Group #14569459 — subgroups

Subgroups — #14569459

Order 2432.

488 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597318	C₂	1	1	yes	maximal, characteristic
3	#11926484	C₂	1	2	yes	maximal, complemented
4	#11926481	C₂	1	2	yes	maximal
5	#11926465	C₂	1	2	yes	maximal, complemented
6	#11926457	C₂	1	2	yes	maximal
7	#11926443	C₂	1	2	yes	maximal, complemented
8	#11926401	C₂	1	2	yes	maximal
9	C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₈	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
20	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
23	#10597318	—	2	4	no	—
24	#10597315	—	2	4	no	—
25	C₁₉×#95	C₂²	1	2	yes	—
26	C₁₉×#95	C₂²	1	2	yes	—
27	C₁₉⋊#95	C₂²	1	4	yes	—
28	C₁₉⋊#95	C₂²	1	4	yes	—
29	C₂³×D₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₉	C₂³	1	4	yes	—
35	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
36	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
38	C₂×C₄×D₁₉	—	2	2	no	—
39	C₂×C₄×D₁₉	—	2	2	no	—
40	C₂×C₄×D₁₉	Q₈	1	4	yes	complemented
41	C₂×Dic₃₈	—	2	4	no	—
42	C₂×Dic₃₈	—	4	4	no	—
43	C₄⋊C₄×C₁₉	—	2	4	no	—
44	C₄²×C₁₉	D₄	1	4	yes	—
45	(C₂×D₁₉)⋊C₄	—	2	2	no	—
46	(C₂×D₁₉)⋊C₄	—	2	2	no	—
47	(C₂×D₁₉)⋊C₄	—	4	4	no	—
48	C₄⋊Dic₁₉	—	2	4	no	—
49	C₄⋊Dic₁₉	—	2	4	no	—
50	C₄⋊Dic₁₉	—	4	4	no	—
51	Dic₁₉⋊C₄	—	2	2	no	—
52	Dic₁₉⋊C₄	—	2	2	no	—
53	C₄×Dic₁₉	—	2	2	no	—
54	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
55	C₂²×D₁₉	—	2	1	no	—
56	C₂²×D₁₉	—	2	1	no	—
57	C₂²×D₁₉	—	2	2	no	—
58	C₂²×D₁₉	—	2	2	no	—
59	C₂²×D₁₉	C₂×Q₈	1	2	yes	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	4	no	—
63	C₂×C₄×C₁₉	—	2	4	no	—
64	C₂×C₄×C₁₉	—	2	4	no	—
65	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
69	C₂×C₄×C₁₉	#41	1	2	yes	—
70	C₂×Dic₁₉	—	2	1	no	—
71	C₂×Dic₁₉	—	2	1	no	—
72	C₂×Dic₁₉	—	2	1	no	—
73	C₂×Dic₁₉	—	2	1	no	—
74	C₂×Dic₁₉	—	2	4	no	—
75	C₂×Dic₁₉	—	2	2	no	—
76	C₂×Dic₁₉	—	2	4	no	—
77	C₂×Dic₁₉	—	2	4	no	—
78	C₂×Dic₁₉	—	2	2	no	—
79	C₂×Dic₁₉	C₂×Q₈	1	2	yes	—
80	C₄×D₁₉	—	2	8	no	—
81	Dic₃₈	—	4	8	no	—
82	#2628	—	19	1	no	maximal, Sylow
83	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
84	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
85	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
86	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
87	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
88	C₂×D₁₉	—	2	2	no	—
89	C₂×D₁₉	—	2	4	no	—
90	C₂×D₁₉	—	4	1	no	—
91	C₂×D₁₉	—	4	1	no	—
92	C₂×D₁₉	—	4	2	no	—
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	4	4	no	—
96	C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
97	Dic₁₉	—	2	2	no	—
98	Dic₁₉	—	4	4	no	—
99	Dic₁₉	—	4	1	no	—
100	Dic₁₉	—	4	1	no	—
101	C₂×C₄⋊Q₈	—	19	1	no	—
102	C₂×#117	—	19	1	no	—
103	#400	—	19	2	no	—
104	#399	—	19	2	no	—
105	#395	—	19	2	no	—
106	#393	—	19	2	no	—
107	#389	—	19	2	no	—
108	#382	D₁₉	1	1	yes	characteristic, complemented
