Group #14570661 — subgroups

Subgroups — #14570661

Order 2432.

592 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10597393	C₂	1	2	yes	maximal, complemented
2	#11926461	C₂	1	2	yes	maximal, complemented
3	#11926454	C₂	1	4	yes	maximal, complemented
4	#11926446	C₂	1	2	yes	maximal, complemented
5	#11926436	C₂	1	4	yes	maximal, complemented
6	C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₇₆	C₂²	1	2	yes	—
9	C₂²×D₇₆	C₂²	1	2	yes	—
10	C₂²×D₇₆	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	#10597393	—	2	8	no	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
16	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
17	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
18	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
19	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
20	C₁₉×#95	C₂²	1	4	yes	—
21	C₁₉⋊#95	C₂²	1	2	yes	—
22	C₂³×D₁₉	C₂³	1	4	yes	—
23	C₂×Q₈×C₁₉	—	4	1	no	—
24	C₂×Q₈×C₁₉	—	4	1	no	—
25	C₂×Q₈×C₁₉	D₄	1	4	yes	complemented
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×Dic₁₉	C₂³	1	4	yes	—
31	C₂×D₇₆	—	2	4	no	—
32	C₂×D₇₆	—	2	4	no	—
33	C₂×D₇₆	—	4	2	no	—
34	C₂×D₇₆	—	4	2	no	—
35	C₂×D₇₆	—	4	2	no	—
36	C₂×D₇₆	—	4	2	no	—
37	C₂×D₇₆	—	4	4	no	—
38	C₂×D₇₆	—	4	2	no	—
39	C₄⋊C₄×C₁₉	—	4	1	no	—
40	C₄²×C₁₉	—	4	1	no	—
41	(C₂×D₁₉)⋊C₄	—	2	8	no	—
42	(C₂×D₁₉)⋊C₄	—	2	8	no	—
43	(C₂×D₁₉)⋊C₄	—	2	8	no	—
44	(C₂×D₁₉)⋊C₄	—	4	4	no	—
45	C₄⋊Dic₁₉	—	4	2	no	—
46	C₄×Dic₁₉	—	2	4	no	—
47	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂²×D₁₉	—	2	4	no	—
49	C₂²×D₁₉	—	2	4	no	—
50	C₂²×D₁₉	—	2	4	no	—
51	C₂²×D₁₉	—	2	4	no	—
52	C₂²×D₁₉	—	2	4	no	—
53	C₂²×D₁₉	—	2	4	no	—
54	C₂²×D₁₉	—	2	4	no	—
55	Q₈×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	4	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
65	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₁₉	#41	1	4	yes	—
67	C₂×Dic₁₉	—	2	4	no	—
68	C₂×Dic₁₉	—	2	4	no	—
69	C₂×Dic₁₉	—	2	4	no	—
70	D₇₆	—	4	8	no	—
71	D₇₆	—	4	8	no	—
72	D₇₆	—	4	8	no	—
73	#2733	—	19	1	no	maximal, Sylow
74	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
75	C₂²×C₁₉	C₂×#41	1	2	yes	—
76	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
77	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
78	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
79	C₂×D₁₉	—	4	4	no	—
80	C₂×D₁₉	—	4	4	no	—
81	C₂×D₁₉	—	4	4	no	—
82	C₂×D₁₉	—	4	4	no	—
83	C₂×D₁₉	—	4	4	no	—
84	C₂×D₁₉	—	4	4	no	—
85	C₂×D₁₉	—	4	4	no	—
86	C₄×C₁₉	—	2	4	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	2	4	no	—
89	C₄×C₁₉	—	4	2	no	—
90	Dic₁₉	—	4	4	no	—
91	C₂×#124	—	19	2	no	—
92	#394	—	19	2	no	—
93	#392	—	19	4	no	—
94	#391	D₁₉	1	1	yes	characteristic, complemented
