Group #14563945 — subgroups

Subgroups — #14563945

Order 2432.

360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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×#10597370	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597372	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597273	C₂	1	2	yes	maximal, complemented
4	#11926307	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
10	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
11	#10597372	—	2	4	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	#10597370	—	2	2	no	—
15	#10597370	C₄	1	4	yes	complemented
16	C₂×Dic₁₉⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₁₉	—	2	1	no	—
18	C₁₉×C₂²⋊C₈	—	2	2	no	—
19	#10597273	—	2	4	no	—
20	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	D₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₉	—	2	1	no	—
28	C₂²×Dic₁₉	—	2	2	no	—
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂×Dic₃₈	—	2	2	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	—	2	1	no	—
33	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂²⋊Dic₁₉	—	2	4	no	—
38	C₂²⋊Dic₁₉	—	2	4	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	2	no	—
41	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
42	C₄⋊Dic₁₉	D₄	1	4	yes	—
43	Dic₁₉⋊C₄	—	2	4	no	—
44	C₄×Dic₁₉	—	2	4	no	—
45	C₂³×C₁₉	—	2	1	no	—
46	C₂³×C₁₉	—	2	1	no	—
47	C₂³×C₁₉	—	2	2	no	—
48	C₂³×C₁₉	—	2	2	no	—
49	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#41	1	2	yes	—
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	2	2	no	—
62	C₂×Dic₁₉	—	2	4	no	—
63	C₂×Dic₁₉	—	4	1	no	—
64	C₂×Dic₁₉	—	4	1	no	—
65	C₂×Dic₁₉	—	4	2	no	—
66	C₂×Dic₁₉	—	4	2	no	—
67	C₂×Dic₁₉	—	4	2	no	—
68	Dic₃₈	—	2	4	no	—
69	Dic₃₈	—	4	2	no	—
70	C₈×C₁₉	—	4	2	no	—
71	#1873	—	19	1	no	maximal, Sylow
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	—	2	2	no	—
74	C₂²×C₁₉	—	2	2	no	—
75	C₂²×C₁₉	—	4	2	no	—
76	C₂²×C₁₉	—	4	2	no	—
77	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₁₉	#120	1	1	yes	characteristic
79	C₂²×C₁₉	#123	1	1	yes	characteristic
80	C₂²×C₁₉	#135	1	2	yes	—
81	C₂²×C₁₉	#137	1	2	yes	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	C₄×D₄	1	2	yes	—
84	C₄×C₁₉	#121	1	2	yes	—
85	Dic₁₉	—	4	2	no	—
86	Dic₁₉	—	4	2	no	—
87	Dic₁₉	—	4	4	no	—
88	C₂×C₂²⋊Q₈	—	19	1	no	—
89	C₂×#117	—	19	1	no	—
90	C₂×#103	—	19	2	no	—
91	C₂×C₂²⋊C₈	D₁₉	1	1	yes	characteristic
92	#340	—	19	2	no	—
93	C₂×C₁₉	—	4	2	no	—
94	C₂×C₁₉	#386	1	1	yes	characteristic
95	C₂×C₁₉	#416	1	1	yes	characteristic
96	C₂×C₁₉	#419	1	1	yes	characteristic
97	C₂×C₁₉	#452	1	2	yes	—
98	C₂×C₁₉	#485	1	2	yes	—
99	C₂²×Q₈	—	19	1	no	—
100	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
101	C₂²×C₈	C₂×D₁₉	1	2	yes	—
102	C₂²⋊Q₈	—	19	4	no	—
103	C₂²⋊Q₈	—	38	2	no	—
104	#117	—	38	4	no	—
105	C₂×C₄⋊C₄	—	19	2	no	—
106	C₂×C₄⋊C₄	—	19	1	no	—
107	C₂×C₄⋊C₄	—	38	1	no	—
108	C₂×C₂²⋊C₄	—	38	1	no	—
109	C₂×C₂²⋊C₄	—	38	1	no	—
110	C₂×C₄²	—	38	1	no	—
111	#103	—	38	4	no	—
112	C₂²⋊C₈	—	2	2	no	—
113	C₁₉	#1873	1	1	yes	characteristic, complemented, Sylow
114	C₂⁴	D₇₆	1	1	yes	characteristic
115	C₂×Q₈	—	19	2	no	—
116	C₂×Q₈	—	38	1	no	—
117	C₂×Q₈	—	38	2	no	—
118	C₂×Q₈	—	38	2	no	—
119	C₂²×C₄	—	2	2	no	—
120	C₂²×C₄	—	2	2	no	—
121	C₂²×C₄	—	38	2	no	—
122	C₂²×C₄	—	38	1	no	—
123	C₂²×C₄	—	38	1	no	—
124	C₂²×C₄	C₄×D₁₉	1	2	yes	—
125	C₂²×C₄	D₇₆	1	1	yes	characteristic
126	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
127	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	2	2	no	—
131	C₄⋊C₄	—	19	2	no	—
132	C₄⋊C₄	—	19	4	no	—
133	C₄⋊C₄	—	38	4	no	—
134	C₄⋊C₄	—	38	2	no	—
135	C₄⋊C₄	—	38	1	no	—
136	C₂²⋊C₄	—	38	4	no	—
137	C₂²⋊C₄	—	38	4	no	—
138	C₄²	—	38	4	no	—
139	C₂³	—	2	1	no	—
140	C₂³	—	2	1	no	—
141	C₂³	—	2	2	no	—
142	C₂³	—	2	2	no	—
143	C₂³	(C₂×D₁₉)⋊C₄	1	2	yes	—
144	C₂³	C₂×D₇₆	1	1	yes	characteristic
145	Q₈	—	38	4	no	—
146	Q₈	—	76	2	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	38	4	no	—
152	C₂×C₄	—	38	2	no	—
153	C₂×C₄	—	38	2	no	—
154	C₂×C₄	—	76	1	no	—
155	C₂×C₄	—	76	1	no	—
156	C₂×C₄	—	76	2	no	—
157	C₂×C₄	—	76	2	no	—
158	C₂×C₄	—	76	2	no	—
159	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
160	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
161	C₂×C₄	D₄×D₁₉	1	2	yes	—
162	C₂×C₄	#64543	1	2	yes	—
163	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
164	C₈	—	4	2	no	—
165	C₂²	—	2	2	no	—
166	C₂²	—	2	2	no	—
167	C₂²	—	2	2	no	—
168	C₂²	—	4	2	no	—
169	C₂²	—	4	2	no	—
170	C₂²	#10597328	1	1	yes	characteristic
171	C₂²	#10597332	1	1	yes	characteristic
172	C₂²	#10597350	1	2	yes	—
173	C₂²	#10597355	1	2	yes	—
174	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
175	C₄	—	2	2	no	—
176	C₄	—	76	2	no	—
177	C₄	—	76	2	no	—
178	C₄	—	76	4	no	—
179	C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
180	C₄	#10597385	1	2	yes	—
181	C₂	—	4	2	no	—
182	C₂	#11926421	1	1	yes	characteristic
183	C₂	#11926541	1	1	yes	characteristic
184	C₂	#11926554	1	1	yes	characteristic
185	C₂	#11926708	1	2	yes	—
186	C₂	#11926886	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal, characteristic

