Group #14575082 — subgroups

Subgroups — #14575082

Order 2432.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927156	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927149	C₂	1	1	yes	maximal, characteristic
3	#11926852	C₂	1	2	yes	maximal, complemented
4	#11926845	C₂	1	2	yes	maximal, complemented
5	#11926790	C₂	1	2	yes	maximal, complemented
6	#11926773	C₂	1	2	yes	maximal, complemented
7	#11926750	C₂	1	2	yes	maximal, complemented
8	#11926745	C₂	1	2	yes	maximal, complemented
9	C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#117	C₂²	1	1	yes	characteristic
13	#10597376	C₂²	1	2	yes	—
14	#10597370	C₂²	1	2	yes	—
15	C₂×#64516	C₂²	1	2	yes	—
16	C₂×#64516	C₂²	1	2	yes	—
17	#10597340	—	2	2	no	—
18	#10597335	—	2	2	no	—
19	#10597330	—	2	2	no	—
20	#10597325	—	2	2	no	—
21	#10597320	C₂²	1	1	yes	characteristic
22	C₄×D₇₆	C₂²	1	2	yes	—
23	#10597316	C₂²	1	1	yes	characteristic
24	#10597316	C₂²	1	1	yes	characteristic
25	#10597315	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₈	C₂²	1	2	yes	—
27	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
28	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
29	#10597278	C₂²	1	2	yes	—
30	#10597278	C₂²	1	2	yes	—
31	#10597275	C₂²	1	2	yes	—
32	#10597274	C₂²	1	2	yes	—
33	#10597273	C₂²	1	2	yes	—
34	#10597273	C₂²	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₂²⋊D₁₉	—	2	2	no	—
37	C₂×D₇₆	—	2	2	no	—
38	C₂×D₇₆	C₂³	1	2	yes	—
39	C₂×C₄×D₁₉	—	2	2	no	—
40	C₂×Dic₃₈	C₂³	1	2	yes	—
41	M₁₆×C₁₉	—	4	1	no	—
42	C₂×C₈×C₁₉	—	4	1	no	—
43	C₂×C₈×C₁₉	C₂³	1	2	yes	—
44	C₂×C₈×C₁₉	C₂³	1	2	yes	—
45	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
46	C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
47	C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²⋊Dic₁₉	—	2	2	no	—
50	(C₂×D₁₉)⋊C₄	—	2	2	no	—
51	(C₂×D₁₉)⋊C₄	—	2	2	no	—
52	C₄⋊Dic₁₉	—	2	2	no	—
53	C₄⋊Dic₁₉	C₂³	1	2	yes	—
54	C₄⋊Dic₁₉	C₂³	1	2	yes	—
55	Dic₁₉⋊C₄	—	2	2	no	—
56	Dic₁₉⋊C₄	—	2	2	no	—
57	Dic₁₉⋊C₄	—	2	2	no	—
58	Dic₁₉⋊C₄	—	2	2	no	—
59	C₄×Dic₁₉	—	2	2	no	—
60	#64516	—	4	2	no	—
61	#64516	—	4	2	no	—
62	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×D₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
70	C₂²⋊D₁₉	—	8	2	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	C₂×Dic₁₉	—	2	2	no	—
73	C₂×Dic₁₉	—	2	2	no	—
74	D₇₆	—	2	2	no	—
75	D₇₆	—	2	2	no	—
76	D₇₆	—	8	2	no	—
77	C₄×D₁₉	—	8	2	no	—
78	Dic₃₈	—	2	2	no	—
79	Dic₃₈	—	2	2	no	—
80	C₈×C₁₉	—	2	2	no	—
81	C₈×C₁₉	—	2	2	no	—
82	#3260	—	19	1	no	maximal, Sylow
83	C₂²×C₁₉	—	2	1	no	—
84	C₂²×C₁₉	—	2	2	no	—
85	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
86	C₂×D₁₉	—	4	2	no	—
87	C₂×D₁₉	—	4	2	no	—
88	C₂×D₁₉	—	4	2	no	—
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
93	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
94	Dic₁₉	—	4	2	no	—
95	Dic₁₉	—	4	2	no	—
