Group #14563669 — subgroups

Subgroups — #14563669

Order 2432.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂²×#64515	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597274	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926401	C₂	1	2	yes	maximal
4	#11926306	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#64515	—	2	2	no	—
13	C₂×#64515	—	2	2	no	—
14	C₂×#64515	C₄	1	4	yes	complemented
15	C₁₉×#107	—	2	2	no	—
16	C₁₉⋊#95	—	2	2	no	—
17	#10597274	—	2	2	no	—
18	C₂³×D₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₉	—	2	2	no	—
22	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄×D₁₉	—	2	1	no	—
24	C₂×C₄×D₁₉	—	2	1	no	—
25	C₂×C₄×D₁₉	—	2	1	no	—
26	C₂×C₄×D₁₉	—	2	1	no	—
27	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄×D₁₉	Q₈	1	2	yes	—
29	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₁₉	D₄	1	2	yes	—
31	C₂×C₈×C₁₉	D₄	1	2	yes	—
32	C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	(C₂×D₁₉)⋊C₄	—	4	4	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
40	#64515	—	2	8	no	—
41	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×D₁₉	—	2	1	no	—
43	C₂²×D₁₉	—	2	1	no	—
44	C₂²×D₁₉	—	2	2	no	—
45	C₂²×D₁₉	—	2	2	no	—
46	C₂²×D₁₉	C₄⋊C₄	1	2	yes	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
56	C₂×Dic₁₉	—	2	1	no	—
57	C₂×Dic₁₉	—	2	1	no	—
58	C₂×Dic₁₉	—	4	2	no	—
59	C₂×Dic₁₉	—	4	2	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
62	C₄×D₁₉	—	2	2	no	—
63	C₄×D₁₉	—	2	2	no	—
64	C₄×D₁₉	—	2	2	no	—
65	C₄×D₁₉	—	2	2	no	—
66	C₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
67	C₁₉⋊C₈	—	2	2	no	—
68	#1809	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₁₉	#121	1	1	yes	characteristic
71	C₂²×C₁₉	#121	1	1	yes	characteristic
72	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
73	C₂²×C₁₉	#137	1	2	yes	—
74	C₂×D₁₉	—	2	2	no	—
75	C₂×D₁₉	—	2	4	no	—
76	C₂×D₁₉	—	4	2	no	—
77	C₂×D₁₉	—	4	1	no	—
78	C₂×D₁₉	—	4	1	no	—
79	C₄×C₁₉	—	8	2	no	—
80	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₄×C₁₉	#117	1	1	yes	characteristic
82	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
83	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
84	Dic₁₉	—	2	2	no	—
85	Dic₁₉	—	8	2	no	—
86	C₂²×M₁₆	—	19	1	no	—
87	C₂×#107	D₁₉	1	1	yes	characteristic, complemented
88	C₂×#106	—	19	1	no	—
89	#380	—	19	2	no	—
90	#340	—	19	2	no	—
91	C₂×C₁₉	#380	1	1	yes	characteristic
92	C₂×C₁₉	#428	1	2	yes	—
93	C₂×C₁₉	#468	1	2	yes	—
94	C₂×C₁₉	#469	1	1	yes	characteristic
95	C₂×C₁₉	#470	1	1	yes	characteristic
96	D₁₉	—	4	2	no	—
97	C₂³×C₄	—	19	1	no	—
98	C₂×M₁₆	—	19	4	no	—
99	C₂×M₁₆	—	38	2	no	—
100	C₂×M₁₆	—	38	2	no	—
101	C₂²×C₈	—	19	1	no	—
102	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
103	C₂×C₄⋊C₄	—	19	2	no	—
104	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
105	C₂×C₂²⋊C₄	—	38	2	no	—
106	#107	—	2	2	no	—
107	#106	—	38	2	no	—
108	#95	—	38	2	no	—
109	C₁₉	#1809	1	1	yes	characteristic, complemented, Sylow
110	C₂⁴	—	19	1	no	—
111	C₂²×C₄	—	2	2	no	—
112	C₂²×C₄	—	19	1	no	—
113	C₂²×C₄	—	19	2	no	—
114	C₂²×C₄	—	19	2	no	—
115	C₂²×C₄	—	38	1	no	—
116	C₂²×C₄	—	38	1	no	—
117	C₂²×C₄	—	38	1	no	—
118	C₂²×C₄	—	38	1	no	—
119	C₂²×C₄	—	38	2	no	—
120	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
121	M₁₆	—	38	8	no	—
122	C₂×C₈	—	19	2	no	—
123	C₂×C₈	—	38	1	no	—
124	C₂×C₈	—	38	1	no	—
125	C₂×C₈	C₄×D₁₉	1	2	yes	—
126	C₂×C₈	D₇₆	1	2	yes	—
127	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
128	C₄⋊C₄	—	2	2	no	—
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	38	2	no	—
131	C₄⋊C₄	—	38	2	no	—
132	C₂²⋊C₄	—	76	4	no	—
133	C₂³	—	19	2	no	—
134	C₂³	—	38	1	no	—
135	C₂³	—	38	1	no	—
136	C₂³	—	38	2	no	—
137	C₂³	—	38	2	no	—
138	C₂³	D₄×D₁₉	1	1	yes	characteristic
139	C₂×C₄	—	4	2	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	19	2	no	—
143	C₂×C₄	—	38	1	no	—
144	C₂×C₄	—	38	1	no	—
145	C₂×C₄	—	38	2	no	—
146	C₂×C₄	—	38	2	no	—
147	C₂×C₄	—	38	2	no	—
148	C₂×C₄	—	38	2	no	—
149	C₂×C₄	—	76	2	no	—
150	C₂×C₄	—	76	2	no	—
151	C₂×C₄	—	76	2	no	—
152	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
153	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
154	C₂×C₄	#64543	1	1	yes	characteristic
155	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
156	C₂×C₄	#64545	1	1	yes	characteristic
157	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
158	C₈	—	38	2	no	—
159	C₈	(C₂×D₁₉)⋊C₄	1	4	yes	complemented
160	C₂²	—	38	4	no	—
161	C₂²	—	38	2	no	—
162	C₂²	—	76	2	no	—
163	C₂²	—	76	1	no	—
164	C₂²	—	76	1	no	—
165	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
166	C₂²	#10597341	1	1	yes	characteristic
167	C₂²	#10597357	1	2	yes	—
168	C₂²	#10597364	1	2	yes	—
169	C₂²	#10597384	1	1	yes	characteristic
170	C₄	—	8	2	no	—
171	C₄	—	38	2	no	—
172	C₄	—	152	2	no	—
173	C₄	#10597338	1	1	yes	characteristic
174	C₄	#10597343	1	1	yes	characteristic
175	C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
176	C₄	#10597392	1	1	yes	characteristic
177	C₂	—	76	2	no	—
178	C₂	#11926401	1	1	yes	characteristic
179	C₂	#11926585	1	2	yes	—
180	C₂	#11926791	1	2	yes	—
181	C₂	#11926794	1	1	yes	characteristic
182	C₂	#11926799	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64515

