Group #19137462 — subgroups

Subgroups — #19137462

Order 5504.

604 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 221 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×#13063281	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582797	C₂	1	2	yes	maximal, complemented
4	#14582784	C₂	1	4	yes	maximal, complemented
5	#14582760	C₂	1	2	yes	maximal
6	#14582759	C₂	1	1	yes	maximal, characteristic
7	C₄×C₄⋊Dic₄₃	C₂	1	2	yes	maximal, complemented
8	C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₄₃	C₂²	1	2	yes	—
10	#13063281	—	2	8	no	—
11	C₂×C₄⋊Dic₄₃	C₄	1	8	yes	complemented
12	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
17	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
18	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
19	C₄₃⋊#95	C₂²	1	2	yes	—
20	C₄₃⋊#95	C₂²	1	4	yes	—
21	C₄₃⋊#95	C₂²	1	4	yes	—
22	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
26	#95×C₄₃	C₂²	1	2	yes	—
27	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	—	2	4	no	—
29	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
31	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
33	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
34	C₂²×Dic₄₃	—	2	4	no	—
35	C₂²×Dic₄₃	—	2	4	no	—
36	C₂²×Dic₄₃	C₂×C₄	1	8	yes	—
37	C₂²×Dic₄₃	C₂³	1	4	yes	—
38	C₂²×Dic₄₃	C₂³	1	2	yes	—
39	C₂²×Dic₄₃	C₂³	1	2	yes	—
40	C₂²⋊C₄×C₄₃	—	2	2	no	—
41	C₂²⋊C₄×C₄₃	D₄	1	4	yes	—
42	C₄²×C₄₃	—	2	4	no	—
43	C₂²⋊Dic₄₃	—	2	4	no	—
44	C₄⋊Dic₄₃	—	2	4	no	—
45	C₄⋊Dic₄₃	C₂×C₄	1	8	yes	—
46	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
47	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
48	Dic₄₃⋊C₄	—	2	8	no	—
49	C₄×Dic₄₃	—	2	8	no	—
50	C₂³×C₄₃	—	2	2	no	—
51	C₂³×C₄₃	—	2	2	no	—
52	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
53	C₂³×C₄₃	C₂×D₄	1	2	yes	—
54	C₂³×C₄₃	#41	1	2	yes	—
55	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
56	C₂×C₄×C₄₃	—	2	2	no	—
57	C₂×C₄×C₄₃	—	2	2	no	—
58	C₂×C₄×C₄₃	—	2	2	no	—
59	C₂×C₄×C₄₃	—	2	8	no	—
60	C₂×C₄×C₄₃	—	2	2	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	2	2	no	—
63	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
64	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
66	C₂×C₄×C₄₃	#41	1	4	yes	—
67	C₂×Dic₄₃	—	2	16	no	—
68	C₂×Dic₄₃	—	2	2	no	—
69	C₂×Dic₄₃	—	2	2	no	—
70	C₂×Dic₄₃	—	2	2	no	—
71	C₂×Dic₄₃	—	2	2	no	—
72	C₂×Dic₄₃	—	2	4	no	—
73	C₂×Dic₄₃	—	2	4	no	—
74	C₂×Dic₄₃	—	2	4	no	—
75	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
76	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
77	C₂²×C₄₃	—	2	2	no	—
78	C₂²×C₄₃	—	2	2	no	—
79	C₂²×C₄₃	—	2	4	no	—
80	C₂²×C₄₃	—	2	4	no	—
81	C₂²×C₄₃	C₄×D₄	1	4	yes	—
82	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
83	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
84	C₂²×C₄₃	C₂×#41	1	2	yes	—
85	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
86	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
87	C₄×C₄₃	—	2	2	no	—
88	C₄×C₄₃	—	2	4	no	—
89	C₄×C₄₃	—	4	2	no	—
90	C₄×C₄₃	#117	1	4	yes	complemented
91	Dic₄₃	—	2	4	no	—
92	Dic₄₃	—	2	4	no	—
93	Dic₄₃	—	4	4	no	—
94	#2344	—	43	1	no	maximal, Sylow
95	C₂×C₄₃	—	2	4	no	—
