Group #19142942 — subgroups

Subgroups — #19142942

Order 5504.

644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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×#13063301	C₂	1	2	yes	maximal
2	C₂×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582806	C₂	1	2	yes	maximal, complemented
4	#14582795	C₂	1	4	yes	maximal, complemented
5	#14582769	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582756	C₂	1	4	yes	maximal
7	C₂×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
10	#13063301	—	2	8	no	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
14	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
15	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
16	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₄²×D₄₃	—	2	4	no	—
18	C₄₃⋊#95	C₂²	1	8	yes	—
19	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
20	C₄⋊Q₈×C₄₃	—	2	4	no	—
21	C₂×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
22	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₂³×D₄₃	C₂³	1	1	yes	characteristic
24	C₂×Q₈×C₄₃	—	2	4	no	—
25	C₂×Q₈×C₄₃	—	2	4	no	—
26	C₂×Q₈×C₄₃	—	2	4	no	—
27	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
28	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
30	C₂²×Dic₄₃	C₂³	1	4	yes	—
31	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
32	C₂²×Dic₄₃	C₂³	1	2	yes	—
33	C₂×C₄×D₄₃	—	2	2	no	—
34	C₂×C₄×D₄₃	—	2	4	no	—
35	C₂×C₄×D₄₃	—	2	2	no	—
36	C₂×C₄×D₄₃	—	2	4	no	—
37	C₂×C₄×D₄₃	D₄	1	4	yes	—
38	C₂×C₄×D₄₃	Q₈	1	8	yes	complemented
39	C₄⋊C₄×C₄₃	—	2	8	no	—
40	C₄²×C₄₃	D₄	1	4	yes	—
41	(C₂×D₄₃)⋊C₄	—	2	8	no	—
42	C₄⋊Dic₄₃	—	2	4	no	—
43	C₄⋊Dic₄₃	—	2	8	no	—
44	Dic₄₃⋊C₄	—	2	8	no	—
45	C₄×Dic₄₃	—	2	2	no	—
46	C₄×Dic₄₃	—	2	4	no	—
47	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
48	C₂²×D₄₃	—	2	1	no	—
49	C₂²×D₄₃	—	2	1	no	—
50	C₂²×D₄₃	—	2	2	no	—
51	C₂²×D₄₃	C₂×D₄	1	2	yes	—
52	C₂²×D₄₃	C₂×Q₈	1	4	yes	—
53	Q₈×C₄₃	—	4	8	no	—
54	C₂×C₄×C₄₃	—	2	4	no	—
55	C₂×C₄×C₄₃	—	2	4	no	—
56	C₂×C₄×C₄₃	—	2	4	no	—
57	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
59	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
60	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
61	C₂×C₄×C₄₃	#41	1	2	yes	—
62	C₂×C₄×C₄₃	#41	1	4	yes	—
63	C₂×Dic₄₃	—	2	1	no	—
64	C₂×Dic₄₃	—	2	2	no	—
65	C₂×Dic₄₃	—	2	1	no	—
66	C₂×Dic₄₃	—	2	2	no	—
67	C₂×Dic₄₃	—	2	4	no	—
68	C₂×Dic₄₃	—	2	8	no	—
69	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
70	C₂×Dic₄₃	C₂×Q₈	1	4	yes	—
71	C₄×D₄₃	—	2	8	no	—
72	C₄×D₄₃	—	2	16	no	—
73	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
74	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
75	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
76	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
77	C₂²×C₄₃	C₂×#41	1	2	yes	—
78	C₂×D₄₃	—	2	2	no	—
79	C₂×D₄₃	—	2	4	no	—
80	C₂×D₄₃	—	2	2	no	—
81	C₂×D₄₃	—	2	4	no	—
82	C₂×D₄₃	C₄⋊Q₈	1	4	yes	complemented
83	C₄×C₄₃	—	4	4	no	—
84	C₄×C₄₃	#121	1	4	yes	—
85	C₄×C₄₃	C₂²⋊Q₈	1	8	yes	complemented
86	Dic₄₃	—	2	2	no	—
87	Dic₄₃	—	2	4	no	—