C₂

yes

maximal, characteristic

C₂×#10597274

C₂

yes

maximal, characteristic, complemented

#11926401

C₂

yes

maximal

#11926306

C₂

yes

maximal, complemented

C₂×C₁₉×#107

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

—

C₄

yes

complemented

C₁₉×#107

—

C₁₉⋊#95

—

#10597274

—

C₂³×D₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

Q₈

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

#64515

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

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×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

complemented

C₁₉⋊C₈

—

#1809

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#137

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂²×M₁₆

—

C₂×#107

D₁₉

yes

characteristic, complemented

C₂×#106

—

#380

—

#340

—

C₂×C₁₉

#380

yes

characteristic

C₂×C₁₉

#428

yes

—

C₂×C₁₉

#468

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

100

C₂×M₁₆

—

101

C₂²×C₈

—

102

C₂²×C₈

C₂×D₁₉

yes

characteristic

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

105

C₂×C₂²⋊C₄

—

106

#107

—

107

#106

—

108

#95

—

109

C₁₉

#1809

yes

characteristic, complemented, Sylow

110

C₂⁴

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

C₂²×D₁₉

yes

characteristic

121

M₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₄×D₁₉

yes

—

126

C₂×C₈

D₇₆

yes

—

127

C₂×C₈

C₂²⋊D₁₉

yes

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₂²⋊C₄

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

D₄×D₁₉

yes

characteristic

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

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

C₂×C₄×D₁₉

yes

characteristic

153

C₂×C₄

C₂×D₇₆

yes

characteristic

154

C₂×C₄

#64543

yes

characteristic

155

C₂×C₄

Q₈×D₁₉

yes

characteristic

156

C₂×C₄

#64545

yes

characteristic

157

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

158

C₈

—

159

C₈

(C₂×D₁₉)⋊C₄

yes

complemented

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

—

164

C₂²

—

165

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

166

C₂²

#10597341

yes

characteristic

167

C₂²

#10597357

yes

—

168

C₂²

#10597364

yes

—

169

C₂²

#10597384

yes

characteristic

170

C₄

—

171

C₄

—

172

C₄

—

152

—

173

C₄

#10597338

yes

characteristic

174

C₄

#10597343

yes

characteristic

175

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

176

C₄

#10597392

yes

characteristic

177

C₂

—

178

C₂

#11926401

yes

characteristic

179

C₂

#11926585

yes

—

180

C₂

#11926791

yes

—

181

C₂

#11926794

yes

characteristic

182

C₂

#11926799

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#107	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂³×D₁₉	D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#107	D₁₉
hypocenter	C₁₉	#1809
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#107

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂³×D₁₉

D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
2. C₂×#10597274	C₂	semidirect
4. #11926306	C₂	semidirect
5. C₂×C₁₉×#107	C₂	semidirect
14. C₂×#64515	C₄	semidirect
66. C₈×C₁₉	C₂²⋊C₄	semidirect
87. C₂×#107	D₁₉	semidirect
109. C₁₉	#1809	semidirect
159. C₈	(C₂×D₁₉)⋊C₄	semidirect

H ≅ G/N

type

2. C₂×#10597274

C₂

semidirect

4. #11926306

C₂

semidirect

5. C₂×C₁₉×#107

C₂

semidirect

14. C₂×#64515

C₄

semidirect

66. C₈×C₁₉

C₂²⋊C₄

semidirect

87. C₂×#107

D₁₉

semidirect

109. C₁₉

#1809

semidirect

159. C₈

(C₂×D₁₉)⋊C₄

semidirect

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

subgroup	index
C₂²×#64515	2
C₂×#10597274	2
#11926401	2
#11926306	2
C₂×C₁₉×#107	2
#1809	19

subgroup

index

C₂²×#64515

C₂×C₁₉×#107

Subgroups — #14563669

Conjugacy classes of subgroups

Complements

Maximal subgroups