Group #14568631 — subgroups

Subgroups — #14568631

Order 2432.

604 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10597393	C₂	1	2	yes	maximal
2	C₂×C₄×D₇₆	C₂	1	1	yes	maximal, characteristic
3	#11926470	C₂	1	4	yes	maximal, complemented
4	#11926451	C₂	1	2	yes	maximal, complemented
5	#11926401	C₂	1	4	yes	maximal, complemented
6	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₂²×D₇₆	C₂²	1	1	yes	characteristic
10	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
11	C₁₉×C₄⋊Q₈	—	2	4	no	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	#10597393	—	2	8	no	—
16	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
17	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
18	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
21	C₄×D₇₆	—	2	4	no	—
22	C₁₉⋊#95	C₂²	1	2	yes	—
23	C₁₉⋊#95	C₂²	1	8	yes	—
24	C₂³×D₁₉	C₂³	1	2	yes	—
25	C₂×Q₈×C₁₉	—	2	4	no	—
26	C₂×Q₈×C₁₉	—	2	4	no	—
27	C₂×Q₈×C₁₉	—	2	4	no	—
28	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	C₂³	1	2	yes	—
33	C₂²×Dic₁₉	C₂³	1	4	yes	—
34	C₂×D₇₆	—	2	2	no	—
35	C₂×D₇₆	—	2	2	no	—
36	C₂×D₇₆	D₄	1	4	yes	—
37	C₂×C₄×D₁₉	—	2	4	no	—
38	C₂×C₄×D₁₉	—	2	8	no	—
39	C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₄⋊C₄×C₁₉	—	2	4	no	—
41	C₄²×C₁₉	D₄	1	4	yes	—
42	(C₂×D₁₉)⋊C₄	—	2	16	no	—
43	(C₂×D₁₉)⋊C₄	—	2	4	no	—
44	C₄⋊Dic₁₉	—	2	2	no	—
45	C₄⋊Dic₁₉	—	2	4	no	—
46	C₄×Dic₁₉	—	2	4	no	—
47	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂²×D₁₉	—	2	2	no	—
49	C₂²×D₁₉	—	2	4	no	—
50	C₂²×D₁₉	—	2	2	no	—
51	C₂²×D₁₉	—	2	4	no	—
52	C₂²×D₁₉	C₂×D₄	1	4	yes	—
53	Q₈×C₁₉	—	4	8	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	4	no	—
56	C₂×C₄×C₁₉	—	2	4	no	—
57	C₂×C₄×C₁₉	—	2	4	no	—
58	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₁₉	#41	1	2	yes	—
63	C₂×C₄×C₁₉	#41	1	4	yes	—
64	C₂×Dic₁₉	—	2	4	no	—
65	C₂×Dic₁₉	—	2	2	no	—
66	C₂×Dic₁₉	—	2	4	no	—
67	C₂×Dic₁₉	—	2	4	no	—
68	C₂×Dic₁₉	—	2	4	no	—
69	D₇₆	—	2	8	no	—
70	C₄×D₁₉	—	4	8	no	—
71	#2547	—	19	1	no	maximal, Sylow
72	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
73	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
74	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
75	C₂²×C₁₉	C₂×#41	1	2	yes	—
76	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
77	C₂×D₁₉	—	2	4	no	—
78	C₂×D₁₉	—	2	8	no	—
79	C₂×D₁₉	—	4	2	no	—
80	C₂×D₁₉	—	4	2	no	—
81	C₂×D₁₉	—	4	4	no	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	4	4	no	—
84	C₄×C₁₉	#121	1	4	yes	—
85	C₄×C₁₉	#124	1	4	yes	complemented
86	Dic₁₉	—	4	2	no	—
87	Dic₁₉	—	4	4	no	—
88	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic, complemented
89	C₂×#124	—	19	2	no	—
90	C₂×C₄×D₄	—	19	1	no	—
91	#397	—	19	4	no	—
92	#391	—	19	2	no	—
93	#380	—	19	4	no	—
94	C₄×C₄⋊C₄	—	19	1	no	—
95	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
