C₄⋊Dic₄₃	—	2	2	no	—
36	Dic₄₃⋊C₄	—	2	4	no	—
37	C₂³×C₄₃	—	2	8	no	—
38	C₂³×C₄₃	—	2	4	no	—
39	C₂³×C₄₃	—	2	4	no	—
40	C₂³×C₄₃	—	2	2	no	—
41	C₂³×C₄₃	—	4	4	no	—
42	C₂³×C₄₃	—	4	2	no	—
43	C₂³×C₄₃	—	4	4	no	—
44	C₂³×C₄₃	—	4	2	no	—
45	C₂³×C₄₃	—	4	4	no	—
46	C₂³×C₄₃	—	4	8	no	—
47	C₂³×C₄₃	—	4	1	no	—
48	C₂³×C₄₃	—	4	2	no	—
49	C₂³×C₄₃	—	4	1	no	—
50	C₂³×C₄₃	C₂×D₄	1	2	yes	—
51	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
53	C₂³×C₄₃	#41	1	1	yes	characteristic
54	C₂³×C₄₃	#41	1	2	yes	—
55	C₂×C₄×C₄₃	—	2	2	no	—
56	C₂×C₄×C₄₃	—	4	2	no	—
57	C₂×C₄×C₄₃	—	4	2	no	—
58	C₂×C₄×C₄₃	—	4	1	no	—
59	C₂×Dic₄₃	—	2	4	no	—
60	C₂×Dic₄₃	—	4	4	no	—
61	C₂×Dic₄₃	—	4	4	no	—
62	C₂×Dic₄₃	—	4	2	no	—
63	Dic₈₆	—	8	2	no	—
64	C₂²×C₄₃	—	2	4	no	—
65	C₂²×C₄₃	—	2	2	no	—
66	C₂²×C₄₃	—	2	8	no	—
67	C₂²×C₄₃	—	2	4	no	—
68	C₂²×C₄₃	—	4	1	no	—
69	C₂²×C₄₃	—	4	1	no	—
70	C₂²×C₄₃	—	4	2	no	—
71	C₂²×C₄₃	—	4	8	no	—
72	C₂²×C₄₃	—	4	4	no	—
73	C₂²×C₄₃	—	4	4	no	—
74	C₂²×C₄₃	—	4	2	no	—
75	C₂²×C₄₃	—	4	2	no	—
76	C₂²×C₄₃	—	4	4	no	—
77	C₂²×C₄₃	#120	1	1	yes	characteristic
78	C₂²×C₄₃	C₂²⋊Q₈	1	2	yes	—
79	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
80	C₂²×C₄₃	#124	1	2	yes	—
81	C₂²×C₄₃	#124	1	1	yes	characteristic
82	C₄×C₄₃	—	4	2	no	—
83	C₄×C₄₃	—	8	1	no	—
84	Dic₄₃	—	4	4	no	—
85	Dic₄₃	—	8	2	no	—
86	#2029	—	43	1	no	maximal, Sylow
87	C₂×C₄₃	—	2	2	no	—
88	C₂×C₄₃	—	2	1	no	—
89	C₂×C₄₃	—	2	2	no	—
90	C₂×C₄₃	—	2	1	no	—
91	C₂×C₄₃	—	4	4	no	—
92	C₂×C₄₃	#393	1	1	yes	characteristic
93	C₂×C₄₃	B(4,𝔽₂)	1	2	yes	—
94	#543	—	43	1	no	—
95	#379	—	43	2	no	—
96	#379	D₄₃	1	1	yes	characteristic
97	#342	—	43	2	no	—
98	#342	—	43	1	no	—
99	C₄₃	#2029	1	1	yes	characteristic, complemented, Sylow
100	C₂⁵	C₂×D₄₃	1	1	yes	characteristic
101	C₂²⋊Q₈	—	86	4	no	—
102	C₂²⋊Q₈	—	86	2	no	—
103	C₂×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₂²⋊C₄	—	43	2	no	—
105	C₂×C₂²⋊C₄	—	43	2	no	—
106	C₂×C₂²⋊C₄	—	86	4	no	—
107	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
108	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
109	C₂⁴	—	2	2	no	—
110	C₂⁴	—	2	1	no	—
111	C₂⁴	—	2	1	no	—
112	C₂⁴	—	2	2	no	—
113	C₂⁴	—	4	4	no	—
114	C₂⁴	Dic₈₆	1	2	yes	complemented
115	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
116	C₂×Q₈	—	86	2	no	—
117	C₂²×C₄	—	2	1	no	—
118	C₂²×C₄	—	43	4	no	—
119	C₂²×C₄	—	86	2	no	—
120	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
121	C₄⋊C₄	—	86	4	no	—
122	C₄⋊C₄	—	86	2	no	—
123	C₂²⋊C₄	—	2	2	no	—
124	C₂²⋊C₄	—	2	2	no	—
125	C₂²⋊C₄	—	4	4	no	—
126	C₂²⋊C₄	—	86	2	no	—
127	C₂²⋊C₄	—	86	2	no	—
128	C₂²⋊C₄	—	86	2	no	—
129	C₂²⋊C₄	—	86	2	no	—
130	C₂²⋊C₄	—	172	8	no	—
131	C₂³	—	2	4	no	—
132	C₂³	—	2	8	no	—
133	C₂³	—	2	4	no	—
134	C₂³	—	2	2	no	—
135	C₂³	—	4	2	no	—
136	C₂³	—	4	4	no	—
137	C₂³	—	4	2	no	—
138	C₂³	—	4	4	no	—
139	C₂³	—	4	4	no	—
140	C₂³	—	4	8	no	—
141	C₂³	—	4	1	no	—
142	C₂³	—	4	2	no	—
143	C₂³	—	4	1	no	—
144	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
145	C₂³	#10621898	1	1	yes	characteristic
146	C₂³	D₄×D₄₃	1	2	yes	—
147	C₂³	#10621900	1	2	yes	—
148	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
149	Q₈	—	344	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	4	2	no	—
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	—	86	4	no	—
155	C₂×C₄	—	172	4	no	—
156	C₂×C₄	—	172	2	no	—
157	C₂×C₄	—	172	4	no	—
158	C₂²	—	2	2	no	—
159	C₂²	—	2	4	no	—
160	C₂²	—	2	8	no	—
161	C₂²	—	2	4	no	—
162	C₂²	—	4	1	no	—
163	C₂²	—	4	1	no	—
164	C₂²	—	4	2	no	—
165	C₂²	—	4	4	no	—
166	C₂²	—	4	8	no	—
167	C₂²	—	4	4	no	—
168	C₂²	—	4	2	no	—
169	C₂²	—	4	2	no	—
170	C₂²	—	4	4	no	—
171	C₂²	#13063293	1	1	yes	characteristic
172	C₂²	#13063302	1	2	yes	—
173	C₂²	#13063304	1	1	yes	characteristic
174	C₂²	#13063311	1	2	yes	—
175	C₂²	#13063312	1	1	yes	characteristic
176	C₄	—	4	2	no	—
177	C₄	—	8	1	no	—
178	C₄	—	344	2	no	—
179	C₄	—	172	4	no	—
180	C₂	—	2	1	no	—
181	C₂	—	2	2	no	—
182	C₂	—	2	2	no	—
183	C₂	—	2	1	no	—
184	C₂	—	4	4	no	—
185	C₂	#14582811	1	1	yes	characteristic
186	C₂	#14583085	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583525