109	#380	—	19	2	no	—
110	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
111	C₂×C₁₉	#535	1	1	yes	characteristic
112	C₂×C₁₉	#536	1	1	yes	characteristic
113	C₂×C₁₉	#542	1	2	yes	—
114	C₂×C₁₉	#544	1	2	yes	—
115	D₁₉	—	4	2	no	—
116	C₂²×Q₈	—	19	2	no	—
117	C₂³×C₄	—	19	1	no	—
118	C₄⋊Q₈	—	38	4	no	—
119	#117	—	38	4	no	—
120	C₂×C₄⋊C₄	—	19	1	no	—
121	C₂×C₄⋊C₄	—	19	1	no	—
122	C₂×C₄⋊C₄	—	19	2	no	—
123	C₂×C₄⋊C₄	—	19	2	no	—
124	C₂×C₄⋊C₄	—	19	4	no	—
125	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
126	C₂×C₂²⋊C₄	—	19	1	no	—
127	C₂×C₂²⋊C₄	—	19	1	no	—
128	C₂×C₂²⋊C₄	—	19	4	no	—
129	C₂×C₄²	—	19	1	no	—
130	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
131	#95	—	19	4	no	—
132	#95	—	19	4	no	—
133	#95	C₂×D₁₉	1	2	yes	—
134	#95	C₂×D₁₉	1	2	yes	—
135	C₁₉	#2628	1	1	yes	characteristic, complemented, Sylow
136	C₂⁴	—	19	1	no	—
137	C₂×Q₈	—	38	4	no	—
138	C₂×Q₈	—	76	4	no	—
139	C₂²×C₄	—	19	1	no	—
140	C₂²×C₄	—	19	4	no	—
141	C₂²×C₄	—	19	1	no	—
142	C₂²×C₄	—	19	4	no	—
143	C₂²×C₄	—	19	1	no	—
144	C₂²×C₄	—	38	2	no	—
145	C₂²×C₄	—	38	2	no	—
146	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
147	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
148	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
149	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	38	2	no	—
152	C₄⋊C₄	—	38	2	no	—
153	C₄⋊C₄	—	38	4	no	—
154	C₄⋊C₄	—	38	4	no	—
155	C₄⋊C₄	—	76	4	no	—
156	C₂²⋊C₄	—	38	2	no	—
157	C₂²⋊C₄	—	38	2	no	—
158	C₂²⋊C₄	—	76	4	no	—
159	C₄²	—	38	2	no	—
160	C₄²	D₇₆	1	4	yes	—
161	C₂³	—	19	2	no	—
162	C₂³	—	38	1	no	—
163	C₂³	—	38	1	no	—
164	C₂³	—	38	2	no	—
165	C₂³	—	38	2	no	—
166	C₂³	C₂³×D₁₉	1	1	yes	characteristic
167	Q₈	—	76	8	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	19	2	no	—
174	C₂×C₄	—	38	1	no	—
175	C₂×C₄	—	38	1	no	—
176	C₂×C₄	—	38	8	no	—
177	C₂×C₄	—	38	1	no	—
178	C₂×C₄	—	38	1	no	—
179	C₂×C₄	—	38	4	no	—
180	C₂×C₄	—	38	4	no	—
181	C₂×C₄	—	38	2	no	—
182	C₂×C₄	—	38	4	no	—
183	C₂×C₄	—	38	2	no	—
184	C₂×C₄	C₂×D₇₆	1	2	yes	—
185	C₂×C₄	C₂×D₇₆	1	2	yes	—
186	C₂×C₄	C₂×D₇₆	1	2	yes	—
187	C₂×C₄	#64543	1	2	yes	—
188	C₂×C₄	Q₈×D₁₉	1	2	yes	—
189	C₂²	—	38	2	no	—
190	C₂²	—	38	4	no	—
191	C₂²	—	76	1	no	—
192	C₂²	—	76	1	no	—
193	C₂²	—	76	2	no	—
194	C₂²	C₂²×D₇₆	1	1	yes	characteristic
195	C₂²	C₂×#64543	1	1	yes	characteristic
196	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
197	C₂²	#10597435	1	2	yes	—
198	C₂²	#10597436	1	2	yes	—
199	C₄	—	2	2	no	—
200	C₄	—	2	2	no	—
201	C₄	—	4	4	no	—
202	C₄	—	38	2	no	—
203	C₄	—	76	4	no	—
204	C₄	—	76	1	no	—
205	C₄	—	76	1	no	—
206	C₄	#10597343	1	4	yes	—
207	C₂	—	76	2	no	—
208	C₂	C₂×#10597343	1	1	yes	characteristic
209	C₂	#11927113	1	1	yes	characteristic
210	C₂	#11927120	1	1	yes	characteristic
211	C₂	#11927163	1	2	yes	—
212	C₂	#11927174	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic, complemented