96	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
97	C₂×C₁₉	#536	1	1	yes	characteristic
98	C₂×C₁₉	#547	1	2	yes	—
99	C₂×C₁₉	#556	1	2	yes	—
100	D₁₉	—	4	4	no	—
101	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
102	C₂²×D₄	—	19	1	no	—
103	C₂³×C₄	—	19	2	no	—
104	C₄⋊Q₈	—	2	4	no	—
105	#124	—	38	8	no	—
106	C₄×D₄	—	38	4	no	—
107	C₂×C₄⋊C₄	—	19	1	no	—
108	C₂×C₄⋊C₄	—	19	2	no	—
109	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
110	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
111	C₂×C₂²⋊C₄	—	19	2	no	—
112	C₂×C₂²⋊C₄	—	19	8	no	—
113	C₂×C₄²	—	19	2	no	—
114	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
115	#95	—	19	2	no	—
116	#95	—	19	8	no	—
117	C₁₉	#2547	1	1	yes	characteristic, complemented, Sylow
118	C₂⁴	—	19	2	no	—
119	C₂×Q₈	—	2	4	no	—
120	C₂×Q₈	—	2	4	no	—
121	C₂×Q₈	—	2	4	no	—
122	C₂×D₄	—	19	4	no	—
123	C₂×D₄	—	38	2	no	—
124	C₂×D₄	—	38	2	no	—
125	C₂²×C₄	—	19	2	no	—
126	C₂²×C₄	—	19	4	no	—
127	C₂²×C₄	—	38	8	no	—
128	C₂²×C₄	—	38	4	no	—
129	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
130	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
131	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
132	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
133	C₄⋊C₄	—	2	4	no	—
134	C₄⋊C₄	—	2	4	no	—
135	C₄⋊C₄	—	38	4	no	—
136	C₄⋊C₄	—	38	2	no	—
137	C₂²⋊C₄	—	38	16	no	—
138	C₂²⋊C₄	—	38	4	no	—
139	C₄²	—	38	4	no	—
140	C₄²	C₂²⋊D₁₉	1	4	yes	—
141	C₂³	—	19	4	no	—
142	C₂³	—	38	2	no	—
143	C₂³	—	38	4	no	—
144	C₂³	—	38	4	no	—
145	C₂³	—	38	2	no	—
146	C₂³	C₂³×D₁₉	1	1	yes	characteristic
147	Q₈	—	4	8	no	—
148	D₄	—	38	8	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	38	4	no	—
154	C₂×C₄	—	38	4	no	—
155	C₂×C₄	—	38	4	no	—
156	C₂×C₄	—	38	4	no	—
157	C₂×C₄	—	38	2	no	—
158	C₂×C₄	—	76	8	no	—
159	C₂×C₄	D₄×D₁₉	1	2	yes	—
160	C₂×C₄	#64543	1	2	yes	—
161	C₂×C₄	#64545	1	4	yes	—
162	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
163	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
164	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
165	C₂²	—	38	8	no	—
166	C₂²	—	38	4	no	—
167	C₂²	—	76	2	no	—
168	C₂²	—	76	2	no	—
169	C₂²	—	76	4	no	—
170	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
171	C₂²	C₂×#64543	1	1	yes	characteristic
172	C₂²	C₂×#64545	1	2	yes	—
173	C₂²	#10597433	1	2	yes	—
174	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
175	C₄	—	2	2	no	—
176	C₄	—	4	4	no	—
177	C₄	—	76	2	no	—
178	C₄	—	76	4	no	—
179	C₄	#10597384	1	4	yes	—
180	C₄	#10597393	1	4	yes	complemented
181	C₂	—	76	4	no	—
182	C₂	C₂×#10597384	1	1	yes	characteristic
183	C₂	C₂×#10597393	1	1	yes	characteristic
184	C₂	#11927118	1	1	yes	characteristic
185	C₂	#11927197	1	2	yes	—
186	C₂	#11927268	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597393

