Group #14565183 — subgroups

Subgroups — #14565183

Order 2432.

238 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10597264	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597265	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597292	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597292	C₂	1	1	yes	maximal, characteristic
5	#11926410	C₂	1	1	yes	maximal, characteristic
6	#11926299	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₁₉×#95	—	2	2	no	—
16	#10597292	—	2	2	no	—
17	#10597292	—	2	2	no	—
18	C₁₉⋊#95	—	2	2	no	—
19	#10597265	—	2	2	no	—
20	#10597264	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	Q₈	1	2	yes	—
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	D₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	2	1	no	—
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₄²×C₁₉	—	2	1	no	—
37	C₄⋊Dic₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₁₉⋊C₈	—	2	1	no	—
42	C₂×C₁₉⋊C₈	—	2	1	no	—
43	C₂×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₁₉⋊C₈	—	2	1	no	—
45	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
46	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
47	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
48	Q₈×C₁₉	—	2	2	no	—
49	Q₈×C₁₉	—	2	2	no	—
50	Q₈×C₁₉	—	4	1	no	—
51	Q₈×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	4	2	no	—
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂×Dic₁₉	—	4	1	no	—
67	C₂×Dic₁₉	—	4	1	no	—
68	C₂×Dic₁₉	—	4	2	no	—
69	C₂×Dic₁₉	—	4	2	no	—
70	C₁₉⋊C₈	—	2	2	no	—
71	C₁₉⋊C₈	—	2	2	no	—
72	#2097	—	19	1	no	maximal, Sylow
73	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
74	C₂²×C₁₉	#123	1	1	yes	characteristic
75	C₂²×C₁₉	#127	1	1	yes	characteristic
76	C₂²×C₁₉	#135	1	2	yes	—
77	C₂²×C₁₉	#137	1	2	yes	—
78	C₄×C₁₉	—	4	2	no	—
79	C₄×C₁₉	—	4	2	no	—
80	C₄×C₁₉	—	8	1	no	—
81	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
82	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
83	C₄×C₁₉	#123	1	1	yes	characteristic
84	C₄×C₁₉	#123	1	1	yes	characteristic
85	Dic₁₉	—	8	1	no	—
86	Dic₁₉	—	8	1	no	—
87	C₂×#107	—	19	1	no	—
88	C₂×#106	—	19	1	no	—
89	C₂×#103	—	19	1	no	—
90	C₂×#103	—	19	1	no	—
91	#391	D₁₉	1	1	yes	characteristic
92	#382	—	19	1	no	—
93	#336	—	19	1	no	—
94	C₂×C₁₉	#399	1	1	yes	characteristic
95	C₂×C₁₉	#479	1	2	yes	—
96	C₂×C₁₉	#485	1	2	yes	—
97	C₂×C₁₉	#495	1	1	yes	characteristic
98	C₂×C₁₉	#497	1	1	yes	characteristic
99	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
100	C₂²×C₈	—	19	1	no	—
101	C₂²×C₈	—	19	1	no	—
102	C₂×C₄⋊C₄	—	19	1	no	—
103	C₂×C₄⋊C₄	—	19	1	no	—
104	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
105	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
106	#107	—	38	2	no	—
107	#106	—	38	2	no	—
108	#103	—	38	2	no	—
109	#103	—	38	2	no	—
110	#95	—	2	2	no	—
111	#95	—	38	2	no	—
112	C₁₉	#2097	1	1	yes	characteristic, complemented, Sylow
113	C₂×Q₈	—	2	1	no	—
114	C₂×Q₈	—	2	1	no	—
115	C₂×Q₈	—	2	1	no	—
116	C₂×Q₈	—	2	1	no	—
117	C₂×Q₈	—	2	1	no	—
118	C₂×Q₈	Dic₃₈	1	2	yes	—
119	C₂²×C₄	—	2	1	no	—
120	C₂²×C₄	—	2	1	no	—
121	C₂²×C₄	—	38	1	no	—
122	C₂²×C₄	—	38	1	no	—
123	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
124	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
125	C₂×C₈	—	19	2	no	—
126	C₂×C₈	—	19	2	no	—
127	C₂×C₈	—	38	1	no	—
128	C₂×C₈	—	38	1	no	—
129	C₂×C₈	—	38	1	no	—
130	C₂×C₈	—	38	1	no	—
131	C₄⋊C₄	—	2	1	no	—
132	C₄⋊C₄	—	2	1	no	—
133	C₄⋊C₄	—	38	1	no	—
134	C₄⋊C₄	—	38	1	no	—
135	C₄⋊C₄	—	38	1	no	—
136	C₄⋊C₄	—	38	1	no	—
137	C₄²	—	2	1	no	—
138	C₄²	—	2	1	no	—
139	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
140	Q₈	—	2	2	no	—
141	Q₈	—	2	2	no	—
142	Q₈	—	4	1	no	—
143	Q₈	—	4	1	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	4	1	no	—
149	C₂×C₄	—	4	1	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	76	1	no	—
153	C₂×C₄	—	76	1	no	—
154	C₂×C₄	—	76	2	no	—
155	C₂×C₄	—	76	2	no	—
156	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
157	C₂×C₄	#64541	1	1	yes	characteristic
158	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
159	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
160	C₂×C₄	#64543	1	1	yes	characteristic
161	C₂×C₄	#64543	1	1	yes	characteristic
162	C₈	—	38	2	no	—
163	C₈	—	38	2	no	—
164	C₂²	#10597370	1	1	yes	characteristic
165	C₂²	#10597381	1	1	yes	characteristic
166	C₂²	#10597386	1	1	yes	characteristic
167	C₂²	#10597388	1	2	yes	—
168	C₂²	#10597396	1	2	yes	—
169	C₄	—	4	2	no	—
170	C₄	—	4	2	no	—
171	C₄	—	8	1	no	—
172	C₄	—	152	1	no	—
173	C₄	—	152	1	no	—
174	C₄	#10597324	1	1	yes	characteristic
175	C₄	#10597324	1	1	yes	characteristic
176	C₄	#10597329	1	1	yes	characteristic
177	C₄	#10597329	1	1	yes	characteristic
178	C₂	#11926480	1	1	yes	characteristic
179	C₂	#11926851	1	2	yes	—
180	C₂	#11926882	1	2	yes	—
181	C₂	#11926926	1	1	yes	characteristic
182	C₂	#11926936	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597264

