Group #19139631 — subgroups

Subgroups — #19139631

Order 5504.

452 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13063316	C₂	1	2	yes	maximal
2	#14582832	C₂	1	4	yes	maximal
3	#14582798	C₂	1	2	yes	maximal
4	#14582795	C₂	1	2	yes	maximal
5	#14582768	C₂	1	2	yes	maximal
6	C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
8	C₄₃×#384	C₂	1	1	yes	maximal, characteristic
9	#13063316	—	2	8	no	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
16	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
17	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
18	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
19	C₄₃⋊#95	C₂²	1	4	yes	—
20	C₄₃⋊#95	C₂²	1	2	yes	—
21	C₄₃⋊#95	C₂²	1	2	yes	—
22	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
25	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
27	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
30	C₂²×Dic₄₃	C₂³	1	2	yes	—
31	C₂²×Dic₄₃	C₂³	1	2	yes	—
32	C₂²×Dic₄₃	C₂³	1	2	yes	—
33	C₂²×Dic₄₃	C₂³	1	2	yes	—
34	C₄⋊C₄×C₄₃	—	2	4	no	—
35	C₄⋊C₄×C₄₃	—	2	4	no	—
36	C₄⋊C₄×C₄₃	—	4	2	no	—
37	C₄²×C₄₃	Q₈	1	4	yes	—
38	C₄⋊Dic₄₃	—	2	2	no	—
39	C₄⋊Dic₄₃	—	2	2	no	—
40	C₄⋊Dic₄₃	—	2	8	no	—
41	C₄⋊Dic₄₃	D₄	1	4	yes	—
42	C₄⋊Dic₄₃	Q₈	1	4	yes	—
43	Dic₄₃⋊C₄	—	2	8	no	—
44	Dic₄₃⋊C₄	—	4	4	no	—
45	C₄×Dic₄₃	—	2	4	no	—
46	C₄×Dic₄₃	—	2	4	no	—
47	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	2	1	no	—
50	C₂×C₄×C₄₃	—	2	4	no	—
51	C₂×C₄×C₄₃	—	2	4	no	—
52	C₂×C₄×C₄₃	—	2	4	no	—
53	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
55	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
56	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
57	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
58	C₂×C₄×C₄₃	#41	1	2	yes	—
59	C₂×C₄×C₄₃	#41	1	2	yes	—
60	C₂×Dic₄₃	—	2	2	no	—
61	C₂×Dic₄₃	—	2	2	no	—
62	C₂×Dic₄₃	—	2	2	no	—
63	C₂×Dic₄₃	—	2	2	no	—
64	C₂×Dic₄₃	—	2	2	no	—
65	C₂×Dic₄₃	—	2	2	no	—
66	C₂×Dic₄₃	—	2	2	no	—
67	C₂×Dic₄₃	—	2	2	no	—
68	C₂×Dic₄₃	—	2	2	no	—
69	C₂×Dic₄₃	—	2	2	no	—
70	C₂×Dic₄₃	C₂×D₄	1	4	yes	—
71	C₂×Dic₄₃	C₂×Q₈	1	4	yes	—
72	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
73	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
74	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
75	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
76	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
77	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
78	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
79	C₄×C₄₃	—	2	2	no	—
80	C₄×C₄₃	—	4	4	no	—
81	C₄×C₄₃	#125	1	4	yes	complemented
82	C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
83	Dic₄₃	—	2	4	no	—
84	Dic₄₃	—	2	4	no	—
85	Dic₄₃	—	4	2	no	—
86	Dic₄₃	—	4	2	no	—
87	#2552	—	43	1	no	maximal, Sylow
88	C₂×C₄₃	C₂×#125	1	1	yes	characteristic
89	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
90	C₂×C₄₃	#544	1	1	yes	characteristic
91	C₂×C₄₃	#547	1	1	yes	characteristic
92	C₂×C₄₃	#550	1	1	yes	characteristic
93	C₂×C₄₃	#554	1	1	yes	characteristic
94	C₂×C₄₃	#557	1	1	yes	characteristic
95	C₂×#125	—	43	2	no	—
96	#398	—	43	4	no	—
97	#389	—	43	2	no	—
98	#389	—	43	2	no	—
99	#384	—	43	2	no	—
100	#384	D₄₃	1	1	yes	characteristic
101	C₄×C₄⋊C₄	—	43	1	no	—
102	C₄×C₄⋊C₄	—	43	1	no	—
103	C₄₃	#2552	1	1	yes	characteristic, complemented, Sylow
104	#125	—	86	8	no	—
105	C₂×C₄⋊C₄	—	43	1	no	—
106	C₂×C₄⋊C₄	—	43	1	no	—
107	C₂×C₄⋊C₄	—	43	4	no	—
108	C₂×C₄⋊C₄	—	43	4	no	—
109	C₂×C₄⋊C₄	—	43	1	no	—
110	C₂×C₄⋊C₄	—	43	1	no	—
111	C₂×C₄⋊C₄	—	43	4	no	—
112	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
113	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
114	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
115	C₂×C₄²	—	43	2	no	—
116	C₂×C₄²	—	43	2	no	—
117	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
118	#95	—	43	2	no	—
119	#95	—	43	2	no	—
120	#95	—	43	4	no	—
121	C₂²×C₄	—	43	2	no	—
122	C₂²×C₄	—	43	2	no	—
123	C₂²×C₄	—	43	2	no	—
124	C₂²×C₄	—	43	2	no	—
125	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
126	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
127	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
128	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
129	C₄⋊C₄	—	2	4	no	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	4	2	no	—
132	C₄⋊C₄	—	43	4	no	—
133	C₄⋊C₄	—	43	4	no	—
134	C₄⋊C₄	—	86	8	no	—
135	C₄⋊C₄	—	86	8	no	—
136	C₄⋊C₄	—	86	2	no	—
137	C₄⋊C₄	—	86	2	no	—
138	C₄⋊C₄	—	172	4	no	—
139	C₄²	—	86	4	no	—
140	C₄²	—	86	4	no	—
141	C₄²	Dic₈₆	1	4	yes	—
142	C₂³	C₂³×D₄₃	1	1	yes	characteristic
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	43	4	no	—
149	C₂×C₄	—	43	4	no	—
150	C₂×C₄	—	86	2	no	—
151	C₂×C₄	—	86	2	no	—
152	C₂×C₄	—	86	2	no	—
153	C₂×C₄	—	86	2	no	—
154	C₂×C₄	—	86	2	no	—
155	C₂×C₄	—	86	2	no	—
156	C₂×C₄	—	86	2	no	—
157	C₂×C₄	—	86	2	no	—
158	C₂×C₄	—	86	2	no	—
159	C₂×C₄	—	86	2	no	—
160	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
161	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
162	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
163	C₂×C₄	D₄×D₄₃	1	2	yes	—
164	C₂×C₄	#10621900	1	2	yes	—
165	C₂×C₄	Q₈×D₄₃	1	2	yes	—
166	C₂×C₄	#10621902	1	2	yes	—
167	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
168	C₂²	C₂×Q₈×D₄₃	1	1	yes	characteristic
169	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
170	C₂²	C₂×#10621900	1	1	yes	characteristic
171	C₂²	C₂×#10621902	1	1	yes	characteristic
172	C₂²	#13063370	1	1	yes	characteristic
173	C₂²	#13063373	1	1	yes	characteristic
174	C₄	—	2	2	no	—
175	C₄	—	4	4	no	—
176	C₄	—	86	4	no	—
177	C₄	—	86	4	no	—
178	C₄	—	172	2	no	—
179	C₄	—	172	2	no	—
180	C₄	#13063316	1	4	yes	complemented
181	C₄	#13063324	1	4	yes	—
182	C₂	C₂×#13063316	1	1	yes	characteristic
183	C₂	C₂×#13063324	1	1	yes	characteristic
184	C₂	#14583530	1	1	yes	characteristic
185	C₂	#14583552	1	1	yes	characteristic
186	C₂	#14583569	1	1	yes	characteristic
187	C₂	#14583610	1	1	yes	characteristic
188	C₂	#14583624	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063316

