Group #14565175 — subgroups

Subgroups — #14565175

Order 2432.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10597265	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597273	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597267	C₂	1	1	yes	maximal, characteristic
4	#11926449	C₂	1	1	yes	maximal, characteristic
5	#11926413	C₂	1	1	yes	maximal, characteristic
6	#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₉⋊C₄	—	2	2	no	—
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₁₉×#106	—	2	2	no	—
17	C₁₉⋊#95	—	2	2	no	—
18	#10597273	—	2	2	no	—
19	#10597267	—	2	2	no	—
20	#10597265	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂²×Dic₁₉	—	2	1	no	—
26	C₂²×Dic₁₉	D₄	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	—	2	1	no	—
32	C₂×Dic₃₈	Q₈	1	2	yes	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	D₄	1	2	yes	—
36	C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	Dic₁₉⋊C₄	—	4	4	no	—
43	C₄×Dic₁₉	—	2	1	no	—
44	C₄×Dic₁₉	—	2	1	no	—
45	C₂×C₁₉⋊C₈	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
48	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂×Dic₁₉	—	2	2	no	—
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	2	2	no	—
62	C₂×Dic₁₉	—	4	1	no	—
63	C₂×Dic₁₉	—	4	1	no	—
64	C₂×Dic₁₉	—	4	1	no	—
65	C₂×Dic₁₉	—	4	2	no	—
66	C₂×Dic₁₉	SD₁₆	1	4	yes	—
67	Dic₃₈	—	2	2	no	—
68	Dic₃₈	—	2	2	no	—
69	Dic₃₈	—	4	1	no	—
70	Dic₃₈	—	4	1	no	—
71	C₈×C₁₉	—	2	2	no	—
72	C₁₉⋊C₈	—	2	2	no	—
73	#2096	—	19	1	no	maximal, Sylow
74	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
75	C₂²×C₁₉	#123	1	1	yes	characteristic
76	C₂²×C₁₉	#127	1	1	yes	characteristic
77	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
78	C₂²×C₁₉	#137	1	2	yes	—
79	C₄×C₁₉	—	8	1	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	—	2	4	no	—
86	Dic₁₉	—	4	2	no	—
87	Dic₁₉	—	8	1	no	—
88	C₂×#106	—	19	1	no	—
89	C₂×#106	D₁₉	1	1	yes	characteristic
90	C₂×#103	—	19	1	no	—
91	C₂×#103	—	19	1	no	—
92	#391	—	19	1	no	—
93	#384	—	19	1	no	—
94	#336	—	19	1	no	—
95	C₂×C₁₉	#399	1	1	yes	characteristic
96	C₂×C₁₉	#475	1	2	yes	—
97	C₂×C₁₉	#483	1	2	yes	—
98	C₂×C₁₉	#492	1	1	yes	characteristic
99	C₂×C₁₉	#497	1	1	yes	characteristic
100	C₂²×Q₈	—	19	1	no	—
101	C₂²×C₈	—	19	1	no	—
102	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
103	C₂×C₄⋊C₄	—	19	1	no	—
104	C₂×C₄⋊C₄	—	38	2	no	—
105	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
106	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
107	C₂×C₄²	—	19	1	no	—
108	#106	—	2	2	no	—
109	#106	—	38	2	no	—
110	#103	—	38	2	no	—
111	#103	—	38	2	no	—
112	#95	—	38	2	no	—
113	C₁₉	#2096	1	1	yes	characteristic, complemented, Sylow
114	C₂×Q₈	—	19	2	no	—
115	C₂×Q₈	—	38	1	no	—
116	C₂×Q₈	—	38	1	no	—
117	C₂×Q₈	—	38	1	no	—
118	C₂×Q₈	—	38	1	no	—
119	C₂×Q₈	—	38	1	no	—
120	C₂²×C₄	—	2	1	no	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	19	2	no	—
123	C₂²×C₄	—	38	1	no	—
124	C₂²×C₄	—	38	1	no	—
125	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	19	2	no	—
129	C₂×C₈	—	38	1	no	—
130	C₂×C₈	—	38	1	no	—
131	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
132	C₄⋊C₄	—	2	1	no	—
133	C₄⋊C₄	—	2	1	no	—
134	C₄⋊C₄	—	2	1	no	—
135	C₄⋊C₄	—	2	1	no	—
136	C₄⋊C₄	—	38	1	no	—
137	C₄⋊C₄	—	38	1	no	—
138	C₄⋊C₄	—	76	4	no	—
139	C₄²	—	38	1	no	—
140	C₄²	—	38	1	no	—
141	C₂³	D₄×D₁₉	1	1	yes	characteristic
142	Q₈	—	38	2	no	—
143	Q₈	—	38	2	no	—
144	Q₈	—	76	1	no	—
145	Q₈	—	76	1	no	—
146	C₂×C₄	—	4	1	no	—
147	C₂×C₄	—	4	1	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	—	4	2	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	1	no	—
155	C₂×C₄	—	76	1	no	—
156	C₂×C₄	—	76	1	no	—
157	C₂×C₄	—	76	2	no	—
158	C₂×C₄	#64541	1	1	yes	characteristic
159	C₂×C₄	#64541	1	1	yes	characteristic
160	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
161	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
162	C₂×C₄	#64545	1	1	yes	characteristic
163	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
164	C₈	—	2	2	no	—
165	C₈	—	38	2	no	—
166	C₂²	#10597340	1	1	yes	characteristic
167	C₂²	#10597342	1	1	yes	characteristic
168	C₂²	SD₁₆×D₁₉	1	2	yes	—
169	C₂²	#10597361	1	2	yes	—
170	C₂²	#10597386	1	1	yes	characteristic
171	C₄	—	8	1	no	—
172	C₄	—	8	1	no	—
173	C₄	—	38	4	no	—
174	C₄	—	76	2	no	—
175	C₄	—	152	1	no	—
176	C₄	#10597340	1	1	yes	characteristic
177	C₄	#10597342	1	1	yes	characteristic
178	C₄	#10597375	1	1	yes	characteristic
179	C₄	#10597392	1	1	yes	characteristic
180	C₂	#11926479	1	1	yes	characteristic
181	C₂	#11926828	1	2	yes	—
182	C₂	#11926876	1	2	yes	—
183	C₂	#11926915	1	1	yes	characteristic
184	C₂	#11926935	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597265