88	Dic₄₃	—	4	4	no	—
89	#2857	—	43	1	no	maximal, Sylow
90	C₂×C₄₃	C₂×#121	1	1	yes	characteristic
91	C₂×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
92	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
93	C₂×C₄₃	#532	1	1	yes	characteristic
94	C₂×C₄₃	#533	1	2	yes	—
95	D₄₃	—	2	4	no	—
96	C₂×C₄⋊Q₈	D₄₃	1	1	yes	characteristic, complemented
97	C₂×C₂²⋊Q₈	—	43	2	no	—
98	C₂²×C₄²	—	43	1	no	—
99	#391	—	43	2	no	—
100	#389	—	43	4	no	—
101	#384	—	43	1	no	—
102	#380	—	43	4	no	—
103	C₄₃	#2857	1	1	yes	characteristic, complemented, Sylow
104	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
105	C₂³×C₄	—	43	1	no	—
106	C₂³×C₄	—	43	2	no	—
107	C₄⋊Q₈	—	2	4	no	—
108	C₂²⋊Q₈	—	86	8	no	—
109	C₂×C₄⋊C₄	—	43	4	no	—
110	C₂×C₄⋊C₄	—	43	2	no	—
111	C₂×C₄⋊C₄	—	43	4	no	—
112	C₂×C₄⋊C₄	C₂×D₄₃	1	4	yes	—
113	C₂×C₂²⋊C₄	—	43	4	no	—
114	C₂×C₄²	—	43	2	no	—
115	C₂×C₄²	—	43	1	no	—
116	C₂×C₄²	—	86	4	no	—
117	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
118	#95	—	43	8	no	—
119	C₂⁴	—	43	1	no	—
120	C₂×Q₈	—	2	4	no	—
121	C₂×Q₈	—	2	4	no	—
122	C₂×Q₈	—	2	4	no	—
123	C₂²×C₄	—	43	2	no	—
124	C₂²×C₄	—	43	1	no	—
125	C₂²×C₄	—	43	4	no	—
126	C₂²×C₄	—	43	8	no	—
127	C₂²×C₄	—	43	4	no	—
128	C₂²×C₄	—	86	2	no	—
129	C₂²×C₄	—	86	4	no	—
130	C₂²×C₄	—	86	2	no	—
131	C₂²×C₄	—	86	4	no	—
132	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
133	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
135	C₄⋊C₄	—	2	8	no	—
136	C₄⋊C₄	—	86	8	no	—
137	C₄⋊C₄	—	86	4	no	—
138	C₄⋊C₄	—	86	8	no	—
139	C₂²⋊C₄	—	86	8	no	—
140	C₄²	—	86	2	no	—
141	C₄²	—	86	4	no	—
142	C₄²	C₂²⋊D₄₃	1	4	yes	—
143	C₂³	—	43	2	no	—
144	C₂³	—	43	4	no	—
145	C₂³	—	86	1	no	—
146	C₂³	—	86	1	no	—
147	C₂³	—	86	2	no	—
148	C₂³	C₂³×D₄₃	1	1	yes	characteristic
149	Q₈	—	4	8	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	43	2	no	—
154	C₂×C₄	—	43	4	no	—
155	C₂×C₄	—	86	1	no	—
156	C₂×C₄	—	86	2	no	—
157	C₂×C₄	—	86	1	no	—
158	C₂×C₄	—	86	2	no	—
159	C₂×C₄	—	86	8	no	—
160	C₂×C₄	—	86	16	no	—
161	C₂×C₄	—	86	4	no	—
162	C₂×C₄	—	86	8	no	—
163	C₂×C₄	D₄×D₄₃	1	2	yes	—
164	C₂×C₄	#10621900	1	2	yes	—
165	C₂×C₄	Q₈×D₄₃	1	4	yes	—
166	C₂×C₄	#10621902	1	4	yes	—
167	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
168	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
169	C₂²	—	43	4	no	—
170	C₂²	—	86	2	no	—
171	C₂²	—	86	4	no	—
172	C₂²	—	86	2	no	—
173	C₂²	—	86	4	no	—
174	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
175	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
176	C₂²	C₂×Q₈×D₄₃	1	2	yes	—
177	C₂²	C₂×#10621900	1	1	yes	characteristic
178	C₂²	C₂×#10621902	1	2	yes	—
179	C₄	—	4	4	no	—
180	C₄	—	86	2	no	—
181	C₄	—	86	4	no	—
182	C₄	—	172	4	no	—
183	C₄	#13063296	1	4	yes	—
184	C₄	#13063301	1	8	yes	complemented
185	C₂	—	86	4	no	—
186	C₂	C₂×#13063296	1	1	yes	characteristic
187	C₂	C₂×#13063301	1	2	yes	—
188	C₂	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
189	C₂	#14583450	1	1	yes	characteristic
190	C₂	#14583454	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063301