95	#390	—	19	2	no	—
96	#388	—	19	4	no	—
97	C₂×C₁₉	#534	1	1	yes	characteristic
98	C₂×C₁₉	#538	1	2	yes	—
99	C₂×C₁₉	#550	1	2	yes	—
100	C₂×C₁₉	#555	1	1	yes	characteristic
101	C₂×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
102	D₁₉	—	8	4	no	—
103	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
104	C₂²×D₄	—	19	2	no	—
105	C₂²×D₄	—	19	2	no	—
106	C₂²×D₄	—	19	2	no	—
107	#124	—	38	8	no	—
108	C₂×C₄⋊C₄	—	19	2	no	—
109	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
110	C₂×C₂²⋊C₄	—	19	4	no	—
111	C₂×C₂²⋊C₄	—	19	4	no	—
112	C₂×C₂²⋊C₄	—	19	4	no	—
113	C₂×C₂²⋊C₄	—	19	4	no	—
114	C₂×C₄²	—	19	2	no	—
115	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
116	#95	—	19	2	no	—
117	#95	C₂×D₁₉	1	4	yes	—
118	C₁₉	#2733	1	1	yes	characteristic, complemented, Sylow
119	C₂⁴	—	19	4	no	—
120	C₂×Q₈	—	4	1	no	—
121	C₂×Q₈	—	4	1	no	—
122	C₂×Q₈	D₇₆	1	4	yes	complemented
123	C₂×D₄	—	38	4	no	—
124	C₂×D₄	—	38	4	no	—
125	C₂×D₄	—	76	2	no	—
126	C₂×D₄	—	76	2	no	—
127	C₂×D₄	—	76	2	no	—
128	C₂×D₄	—	76	2	no	—
129	C₂×D₄	—	76	2	no	—
130	C₂×D₄	—	76	4	no	—
131	C₂²×C₄	—	19	4	no	—
132	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
133	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
134	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
135	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
136	C₄⋊C₄	—	4	1	no	—
137	C₄⋊C₄	—	76	2	no	—
138	C₂²⋊C₄	—	38	8	no	—
139	C₂²⋊C₄	—	38	8	no	—
140	C₂²⋊C₄	—	38	8	no	—
141	C₂²⋊C₄	—	76	4	no	—
142	C₄²	—	4	1	no	—
143	C₄²	—	38	4	no	—
144	C₂³	—	38	4	no	—
145	C₂³	—	38	4	no	—
146	C₂³	—	38	4	no	—
147	C₂³	—	38	4	no	—
148	C₂³	—	38	4	no	—
149	C₂³	—	38	4	no	—
150	C₂³	—	38	4	no	—
151	C₂³	C₂³×D₁₉	1	1	yes	characteristic
152	Q₈	—	4	4	no	—
153	D₄	—	76	8	no	—
154	D₄	—	76	8	no	—
155	D₄	—	76	8	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	38	4	no	—
165	C₂×C₄	—	38	4	no	—
166	C₂×C₄	—	38	4	no	—
167	C₂×C₄	C₂×D₇₆	1	4	yes	—
168	C₂×C₄	C₂×D₇₆	1	2	yes	—
169	C₂×C₄	#64545	1	4	yes	—
170	C₂²	—	76	4	no	—
171	C₂²	—	76	4	no	—
172	C₂²	—	76	4	no	—
173	C₂²	—	76	4	no	—
174	C₂²	—	76	4	no	—
175	C₂²	—	76	4	no	—
176	C₂²	—	76	4	no	—
177	C₂²	C₂²×D₇₆	1	1	yes	characteristic
178	C₂²	#10597430	1	1	yes	characteristic
179	C₂²	#10597430	1	1	yes	characteristic
180	C₂²	C₂×#64545	1	2	yes	—
181	C₂²	#10597435	1	2	yes	—
182	C₄	—	2	4	no	—
183	C₄	—	2	2	no	—
184	C₄	—	2	4	no	—
185	C₄	—	4	2	no	—
186	C₄	—	76	4	no	—
187	C₂	—	152	4	no	—
188	C₂	#11927106	1	1	yes	characteristic
189	C₂	#11927134	1	2	yes	—
190	C₂	#11927216	1	2	yes	—
191	C₂	#11927260	1	1	yes	characteristic
192	C₂	#11927286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597393