C₂×#10597318

C₂

yes

maximal, characteristic

#11926484

C₂

yes

maximal, complemented

#11926481

C₂

yes

maximal

#11926465

C₂

yes

maximal, complemented

#11926457

C₂

yes

maximal

#11926443

C₂

yes

maximal, complemented

#11926401

C₂

yes

maximal

C₁₉×#382

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

#10597318

—

#10597315

—

C₁₉×#95

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

Q₈

yes

complemented

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

C₄×D₁₉

—

Dic₃₈

—

#2628

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

100

Dic₁₉

—

101

C₂×C₄⋊Q₈

—

102

C₂×#117

—

103

#400

—

104

#399

—

105

#395

—

106

#393

—

107

#389

—

108

#382

D₁₉

yes

characteristic, complemented

109

#380

—

110

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

111

C₂×C₁₉

#535

yes

characteristic

112

C₂×C₁₉

#536

yes

characteristic

113

C₂×C₁₉

#542

yes

—

114

C₂×C₁₉

#544

yes

—

115

D₁₉

—

116

C₂²×Q₈

—

117

C₂³×C₄

—

118

C₄⋊Q₈

—

119

#117

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

126

C₂×C₂²⋊C₄

—

127

C₂×C₂²⋊C₄

—

128

C₂×C₂²⋊C₄

—

129

C₂×C₄²

—

130

C₂×C₄²

C₂×D₁₉

yes

characteristic

131

#95

—

132

#95

—

133

#95

C₂×D₁₉

yes

—

134

#95

C₂×D₁₉

yes

—

135

C₁₉

#2628

yes

characteristic, complemented, Sylow

136

C₂⁴

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

C₂²×D₁₉

yes

—

147

C₂²×C₄

C₂²×D₁₉

yes

characteristic

148

C₂²×C₄

C₂²×D₁₉

yes

characteristic

149

C₂²×C₄

C₂²×D₁₉

yes

characteristic

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₂²⋊C₄

—

157

C₂²⋊C₄

—

158

C₂²⋊C₄

—

159

C₄²

—

160

C₄²

D₇₆

yes

—

161

C₂³

—

162

C₂³

—

163

C₂³

—

164

C₂³

—

165

C₂³

—

166

C₂³

C₂³×D₁₉

yes

characteristic

167

Q₈

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

C₂×D₇₆

yes

—

185

C₂×C₄

C₂×D₇₆

yes

—

186

C₂×C₄

C₂×D₇₆

yes

—

187

C₂×C₄

#64543

yes

—

188

C₂×C₄

Q₈×D₁₉

yes

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

C₂²×D₇₆

yes

characteristic

195

C₂²

C₂×#64543

yes

characteristic

196

C₂²

C₂×Q₈×D₁₉

yes

characteristic

197

C₂²

#10597435

yes

—

198

C₂²

#10597436

yes

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

#10597343

yes

—

207

C₂

—

208

C₂

C₂×#10597343

yes

characteristic

209

C₂

#11927113

yes

characteristic

210

C₂

#11927120

yes

characteristic

211

C₂

#11927163

yes

—

212

C₂

#11927174

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#382	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	#382	D₁₉
hypocenter	C₁₉	#2628
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#382

C₂

prime radical

C₂³×D₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
1. C₂×#10597315	C₂	semidirect
3. #11926484	C₂	semidirect
5. #11926465	C₂	semidirect
7. #11926443	C₂	semidirect
9. C₁₉×#382	C₂	semidirect
40. C₂×C₄×D₁₉	Q₈	semidirect
108. #382	D₁₉	semidirect
135. C₁₉	#2628	semidirect

H ≅ G/N

type

1. C₂×#10597315

C₂

semidirect

3. #11926484

C₂

semidirect

5. #11926465

C₂

semidirect

7. #11926443

C₂

semidirect

9. C₁₉×#382

C₂

semidirect

40. C₂×C₄×D₁₉

Q₈

semidirect

108. #382

D₁₉

semidirect

135. C₁₉

#2628

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10597315	2
C₂×#10597318	2
#11926484	2
#11926481	2
#11926465	2
#11926457	2
#11926443	2
#11926401	2
C₁₉×#382	2
#2628	19

subgroup

index

C₁₉×#382

Subgroups — #14569459

Conjugacy classes of subgroups

Complements

Maximal subgroups