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal, characteristic

#11926410

C₂

yes

maximal, characteristic

#11926299

C₂

yes

maximal, characteristic

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#95

—

#10597292

—

#10597292

—

C₁₉⋊#95

—

#10597265

—

#10597264

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2097

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

#382

—

#336

—

C₂×C₁₉

#399

yes

characteristic

C₂×C₁₉

#479

yes

—

C₂×C₁₉

#485

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

characteristic

100

C₂²×C₈

—

101

C₂²×C₈

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

105

C₂×C₄²

C₂×D₁₉

yes

characteristic

106

#107

—

107

#106

—

108

#103

—

109

#103

—

110

#95

—

111

#95

—

112

C₁₉

#2097

yes

characteristic, complemented, Sylow

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

Dic₃₈

yes

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

C₂²⋊D₁₉

yes

—

124

C₂²×C₄

C₂²×D₁₉

yes

characteristic

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

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

C₄⋊C₄

—

137

C₄²

—

138

C₄²

—

139

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

140

Q₈

—

141

Q₈

—

142

Q₈

—

143

Q₈

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

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

C₂×Dic₃₈

yes

characteristic

157

C₂×C₄

#64541

yes

characteristic

158

C₂×C₄

D₄×D₁₉

yes

characteristic

159

C₂×C₄

D₄×D₁₉

yes

characteristic

160

C₂×C₄

#64543

yes

characteristic

161

C₂×C₄

#64543

yes

characteristic

162

C₈

—

163

C₈

—

164

C₂²

#10597370

yes

characteristic

165

C₂²

#10597381

yes

characteristic

166

C₂²

#10597386

yes

characteristic

167

C₂²

#10597388

yes

—

168

C₂²

#10597396

yes

—

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

—

152

—

173

C₄

—

152

—

174

C₄

#10597324

yes

characteristic

175

C₄

#10597324

yes

characteristic

176

C₄

#10597329

yes

characteristic

177

C₄

#10597329

yes

characteristic

178

C₂

#11926480

yes

characteristic

179

C₂

#11926851

yes

—

180

C₂

#11926882

yes

—

181

C₂

#11926926

yes

characteristic

182

C₂

#11926936

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2097
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
112. C₁₉	#2097	semidirect

H ≅ G/N

type

112. C₁₉

#2097

semidirect

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

subgroup	index
C₂×#10597264	2
C₂×#10597265	2
C₂×#10597292	2
#11926410	2
#11926299	2
C₁₉×#391	2
#2097	19

subgroup

index

C₁₉×#391

Subgroups — #14565183

Conjugacy classes of subgroups

Complements

Maximal subgroups