Group #14563628 — subgroups

Subgroups — #14563628

Order 2432.

272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#11926568	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597281	C₂	1	2	yes	maximal
4	#11926312	C₂	1	2	yes	maximal
5	C₁₉×#423	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₉⋊C₄	C₄	1	2	yes	—
11	C₂×C₄×Dic₁₉	C₄	1	2	yes	—
12	C₂×#64520	C₂²	1	2	yes	—
13	C₄×Dic₃₈	—	2	1	no	—
14	C₄×Dic₃₈	—	2	1	no	—
15	C₄×Dic₃₈	—	2	1	no	—
16	C₄×Dic₃₈	—	2	1	no	—
17	C₁₉×C₄⋊C₈	—	2	1	no	—
18	C₁₉×C₄⋊C₈	—	2	1	no	—
19	#10597281	—	2	4	no	—
20	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
26	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
27	C₂×Dic₃₈	—	2	1	no	—
28	C₂×Dic₃₈	—	2	1	no	—
29	C₂×Dic₃₈	—	2	1	no	—
30	C₂×Dic₃₈	—	2	1	no	—
31	C₂×Dic₃₈	D₄	1	2	yes	—
32	C₂×Dic₃₈	Q₈	1	2	yes	—
33	M₁₆×C₁₉	—	2	2	no	—
34	M₁₆×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	Dic₁₉⋊C₄	—	2	2	no	—
43	Dic₁₉⋊C₄	—	2	2	no	—
44	C₄×Dic₁₉	—	2	2	no	—
45	C₄×Dic₁₉	—	2	2	no	—
46	#64520	—	2	2	no	—
47	#64520	—	2	2	no	—
48	C₂×C₁₉⋊C₈	—	2	2	no	—
49	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂×Dic₁₉	—	2	2	no	—
63	C₂×Dic₁₉	—	2	2	no	—
64	C₂×Dic₁₉	—	2	2	no	—
65	C₂×Dic₁₉	—	4	2	no	—
66	C₂×Dic₁₉	C₄⋊C₄	1	4	yes	—
67	Dic₃₈	—	2	2	no	—
68	Dic₃₈	—	2	2	no	—
69	Dic₃₈	—	2	2	no	—
70	Dic₃₈	—	2	2	no	—
71	C₈×C₁₉	—	4	2	no	—
72	C₁₉⋊C₈	—	4	2	no	—
73	#1801	—	19	1	no	maximal, Sylow
74	C₂²×C₁₉	—	2	1	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₁₉	#117	1	1	yes	characteristic
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	2	1	no	—
81	C₄×C₁₉	—	2	1	no	—
82	C₄×C₁₉	#101	1	2	yes	complemented
83	C₄×C₁₉	#121	1	1	yes	characteristic
84	C₄×C₁₉	#121	1	1	yes	characteristic
85	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
86	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
87	Dic₁₉	—	2	4	no	—
88	Dic₁₉	—	4	2	no	—
89	C₂×C₄×Q₈	—	19	1	no	—
90	#423	—	19	1	no	—
91	#423	D₁₉	1	1	yes	characteristic
92	C₂×#101	—	19	2	no	—
93	#343	—	19	2	no	—
94	C₂×C₁₉	—	2	1	no	—
95	C₂×C₁₉	—	2	1	no	—
96	C₂×C₁₉	#380	1	1	yes	characteristic
97	C₂×C₁₉	C₂×#101	1	1	yes	characteristic
98	C₂×C₁₉	#413	1	1	yes	characteristic
99	C₂²×Q₈	—	19	1	no	—
100	C₂×M₁₆	—	19	2	no	—
101	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
102	C₄×Q₈	—	38	1	no	—
103	C₄×Q₈	—	38	1	no	—
104	C₄×Q₈	—	38	1	no	—
105	C₄×Q₈	—	38	1	no	—
106	C₂×C₄⋊C₄	—	19	2	no	—
107	C₂×C₄⋊C₄	—	19	1	no	—
108	C₂×C₄²	—	19	2	no	—
109	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
110	C₄⋊C₈	—	2	1	no	—
111	C₄⋊C₈	—	2	1	no	—
112	C₄⋊C₈	—	38	1	no	—
113	C₄⋊C₈	—	38	1	no	—
114	#101	—	38	4	no	—
115	C₁₉	#1801	1	1	yes	characteristic, complemented, Sylow
116	C₂×Q₈	—	19	2	no	—
117	C₂×Q₈	—	19	2	no	—
118	C₂×Q₈	—	38	1	no	—
119	C₂×Q₈	—	38	1	no	—
120	C₂×Q₈	—	38	1	no	—
121	C₂×Q₈	—	38	1	no	—
122	C₂²×C₄	—	19	2	no	—
123	C₂²×C₄	—	19	2	no	—
124	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
125	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
126	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
127	M₁₆	—	2	2	no	—
128	M₁₆	—	2	2	no	—
129	M₁₆	—	38	2	no	—
130	M₁₆	—	38	2	no	—
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	38	2	no	—
133	C₄⋊C₄	—	38	2	no	—
134	C₄⋊C₄	—	38	2	no	—
135	C₄⋊C₄	—	38	1	no	—
136	C₄⋊C₄	—	38	1	no	—
137	C₄²	—	38	2	no	—
138	C₄²	—	38	2	no	—
139	C₄²	D₇₆	1	1	yes	characteristic
140	C₄²	D₇₆	1	1	yes	characteristic
141	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
142	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
143	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
144	Q₈	—	38	2	no	—
145	Q₈	—	38	2	no	—
146	Q₈	—	38	2	no	—
147	Q₈	—	38	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	4	1	no	—
150	C₂×C₄	—	19	4	no	—
151	C₂×C₄	—	38	2	no	—
152	C₂×C₄	—	38	2	no	—
153	C₂×C₄	—	38	2	no	—
154	C₂×C₄	—	76	2	no	—
155	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
156	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
157	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
158	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
159	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
160	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
161	C₂×C₄	#64543	1	1	yes	characteristic
162	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
163	C₂×C₄	#64545	1	1	yes	characteristic
164	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
165	C₈	—	4	2	no	—
166	C₈	—	76	2	no	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	1	no	—
169	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
170	C₂²	#10597338	1	1	yes	characteristic
171	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
172	C₄	—	2	1	no	—
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	38	4	no	—
176	C₄	—	76	2	no	—
177	C₄	#10597281	1	2	yes	complemented
178	C₄	#10597341	1	1	yes	characteristic
179	C₄	#10597343	1	1	yes	characteristic
180	C₄	#10597384	1	1	yes	characteristic
181	C₄	#10597392	1	1	yes	characteristic
182	C₂	—	2	1	no	—
183	C₂	—	2	1	no	—
184	C₂	#11926401	1	1	yes	characteristic
185	C₂	C₂×#10597281	1	1	yes	characteristic
186	C₂	#11926526	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic

#11926568

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal

#11926312

C₂

yes

maximal

C₁₉×#423

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

C₄

yes

—

C₂×C₄×Dic₁₉

C₄

yes

—

C₂×#64520

C₂²

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

#10597281

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×Dic₃₈

Q₈

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1801

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×C₄×Q₈

—

#423

—

#423

D₁₉

yes

characteristic

C₂×#101

—

#343

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

100

C₂×M₁₆

—

101

C₂×M₁₆

C₂×D₁₉

yes

—

102

C₄×Q₈

—

103

C₄×Q₈

—

104

C₄×Q₈

—

105

C₄×Q₈

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄²

—

109

C₂×C₄²

C₂×D₁₉

yes

characteristic

110

C₄⋊C₈

—

111

C₄⋊C₈

—

112

C₄⋊C₈

—

113

C₄⋊C₈

—

114

#101

—

115

C₁₉

#1801

yes

characteristic, complemented, Sylow

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₄×D₁₉

yes

characteristic

125

C₂²×C₄

C₄×D₁₉

yes

characteristic

126

C₂²×C₄

C₂²×D₁₉

yes

characteristic

127

M₁₆

—

128

M₁₆

—

129

M₁₆

—

130

M₁₆

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄²

—

138

C₄²

—

139

C₄²

D₇₆

yes

characteristic

140

C₄²

D₇₆

yes

characteristic

141

C₄²

C₂²⋊D₁₉

yes

characteristic

142

C₄²

C₂²⋊D₁₉

yes

characteristic

143

C₂³

C₂×C₄×D₁₉

yes

characteristic

144

Q₈

—

145

Q₈

—

146

Q₈

—

147

Q₈

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

156

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

157

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

158

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

159

C₂×C₄

C₂×D₇₆

yes

characteristic

160

C₂×C₄

D₄×D₁₉

yes

characteristic

161

C₂×C₄

#64543

yes

characteristic

162

C₂×C₄

Q₈×D₁₉

yes

characteristic

163

C₂×C₄

#64545

yes

characteristic

164

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

165

C₈

—

166

C₈

—

167

C₂²

—

168

C₂²

—

169

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

170

C₂²

#10597338

yes

characteristic

171

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

#10597281

yes

complemented

178

C₄

#10597341

yes

characteristic

179

C₄

#10597343

yes

characteristic

180

C₄

#10597384

yes

characteristic

181

C₄

#10597392

yes

characteristic

182

C₂

—

183

C₂

—

184

C₂

#11926401

yes

characteristic

185

C₂

C₂×#10597281

yes

characteristic

186

C₂

#11926526

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator, prime radical	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#423	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#423	D₁₉
hypocenter	C₁₉	#1801
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator, prime radical

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#423

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
82. C₄×C₁₉	#101	semidirect
115. C₁₉	#1801	semidirect
177. C₄	#10597281	semidirect

H ≅ G/N

type

82. C₄×C₁₉

#101

semidirect

115. C₁₉

#1801

semidirect

177. C₄

#10597281

semidirect

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

subgroup	index
C₂×C₄×Dic₃₈	2
#11926568	2
C₂×#10597281	2
#11926312	2
C₁₉×#423	2
#1801	19

subgroup

index

C₂×C₄×Dic₃₈

C₁₉×#423

Subgroups — #14563628

Conjugacy classes of subgroups

Complements

Maximal subgroups