C₂

yes

maximal

C₂×C₄²×D₄₃

C₂

yes

maximal, characteristic

#14582806

C₂

yes

maximal, complemented

#14582795

C₂

yes

maximal, complemented

#14582769

C₂

yes

maximal, characteristic, complemented

#14582756

C₂

yes

maximal

C₂×C₄⋊Q₈×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

characteristic

C₂²×C₄×D₄₃

C₂²

yes

—

#13063301

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₄²×D₄₃

—

C₄₃⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

C₂³

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

D₄

yes

—

C₂×C₄×D₄₃

Q₈

yes

complemented

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂×D₄

yes

—

C₂²×D₄₃

C₂×Q₈

yes

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×Q₈

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₄⋊Q₈

yes

complemented

C₄×C₄₃

—

C₄×C₄₃

#121

yes

—

C₄×C₄₃

C₂²⋊Q₈

yes

complemented

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₂²⋊Q₈

yes

—

C₂×C₄₃

C₂×C₄⋊Q₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

C₂×C₄⋊Q₈

D₄₃

yes

characteristic, complemented

C₂×C₂²⋊Q₈

—

C₂²×C₄²

—

#391

—

100

#389

—

101

#384

—

102

#380

—

103

C₄₃

#2857

yes

characteristic, complemented, Sylow

104

C₂²×Q₈

C₂×D₄₃

yes

—

105

C₂³×C₄

—

106

C₂³×C₄

—

107

C₄⋊Q₈

—

108

C₂²⋊Q₈

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

113

C₂×C₂²⋊C₄

—

114

C₂×C₄²

—

115

C₂×C₄²

—

116

C₂×C₄²

—

117

C₂×C₄²

C₂×D₄₃

yes

characteristic

118

#95

—

119

C₂⁴

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

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

—

132

C₂²×C₄

C₂²×D₄₃

yes

—

133

C₂²×C₄

C₂²×D₄₃

yes

characteristic

134

C₂²×C₄

C₂²×D₄₃

yes

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₂²⋊C₄

—

140

C₄²

—

141

C₄²

—

142

C₄²

C₂²⋊D₄₃

yes

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

—

148

C₂³

C₂³×D₄₃

yes

characteristic

149

Q₈

—

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

D₄×D₄₃

yes

—

164

C₂×C₄

#10621900

yes

—

165

C₂×C₄

Q₈×D₄₃

yes

—

166

C₂×C₄

#10621902

yes

—

167

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

168

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

C₂×D₄×D₄₃

yes

characteristic

175

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

176

C₂²

C₂×Q₈×D₄₃

yes

—

177

C₂²

C₂×#10621900

yes

characteristic

178

C₂²

C₂×#10621902

yes

—

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

172

—

183

C₄

#13063296

yes

—

184

C₄

#13063301

yes

complemented

185

C₂

—

186

C₂

C₂×#13063296

yes

characteristic

187

C₂

C₂×#13063301

yes

—

188

C₂

C₄⋊Q₈×D₄₃

yes

characteristic

189

C₂

#14583450

yes

characteristic

190

C₂

#14583454

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂×C₄⋊Q₈×C₄₃	C₂
hypercenter	C₂×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#2857
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂×C₄⋊Q₈×C₄₃

C₂

hypercenter

C₂×C₄⋊Q₈

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
3. #14582806	C₂	semidirect
4. #14582795	C₂	semidirect
5. #14582769	C₂	semidirect
7. C₂×C₄⋊Q₈×C₄₃	C₂	semidirect
38. C₂×C₄×D₄₃	Q₈	semidirect
82. C₂×D₄₃	C₄⋊Q₈	semidirect
85. C₄×C₄₃	C₂²⋊Q₈	semidirect
96. C₂×C₄⋊Q₈	D₄₃	semidirect
103. C₄₃	#2857	semidirect
184. C₄	#13063301	semidirect

H ≅ G/N

type

3. #14582806

C₂

semidirect

4. #14582795

C₂

semidirect

5. #14582769

C₂

semidirect

7. C₂×C₄⋊Q₈×C₄₃

C₂

semidirect

38. C₂×C₄×D₄₃

Q₈

semidirect

82. C₂×D₄₃

C₄⋊Q₈

semidirect

85. C₄×C₄₃

C₂²⋊Q₈

semidirect

96. C₂×C₄⋊Q₈

D₄₃

semidirect

103. C₄₃

#2857

semidirect

184. C₄

#13063301

semidirect

Subgroups — #19142942

Conjugacy classes of subgroups

Complements