C₂

yes

maximal

C₂×C₄×D₇₆

C₂

yes

maximal, characteristic

#11926470

C₂

yes

maximal, complemented

#11926451

C₂

yes

maximal, complemented

#11926401

C₂

yes

maximal, complemented

C₄×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×C₄×D₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597393

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

—

C₄×D₇₆

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

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

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×D₄

yes

—

Q₈×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×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

#2547

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#124

yes

complemented

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic, complemented

C₂×#124

—

C₂×C₄×D₄

—

#397

—

#391

—

#380

—

C₄×C₄⋊C₄

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#556

yes

—

100

D₁₉

—

101

C₂²×Q₈

C₂×D₁₉

yes

—

102

C₂²×D₄

—

103

C₂³×C₄

—

104

C₄⋊Q₈

—

105

#124

—

106

C₄×D₄

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

110

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

111

C₂×C₂²⋊C₄

—

112

C₂×C₂²⋊C₄

—

113

C₂×C₄²

—

114

C₂×C₄²

C₂×D₁₉

yes

characteristic

115

#95

—

116

#95

—

117

C₁₉

#2547

yes

characteristic, complemented, Sylow

118

C₂⁴

—

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×D₄

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

C₂²×D₁₉

yes

—

130

C₂²×C₄

C₂²×D₁₉

yes

characteristic

131

C₂²×C₄

C₂²×D₁₉

yes

characteristic

132

C₂²×C₄

C₂²×D₁₉

yes

characteristic

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₂²⋊C₄

—

138

C₂²⋊C₄

—

139

C₄²

—

140

C₄²

C₂²⋊D₁₉

yes

—

141

C₂³

—

142

C₂³

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

C₂³×D₁₉

yes

characteristic

147

Q₈

—

148

D₄

—

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

D₄×D₁₉

yes

—

160

C₂×C₄

#64543

yes

—

161

C₂×C₄

#64545

yes

—

162

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

163

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

164

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

C₂×D₄×D₁₉

yes

characteristic

171

C₂²

C₂×#64543

yes

characteristic

172

C₂²

C₂×#64545

yes

—

173

C₂²

#10597433

yes

—

174

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

#10597384

yes

—

180

C₄

#10597393

yes

complemented

181

C₂

—

182

C₂

C₂×#10597384

yes

characteristic

183

C₂

C₂×#10597393

yes

characteristic

184

C₂

#11927118

yes

characteristic

185

C₂

#11927197

yes

—

186

C₂

#11927268

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
prime radical	C₂²×D₇₆	C₂²
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2547
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

prime radical

C₂²×D₇₆

C₂²

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
3. #11926470	C₂	semidirect
4. #11926451	C₂	semidirect
5. #11926401	C₂	semidirect
6. C₄×C₄⋊Dic₁₉	C₂	semidirect
7. C₂×C₁₉×C₄⋊Q₈	C₂	semidirect
85. C₄×C₁₉	#124	semidirect
88. C₂×C₄⋊Q₈	D₁₉	semidirect
117. C₁₉	#2547	semidirect
180. C₄	#10597393	semidirect

H ≅ G/N

type

3. #11926470

C₂

semidirect

4. #11926451

C₂

semidirect

5. #11926401

C₂

semidirect

6. C₄×C₄⋊Dic₁₉

C₂

semidirect

7. C₂×C₁₉×C₄⋊Q₈

C₂

semidirect

85. C₄×C₁₉

#124

semidirect

88. C₂×C₄⋊Q₈

D₁₉

semidirect

117. C₁₉

#2547

semidirect

180. C₄

#10597393

semidirect

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

subgroup	index
C₂×#10597393	2
C₂×C₄×D₇₆	2
#11926470	2
#11926451	2
#11926401	2
C₄×C₄⋊Dic₁₉	2
C₂×C₁₉×C₄⋊Q₈	2
#2547	19

subgroup

index

C₂×C₄×D₇₆

C₄×C₄⋊Dic₁₉

C₂×C₁₉×C₄⋊Q₈

#2547

Subgroups — #14568631

Conjugacy classes of subgroups

Complements

Maximal subgroups