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal, characteristic

#11926449

C₂

yes

maximal, characteristic

#11926413

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, characteristic

C₂×C₁₉×#106

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#106

—

C₁₉⋊#95

—

#10597273

—

#10597267

—

#10597265

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

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

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2096

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#106

—

C₂×#106

D₁₉

yes

—

—

—

—

—

C₂×C₁₉

#399

yes

characteristic

C₂×C₁₉

#475

yes

—

C₂×C₁₉

#483

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

100

C₂²×Q₈

—

101

C₂²×C₈

—

102

C₂²×C₈

C₂×D₁₉

yes

characteristic

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

106

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

107

C₂×C₄²

—

108

#106

—

109

#106

—

110

#103

—

111

#103

—

112

#95

—

113

C₁₉

#2096

yes

characteristic, complemented, Sylow

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

C₂²×D₁₉

yes

characteristic

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

C₂²⋊D₁₉

yes

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄²

—

140

C₄²

—

141

C₂³

D₄×D₁₉

yes

characteristic

142

Q₈

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

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

—

157

C₂×C₄

—

158

C₂×C₄

#64541

yes

characteristic

159

C₂×C₄

#64541

yes

characteristic

160

C₂×C₄

D₄×D₁₉

yes

characteristic

161

C₂×C₄

Q₈×D₁₉

yes

characteristic

162

C₂×C₄

#64545

yes

characteristic

163

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

164

C₈

—

165

C₈

—

166

C₂²

#10597340

yes

characteristic

167

C₂²

#10597342

yes

characteristic

168

C₂²

SD₁₆×D₁₉

yes

—

169

C₂²

#10597361

yes

—

170

C₂²

#10597386

yes

characteristic

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

152

—

176

C₄

#10597340

yes

characteristic

177

C₄

#10597342

yes

characteristic

178

C₄

#10597375

yes

characteristic

179

C₄

#10597392

yes

characteristic

180

C₂

#11926479

yes

characteristic

181

C₂

#11926828

yes

—

182

C₂

#11926876

yes

—

183

C₂

#11926915

yes

characteristic

184

C₂

#11926935

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	#2096
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
113. C₁₉	#2096	semidirect

H ≅ G/N

type

113. C₁₉

#2096

semidirect

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

subgroup	index
C₂×#10597265	2
C₂×#10597273	2
C₂×#10597267	2
#11926449	2
#11926413	2
#11926298	2
C₂×C₁₉×#106	2
#2096	19

subgroup

index

C₂×C₁₉×#106

Subgroups — #14565175

Conjugacy classes of subgroups

Complements

Maximal subgroups