96	C₂×C₄₃	C₂×#117	1	1	yes	characteristic
97	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
98	C₂×C₄₃	#519	1	1	yes	characteristic
99	C₂×C₄₃	#547	1	2	yes	—
100	C₂×C₄₃	#552	1	2	yes	—
101	C₂×#117	—	43	2	no	—
102	C₂²×C₄⋊C₄	—	43	1	no	—
103	#389	—	43	2	no	—
104	#387	—	43	4	no	—
105	#381	—	43	2	no	—
106	#380	—	43	1	no	—
107	C₄×C₄⋊C₄	—	43	2	no	—
108	C₄×C₂²⋊C₄	D₄₃	1	1	yes	characteristic
109	C₄₃	#2344	1	1	yes	characteristic, complemented, Sylow
110	C₂³×C₄	—	43	2	no	—
111	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
112	#117	—	86	8	no	—
113	C₂×C₄⋊C₄	—	43	1	no	—
114	C₂×C₄⋊C₄	—	43	2	no	—
115	C₂×C₄⋊C₄	—	43	1	no	—
116	C₂×C₄⋊C₄	—	43	8	no	—
117	C₂×C₄⋊C₄	—	43	4	no	—
118	C₂×C₄⋊C₄	—	43	2	no	—
119	C₂×C₂²⋊C₄	—	43	2	no	—
120	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
121	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
122	C₂×C₄²	—	43	4	no	—
123	C₂×C₄²	C₂×D₄₃	1	2	yes	—
124	#95	—	43	4	no	—
125	#95	—	43	2	no	—
126	#95	—	43	4	no	—
127	#95	C₂×D₄₃	1	2	yes	—
128	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
129	C₂²×C₄	—	2	4	no	—
130	C₂²×C₄	—	43	8	no	—
131	C₂²×C₄	—	43	2	no	—
132	C₂²×C₄	—	43	2	no	—
133	C₂²×C₄	—	43	4	no	—
134	C₂²×C₄	—	86	4	no	—
135	C₂²×C₄	—	86	4	no	—
136	C₂²×C₄	C₄×D₄₃	1	4	yes	—
137	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
138	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
139	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
140	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
141	C₄⋊C₄	—	43	8	no	—
142	C₄⋊C₄	—	43	4	no	—
143	C₄⋊C₄	—	43	4	no	—
144	C₄⋊C₄	—	86	8	no	—
145	C₄⋊C₄	—	86	4	no	—
146	C₂²⋊C₄	—	2	2	no	—
147	C₂²⋊C₄	—	86	4	no	—
148	C₂²⋊C₄	D₁₇₂	1	4	yes	—
149	C₄²	—	2	4	no	—
150	C₄²	—	86	8	no	—
151	C₂³	—	2	2	no	—
152	C₂³	—	2	2	no	—
153	C₂³	C₂×C₄×D₄₃	1	2	yes	—
154	C₂³	C₂×D₁₇₂	1	2	yes	—
155	C₂³	#10621898	1	2	yes	—
156	C₂³	C₂³×D₄₃	1	1	yes	characteristic
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	43	4	no	—
165	C₂×C₄	—	43	4	no	—
166	C₂×C₄	—	86	16	no	—
167	C₂×C₄	—	86	2	no	—
168	C₂×C₄	—	86	2	no	—
169	C₂×C₄	—	86	2	no	—
170	C₂×C₄	—	86	2	no	—
171	C₂×C₄	—	86	4	no	—
172	C₂×C₄	—	86	4	no	—
173	C₂×C₄	—	86	4	no	—
174	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
175	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
176	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
177	C₂×C₄	#10621900	1	4	yes	—
178	C₂²	—	2	4	no	—
179	C₂²	—	2	4	no	—
180	C₂²	—	2	2	no	—
181	C₂²	—	2	2	no	—
182	C₂²	C₄×D₁₇₂	1	4	yes	—
183	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
184	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
185	C₂²	C₂×#10621900	1	2	yes	—
186	C₂²	C₂×#10621898	1	1	yes	characteristic
187	C₂²	#13063372	1	2	yes	—
188	C₄	—	2	4	no	—
189	C₄	—	2	2	no	—
190	C₄	—	4	2	no	—
191	C₄	—	86	4	no	—
192	C₄	—	86	4	no	—
193	C₄	—	172	4	no	—
194	C₄	#13063281	1	4	yes	complemented
195	C₂	—	2	4	no	—
196	C₂	C₂×#13063281	1	1	yes	characteristic
197	C₂	C₂×C₄×D₁₇₂	1	1	yes	characteristic
198	C₂	#14583376	1	1	yes	characteristic
199	C₂	#14583553	1	2	yes	—
200	C₂	#14583589	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063281