C₂

yes

maximal, characteristic, complemented

#14582755

C₂

yes

maximal

#14582666

C₂

yes

maximal, characteristic, complemented

#14582665

C₂

yes

maximal, complemented

C₄₃×#379

C₂

yes

maximal, characteristic

#13063304

—

#13063302

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂⁵×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

Q₈

yes

complemented

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂³×C₄₃

C₂×Q₈

yes

C₂³×C₄₃

yes

C₂³×C₄₃

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

—

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

#124

yes

—

C₂²×C₄₃

#124

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2029

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#393

yes

characteristic

C₂×C₄₃

B(4,𝔽₂)

yes

—

#543

—

#379

—

#379

D₄₃

yes

characteristic

#342

—

#342

—

C₄₃

#2029

yes

characteristic, complemented, Sylow

100

C₂⁵

C₂×D₄₃

yes

characteristic

101

C₂²⋊Q₈

—

102

C₂²⋊Q₈

—

103

C₂×C₂²⋊C₄

—

104

C₂×C₂²⋊C₄

—

105

C₂×C₂²⋊C₄

—

106

C₂×C₂²⋊C₄

—

107

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

108

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

109

C₂⁴

—

110

C₂⁴

—

111

C₂⁴

—

112

C₂⁴

—

113

C₂⁴

—

114

C₂⁴

Dic₈₆

yes

complemented

115

C₂⁴

C₂²×D₄₃

yes

characteristic

116

C₂×Q₈

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

C₂²⋊D₄₃

yes

—

121

C₄⋊C₄

—

122

C₄⋊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

—

172

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

—

144

C₂³

C₂×Dic₈₆

yes

characteristic

145

C₂³

#10621898

yes

characteristic

146

C₂³

D₄×D₄₃

yes

—

147

C₂³

#10621900

yes

—

148

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

149

Q₈

—

344

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

172

—

156

C₂×C₄

—

172

—

157

C₂×C₄

—

172

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

#13063293

yes

characteristic

172

C₂²

#13063302

yes

—

173

C₂²

#13063304

yes

characteristic

174

C₂²

#13063311

yes

—

175

C₂²

#13063312

yes

characteristic

176

C₄

—

177

C₄

—

178

C₄

—

344

—

179

C₄

—

172

—

180

C₂

—

181

C₂

—

182

C₂

—

183

C₂

—

184

C₂

—

185

C₂

#14582811

yes

characteristic

186

C₂

#14583085

yes

—

	subgroup	G/H
center	C₂²	#13063293
commutator	C₂⁴×C₄₃	C₂³
Frattini	C₂⁴	C₂²×D₄₃
Fitting	C₄₃×#379	C₂
socle	C₂²×C₄₃	#120
hypercenter	#379	D₄₃
hypocenter	C₄₃	#2029
LCS	G ▷ C₂⁴×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #379

subgroup

G/H

center

C₂²

#13063293

commutator

C₂⁴×C₄₃

C₂³

Frattini

C₂⁴

C₂²×D₄₃

Fitting

C₄₃×#379

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂⁴×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂⁴ ◁ #379

N	H ≅ G/N	type
1. #14583525	C₂	semidirect
3. #14582666	C₂	semidirect
4. #14582665	C₂	semidirect
20. C₂⁴×C₄₃	Q₈	semidirect
99. C₄₃	#2029	semidirect
114. C₂⁴	Dic₈₆	semidirect

H ≅ G/N

type

1. #14583525

C₂

semidirect

3. #14582666

C₂

semidirect

4. #14582665

C₂

semidirect

20. C₂⁴×C₄₃

Q₈

semidirect

99. C₄₃

#2029

semidirect

114. C₂⁴

Dic₈₆

semidirect

Subgroups — #19135759

Conjugacy classes of subgroups

Complements