C₂

yes

maximal

#14582832

C₂

yes

maximal

#14582798

C₂

yes

maximal

#14582795

C₂

yes

maximal

#14582768

C₂

yes

maximal

C₄×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

C₄₃×#384

C₂

yes

maximal, characteristic

#13063316

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

C₄⋊Dic₄₃

Q₈

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

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×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#125

yes

complemented

C₄×C₄₃

C₄⋊Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄⋊Q₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

—

—

100

#384

D₄₃

yes

characteristic

101

C₄×C₄⋊C₄

—

102

C₄×C₄⋊C₄

—

103

C₄₃

#2552

yes

characteristic, complemented, Sylow

104

#125

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

113

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

114

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

115

C₂×C₄²

—

116

C₂×C₄²

—

117

C₂×C₄²

C₂×D₄₃

yes

characteristic

118

#95

—

119

#95

—

120

#95

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

C₂²×D₄₃

yes

—

126

C₂²×C₄

C₂²×D₄₃

yes

characteristic

127

C₂²×C₄

C₂²×D₄₃

yes

characteristic

128

C₂²×C₄

C₂²×D₄₃

yes

characteristic

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

172

—

139

C₄²

—

140

C₄²

—

141

C₄²

Dic₈₆

yes

—

142

C₂³

C₂³×D₄₃

yes

characteristic

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

—

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

C₂×Dic₈₆

yes

—

161

C₂×C₄

C₂×Dic₈₆

yes

—

162

C₂×C₄

C₂×Dic₈₆

yes

—

163

C₂×C₄

D₄×D₄₃

yes

—

164

C₂×C₄

#10621900

yes

—

165

C₂×C₄

Q₈×D₄₃

yes

—

166

C₂×C₄

#10621902

yes

—

167

C₂²

C₂×D₄×D₄₃

yes

characteristic

168

C₂²

C₂×Q₈×D₄₃

yes

characteristic

169

C₂²

C₂²×Dic₈₆

yes

characteristic

170

C₂²

C₂×#10621900

yes

characteristic

171

C₂²

C₂×#10621902

yes

characteristic

172

C₂²

#13063370

yes

characteristic

173

C₂²

#13063373

yes

characteristic

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

172

—

179

C₄

—

172

—

180

C₄

#13063316

yes

complemented

181

C₄

#13063324

yes

—

182

C₂

C₂×#13063316

yes

characteristic

183

C₂

C₂×#13063324

yes

characteristic

184

C₂

#14583530

yes

characteristic

185

C₂

#14583552

yes

characteristic

186

C₂

#14583569

yes

characteristic

187

C₂

#14583610

yes

characteristic

188

C₂

#14583624

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#384	C₂
hypercenter	#384	D₄₃
hypocenter	C₄₃	#2552
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#384

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
81. C₄×C₄₃	#125	semidirect
103. C₄₃	#2552	semidirect
180. C₄	#13063316	semidirect

H ≅ G/N

type

81. C₄×C₄₃

#125

semidirect

103. C₄₃

#2552

semidirect

180. C₄

#13063316

semidirect

Subgroups — #19139631

Conjugacy classes of subgroups

Complements