C₂

yes

maximal

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

#14582797

C₂

yes

maximal, complemented

#14582784

C₂

yes

maximal, complemented

#14582760

C₂

yes

maximal

#14582759

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₄₃

C₂

yes

maximal, complemented

C₄×C₂²⋊C₄×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

—

#13063281

—

C₂×C₄⋊Dic₄₃

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×D₄

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#117

yes

complemented

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2344

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#117

yes

characteristic

C₂×C₄₃

C₂×C₄×D₄

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

100

C₂×C₄₃

#552

yes

—

101

C₂×#117

—

102

C₂²×C₄⋊C₄

—

103

#389

—

104

#387

—

105

#381

—

106

#380

—

107

C₄×C₄⋊C₄

—

108

C₄×C₂²⋊C₄

D₄₃

yes

characteristic

109

C₄₃

#2344

yes

characteristic, complemented, Sylow

110

C₂³×C₄

—

111

C₂³×C₄

C₂×D₄₃

yes

characteristic

112

#117

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₂²⋊C₄

—

120

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

121

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

122

C₂×C₄²

—

123

C₂×C₄²

C₂×D₄₃

yes

—

124

#95

—

125

#95

—

126

#95

—

127

#95

C₂×D₄₃

yes

—

128

C₂⁴

C₂²×D₄₃

yes

characteristic

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

C₄×D₄₃

yes

—

137

C₂²×C₄

C₂²×D₄₃

yes

—

138

C₂²×C₄

C₂²×D₄₃

yes

characteristic

139

C₂²×C₄

C₂²×D₄₃

yes

—

140

C₂²×C₄

C₂²×D₄₃

yes

characteristic

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₂²⋊C₄

—

147

C₂²⋊C₄

—

148

C₂²⋊C₄

D₁₇₂

yes

—

149

C₄²

—

150

C₄²

—

151

C₂³

—

152

C₂³

—

153

C₂³

C₂×C₄×D₄₃

yes

—

154

C₂³

C₂×D₁₇₂

yes

—

155

C₂³

#10621898

yes

—

156

C₂³

C₂³×D₄₃

yes

characteristic

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

C₂×C₄×D₄₃

yes

—

175

C₂×C₄

C₂×C₄×D₄₃

yes

—

176

C₂×C₄

C₂×D₁₇₂

yes

—

177

C₂×C₄

#10621900

yes

—

178

C₂²

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

C₄×D₁₇₂

yes

—

183

C₂²

C₂²×C₄×D₄₃

yes

characteristic

184

C₂²

C₂²×D₁₇₂

yes

characteristic

185

C₂²

C₂×#10621900

yes

—

186

C₂²

C₂×#10621898

yes

characteristic

187

C₂²

#13063372

yes

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

172

—

194

C₄

#13063281

yes

complemented

195

C₂

—

196

C₂

C₂×#13063281

yes

characteristic

197

C₂

C₂×C₄×D₁₇₂

yes

characteristic

198

C₂

#14583376

yes

characteristic

199

C₂

#14583553

yes

—

200

C₂

#14583589

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₄×C₂²⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₄×C₂²⋊C₄	D₄₃
hypocenter	C₄₃	#2344
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Fitting

C₄×C₂²⋊C₄×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

hypercenter

C₄×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

N	H ≅ G/N	type
3. #14582797	C₂	semidirect
4. #14582784	C₂	semidirect
7. C₄×C₄⋊Dic₄₃	C₂	semidirect
11. C₂×C₄⋊Dic₄₃	C₄	semidirect
90. C₄×C₄₃	#117	semidirect
109. C₄₃	#2344	semidirect
194. C₄	#13063281	semidirect

H ≅ G/N

type

3. #14582797

C₂

semidirect

4. #14582784

C₂

semidirect

7. C₄×C₄⋊Dic₄₃

C₂

semidirect

11. C₂×C₄⋊Dic₄₃

C₄

semidirect

90. C₄×C₄₃

#117

semidirect

109. C₄₃

#2344

semidirect

194. C₄

#13063281

semidirect

Subgroups — #19137462

Conjugacy classes of subgroups

Complements