96	Dic₁₉	—	4	2	no	—
97	#541	—	19	1	no	—
98	#540	—	19	1	no	—
99	#479	—	19	2	no	—
100	#478	—	19	2	no	—
101	#468	—	19	2	no	—
102	#465	—	19	2	no	—
103	#461	—	19	2	no	—
104	#460	—	19	2	no	—
105	#424	D₁₉	1	1	yes	characteristic, complemented
106	C₂×C₁₉	—	4	1	no	—
107	C₂×C₁₉	#537	1	1	yes	characteristic
108	C₂×C₁₉	#577	1	2	yes	—
109	D₁₉	—	8	2	no	—
110	C₂×SD₁₆	—	19	2	no	—
111	C₂×SD₁₆	—	19	2	no	—
112	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
113	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
114	C₄⋊Q₈	—	19	1	no	—
115	#127	—	19	1	no	—
116	#126	—	38	2	no	—
117	#125	—	19	1	no	—
118	#125	—	19	1	no	—
119	#125	—	38	2	no	—
120	#123	—	38	2	no	—
121	C₂²⋊Q₈	—	19	2	no	—
122	#121	—	19	2	no	—
123	#121	—	38	2	no	—
124	C₄×Q₈	—	19	2	no	—
125	C₄×D₄	—	19	2	no	—
126	#117	C₂×D₁₉	1	1	yes	characteristic
127	#107	—	19	2	no	—
128	#106	—	19	2	no	—
129	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
130	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
131	#103	—	19	2	no	—
132	#103	—	19	2	no	—
133	#102	—	19	2	no	—
134	#102	—	19	2	no	—
135	C₁₉	#3260	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₈	—	19	2	no	—
137	C₂×D₄	—	19	2	no	—
138	C₂×D₄	—	38	2	no	—
139	C₂×D₄	—	38	2	no	—
140	C₂²×C₄	—	38	2	no	—
141	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
142	SD₁₆	—	76	2	no	—
143	SD₁₆	—	76	2	no	—
144	M₁₆	—	4	1	no	—
145	C₂×C₈	—	4	1	no	—
146	C₂×C₈	C₂²×D₁₉	1	2	yes	—
147	C₂×C₈	C₂²×D₁₉	1	2	yes	—
148	C₄⋊C₄	—	19	2	no	—
149	C₄⋊C₄	—	19	2	no	—
150	C₄⋊C₄	—	38	2	no	—
151	C₄⋊C₄	—	38	2	no	—
152	C₄⋊C₄	—	38	2	no	—
153	C₄⋊C₄	—	38	2	no	—
154	C₄⋊C₄	—	38	2	no	—
155	C₄⋊C₄	D₇₆	1	2	yes	—
156	C₂²⋊C₄	—	38	2	no	—
157	C₂²⋊C₄	—	38	2	no	—
158	C₂²⋊C₄	—	38	2	no	—
159	C₂²⋊C₄	D₇₆	1	2	yes	—
160	C₄²	—	38	2	no	—
161	C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	C₄²	C₂²×D₁₉	1	1	yes	characteristic
163	C₂³	—	38	2	no	—
164	C₂³	C₂×D₇₆	1	1	yes	characteristic
165	Q₈	—	38	2	no	—
166	Q₈	—	38	2	no	—
167	D₄	—	38	2	no	—
168	D₄	—	38	2	no	—
169	D₄	—	152	2	no	—
170	D₄	—	152	2	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	38	2	no	—
175	C₂×C₄	—	38	2	no	—
176	C₂×C₄	—	152	2	no	—
177	C₂×C₄	C₂×D₇₆	1	2	yes	—
178	C₂×C₄	C₂×D₇₆	1	2	yes	—
179	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
180	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
181	C₈	—	2	2	no	—
182	C₈	—	2	2	no	—
183	C₂²	—	2	2	no	—
184	C₂²	—	2	1	no	—
185	C₂²	—	76	2	no	—
186	C₂²	—	76	2	no	—
187	C₂²	—	76	2	no	—
188	C₂²	C₂²×D₇₆	1	1	yes	characteristic
189	C₄	—	2	2	no	—
190	C₄	—	2	2	no	—
191	C₄	—	2	1	no	—
192	C₄	—	76	2	no	—
193	C₄	—	76	2	no	—
194	C₄	—	76	2	no	—
195	C₄	#10597430	1	1	yes	characteristic
196	C₄	#10597433	1	1	yes	characteristic
197	C₂	—	4	1	no	—
198	C₂	—	152	2	no	—
199	C₂	#11927125	1	1	yes	characteristic
200	C₂	#11927356	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927156