C₂×#10597372

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, complemented

#11926307

C₂

yes

maximal, complemented

C₂×C₁₉×C₂²⋊C₈

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

#10597372

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

#10597370

C₄

yes

complemented

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₁₉×C₂²⋊C₈

—

#10597273

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#1873

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₂²⋊Q₈

—

C₂×#117

—

C₂×#103

—

C₂×C₂²⋊C₈

D₁₉

yes

characteristic

#340

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#485

yes

—

C₂²×Q₈

—

100

C₂³×C₄

C₂×D₁₉

yes

characteristic

101

C₂²×C₈

C₂×D₁₉

yes

—

102

C₂²⋊Q₈

—

103

C₂²⋊Q₈

—

104

#117

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

—

108

C₂×C₂²⋊C₄

—

109

C₂×C₂²⋊C₄

—

110

C₂×C₄²

—

111

#103

—

112

C₂²⋊C₈

—

113

C₁₉

#1873

yes

characteristic, complemented, Sylow

114

C₂⁴

D₇₆

yes

characteristic

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₄×D₁₉

yes

—

125

C₂²×C₄

D₇₆

yes

characteristic

126

C₂²×C₄

C₂²⋊D₁₉

yes

—

127

C₂²×C₄

C₂²×D₁₉

yes

characteristic

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₂²⋊C₄

—

137

C₂²⋊C₄

—

138

C₄²

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

(C₂×D₁₉)⋊C₄

yes

—

144

C₂³

C₂×D₇₆

yes

characteristic

145

Q₈

—

146

Q₈

—

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

(C₂×D₁₉)⋊C₄

yes

—

160

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

161

C₂×C₄

D₄×D₁₉

yes

—

162

C₂×C₄

#64543

yes

—

163

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

164

C₈

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

#10597328

yes

characteristic

171

C₂²

#10597332

yes

characteristic

172

C₂²

#10597350

yes

—

173

C₂²

#10597355

yes

—

174

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

180

C₄

#10597385

yes

—

181

C₂

—

182

C₂

#11926421

yes

characteristic

183

C₂

#11926541

yes

characteristic

184

C₂

#11926554

yes

characteristic

185

C₂

#11926708

yes

—

186

C₂

#11926886

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×C₂²⋊C₈	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂⁴×C₁₉	D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₂²⋊C₈	D₁₉
hypocenter	C₁₉	#1873
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×C₂²⋊C₈

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂⁴×C₁₉

D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₂²⋊C₈

D₁₉

hypocenter

C₁₉

#1873

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
3. C₂×#10597273	C₂	semidirect
4. #11926307	C₂	semidirect
15. #10597370	C₄	semidirect
113. C₁₉	#1873	semidirect

H ≅ G/N

type

3. C₂×#10597273

C₂

semidirect

4. #11926307

C₂

semidirect

15. #10597370

C₄

semidirect

113. C₁₉

#1873

semidirect

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

subgroup	index
C₂×#10597370	2
C₂×#10597372	2
C₂×#10597273	2
#11926307	2
C₂×C₁₉×C₂²⋊C₈	2
#1873	19

subgroup

index

C₂×C₁₉×C₂²⋊C₈

Subgroups — #14563945

Conjugacy classes of subgroups

Complements

Maximal subgroups