C₂

yes

maximal, complemented

#11926461

C₂

yes

maximal, complemented

#11926454

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal, complemented

#11926436

C₂

yes

maximal, complemented

C₁₉×#391

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597393

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

#2733

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#390

—

#388

—

C₂×C₁₉

#534

yes

characteristic

C₂×C₁₉

#538

yes

—

C₂×C₁₉

#550

yes

—

100

C₂×C₁₉

#555

yes

characteristic

101

C₂×C₁₉

H(3,𝔽₄)

yes

characteristic

102

D₁₉

—

103

C₂²×Q₈

C₂×D₁₉

yes

characteristic

104

C₂²×D₄

—

105

C₂²×D₄

—

106

C₂²×D₄

—

107

#124

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

110

C₂×C₂²⋊C₄

—

111

C₂×C₂²⋊C₄

—

112

C₂×C₂²⋊C₄

—

113

C₂×C₂²⋊C₄

—

114

C₂×C₄²

—

115

C₂×C₄²

C₂×D₁₉

yes

characteristic

116

#95

—

117

#95

C₂×D₁₉

yes

—

118

C₁₉

#2733

yes

characteristic, complemented, Sylow

119

C₂⁴

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

D₇₆

yes

complemented

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂²×C₄

—

132

C₂²×C₄

C₂²×D₁₉

yes

—

133

C₂²×C₄

C₂²×D₁₉

yes

—

134

C₂²×C₄

C₂²×D₁₉

yes

characteristic

135

C₂²×C₄

C₂²×D₁₉

yes

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₂²⋊C₄

—

139

C₂²⋊C₄

—

140

C₂²⋊C₄

—

141

C₂²⋊C₄

—

142

C₄²

—

143

C₄²

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

C₂³×D₁₉

yes

characteristic

152

Q₈

—

153

D₄

—

154

D₄

—

155

D₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

C₂×D₇₆

yes

—

168

C₂×C₄

C₂×D₇₆

yes

—

169

C₂×C₄

#64545

yes

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

C₂²×D₇₆

yes

characteristic

178

C₂²

#10597430

yes

characteristic

179

C₂²

#10597430

yes

characteristic

180

C₂²

C₂×#64545

yes

—

181

C₂²

#10597435

yes

—

182

C₄

—

183

C₄

—

184

C₄

—

185

C₄

—

186

C₄

—

187

C₂

—

152

—

188

C₂

#11927106

yes

characteristic

189

C₂

#11927134

yes

—

190

C₂

#11927216

yes

—

191

C₂

#11927260

yes

characteristic

192

C₂

#11927286

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#391	C₂
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2733
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #391

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#391

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #391

N	H ≅ G/N	type
1. C₂×#10597393	C₂	semidirect
2. #11926461	C₂	semidirect
3. #11926454	C₂	semidirect
4. #11926446	C₂	semidirect
5. #11926436	C₂	semidirect
6. C₁₉×#391	C₂	semidirect
25. C₂×Q₈×C₁₉	D₄	semidirect
94. #391	D₁₉	semidirect
118. C₁₉	#2733	semidirect
122. C₂×Q₈	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597393

C₂

semidirect

2. #11926461

C₂

semidirect

3. #11926454

C₂

semidirect

4. #11926446

C₂

semidirect

5. #11926436

C₂

semidirect

6. C₁₉×#391

C₂

semidirect

25. C₂×Q₈×C₁₉

D₄

semidirect

94. #391

D₁₉

semidirect

118. C₁₉

#2733

semidirect

122. C₂×Q₈

D₇₆

semidirect

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

subgroup	index
C₂×#10597393	2
#11926461	2
#11926454	2
#11926446	2
#11926436	2
C₁₉×#391	2
#2733	19

subgroup

index

C₁₉×#391

Subgroups — #14570661

Conjugacy classes of subgroups

Complements

Maximal subgroups