C₂

yes

maximal, characteristic, complemented

#11927149

C₂

yes

maximal, characteristic

#11926852

C₂

yes

maximal, complemented

#11926845

C₂

yes

maximal, complemented

#11926790

C₂

yes

maximal, complemented

#11926773

C₂

yes

maximal, complemented

#11926750

C₂

yes

maximal, complemented

#11926745

C₂

yes

maximal, complemented

C₁₉×#424

C₂

yes

maximal, characteristic, complemented

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597376

C₂²

yes

—

#10597370

C₂²

yes

—

C₂×#64516

C₂²

yes

—

C₂×#64516

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₄×D₇₆

C₂²

yes

—

#10597316

C₂²

yes

characteristic

#10597316

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

#10597278

C₂²

yes

—

#10597278

C₂²

yes

—

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

#10597273

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₂³

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64516

—

#64516

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

#3260

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

H(5,𝔽₂)

yes

characteristic

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#541

—

#540

—

#479

—

100

#478

—

101

#468

—

102

#465

—

103

#461

—

104

#460

—

105

#424

D₁₉

yes

characteristic, complemented

106

C₂×C₁₉

—

107

C₂×C₁₉

#537

yes

characteristic

108

C₂×C₁₉

#577

yes

—

109

D₁₉

—

110

C₂×SD₁₆

—

111

C₂×SD₁₆

—

112

C₂×M₁₆

C₂×D₁₉

yes

characteristic

113

C₂²×C₈

C₂×D₁₉

yes

characteristic

114

C₄⋊Q₈

—

115

#127

—

116

#126

—

117

#125

—

118

#125

—

119

#125

—

120

#123

—

121

C₂²⋊Q₈

—

122

#121

—

123

#121

—

124

C₄×Q₈

—

125

C₄×D₄

—

126

#117

C₂×D₁₉

yes

characteristic

127

#107

—

128

#106

—

129

C₄⋊C₈

C₂×D₁₉

yes

—

130

C₄⋊C₈

C₂×D₁₉

yes

—

131

#103

—

132

#103

—

133

#102

—

134

#102

—

135

C₁₉

#3260

yes

characteristic, complemented, Sylow

136

C₂×Q₈

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂×D₄

—

140

C₂²×C₄

—

141

C₂²×C₄

C₂²×D₁₉

yes

characteristic

142

SD₁₆

—

143

SD₁₆

—

144

M₁₆

—

145

C₂×C₈

—

146

C₂×C₈

C₂²×D₁₉

yes

—

147

C₂×C₈

C₂²×D₁₉

yes

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

D₇₆

yes

—

156

C₂²⋊C₄

—

157

C₂²⋊C₄

—

158

C₂²⋊C₄

—

159

C₂²⋊C₄

D₇₆

yes

—

160

C₄²

—

161

C₄²

C₂²×D₁₉

yes

characteristic

162

C₄²

C₂²×D₁₉

yes

characteristic

163

C₂³

—

164

C₂³

C₂×D₇₆

yes

characteristic

165

Q₈

—

166

Q₈

—

167

D₄

—

168

D₄

—

169

D₄

—

152

—

170

D₄

—

152

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

152

—

177

C₂×C₄

C₂×D₇₆

yes

—

178

C₂×C₄

C₂×D₇₆

yes

—

179

C₂×C₄

C₂×D₇₆

yes

characteristic

180

C₂×C₄

C₂³×D₁₉

yes

characteristic

181

C₈

—

182

C₈

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

C₂²×D₇₆

yes

characteristic

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

#10597430

yes

characteristic

196

C₄

#10597433

yes

characteristic

197

C₂

—

198

C₂

—

152

—

199

C₂

#11927125

yes

characteristic

200

C₂

#11927356

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#424	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11927149	C₂
hypercenter	#424	D₁₉
hypocenter	C₁₉	#3260
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #424

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#424

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ #117 ◁ #424

N	H ≅ G/N	type
1. #11927156	C₂	semidirect
3. #11926852	C₂	semidirect
4. #11926845	C₂	semidirect
5. #11926790	C₂	semidirect
6. #11926773	C₂	semidirect
7. #11926750	C₂	semidirect
8. #11926745	C₂	semidirect
9. C₁₉×#424	C₂	semidirect
105. #424	D₁₉	semidirect
135. C₁₉	#3260	semidirect

H ≅ G/N

type

1. #11927156

C₂

semidirect

3. #11926852

C₂

semidirect

4. #11926845

C₂

semidirect

5. #11926790

C₂

semidirect

6. #11926773

C₂

semidirect

7. #11926750

C₂

semidirect

8. #11926745

C₂

semidirect

9. C₁₉×#424

C₂

semidirect

105. #424

D₁₉

semidirect

135. C₁₉

#3260

semidirect

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

subgroup	index
#11927156	2
#11927149	2
#11926852	2
#11926845	2
#11926790	2
#11926773	2
#11926750	2
#11926745	2
C₁₉×#424	2
#3260	19

subgroup

index

C₁₉×#424

Subgroups — #14575082

Conjugacy classes of subgroups

Complements

Maximal subgroups