Group #14564991 — subgroups

Subgroups — #14564991

Order 2432.

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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×#10597279	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926586	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926572	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926549	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597289	C₂	1	1	yes	maximal, characteristic
6	#11926312	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#100	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	#10597372	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₁₉×#100	—	2	2	no	—
16	#10597289	—	2	1	no	—
17	#10597289	—	2	1	no	—
18	#10597289	—	2	2	no	—
19	#10597279	—	2	2	no	—
20	#10597275	—	2	1	no	—
21	#10597274	—	2	1	no	—
22	Dic₁₉⋊C₈	—	2	2	no	—
23	C₂⁴×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	—	2	1	no	—
29	C₂×D₄×C₁₉	Q₈	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	2	1	no	—
32	M₁₆×C₁₉	—	2	1	no	—
33	M₁₆×C₁₉	—	2	1	no	—
34	M₁₆×C₁₉	—	2	1	no	—
35	M₁₆×C₁₉	D₄	1	2	yes	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂²⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
42	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
43	C₄×Dic₁₉	—	2	1	no	—
44	#64520	—	2	1	no	—
45	#64520	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂×C₁₉⋊C₈	—	2	1	no	—
49	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
50	C₂³×C₁₉	—	2	2	no	—
51	C₂³×C₁₉	—	4	1	no	—
52	C₂³×C₁₉	—	4	1	no	—
53	C₂³×C₁₉	—	8	1	no	—
54	C₂³×C₁₉	—	8	1	no	—
55	C₂³×C₁₉	#41	1	1	yes	characteristic
56	D₄×C₁₉	—	2	2	no	—
57	D₄×C₁₉	—	2	2	no	—
58	D₄×C₁₉	—	4	1	no	—
59	D₄×C₁₉	—	4	1	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×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×Q₈	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	—	2	1	no	—
67	C₂×Dic₁₉	—	2	1	no	—
68	C₂×Dic₁₉	—	4	1	no	—
69	C₂×Dic₁₉	—	8	1	no	—
70	C₈×C₁₉	—	2	2	no	—
71	C₈×C₁₉	—	4	1	no	—
72	C₁₉⋊C₈	—	2	2	no	—
73	C₁₉⋊C₈	—	4	1	no	—
74	#2063	—	19	1	no	maximal, Sylow
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	—	4	2	no	—
78	C₂²×C₁₉	—	8	2	no	—
79	C₂²×C₁₉	—	8	2	no	—
80	C₂²×C₁₉	—	8	1	no	—
81	C₂²×C₁₉	—	8	1	no	—
82	C₂²×C₁₉	#121	1	1	yes	characteristic
83	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
84	C₂²×C₁₉	#126	1	1	yes	characteristic
85	C₄×C₁₉	#121	1	1	yes	characteristic
86	C₄×C₁₉	#121	1	1	yes	characteristic
87	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
89	Dic₁₉	—	4	1	no	—
90	Dic₁₉	—	4	1	no	—
91	Dic₁₉	—	8	1	no	—
92	C₂×#108	—	19	1	no	—
93	#428	—	19	1	no	—
94	#424	—	19	1	no	—
95	#418	—	19	1	no	—
96	C₂×#102	—	19	1	no	—
97	C₂×#100	D₁₉	1	1	yes	characteristic
98	#343	—	19	1	no	—
99	C₂×C₁₉	—	2	1	no	—
100	C₂×C₁₉	—	2	1	no	—
101	C₂×C₁₉	—	8	2	no	—
102	C₂×C₁₉	#396	1	1	yes	characteristic
103	C₂×C₁₉	#471	1	1	yes	characteristic
104	C₂×C₁₉	#472	1	1	yes	characteristic
105	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
106	C₂×M₁₆	—	19	1	no	—
107	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
108	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
109	C₂²×C₈	—	19	1	no	—
110	#117	—	19	1	no	—
111	C₂×C₄⋊C₄	—	19	1	no	—
112	#108	—	38	2	no	—
113	#107	—	38	1	no	—
114	#106	—	38	1	no	—
115	C₄⋊C₈	—	38	2	no	—
116	#102	—	38	1	no	—
117	#102	—	38	1	no	—
118	#102	—	38	2	no	—
119	#100	—	2	2	no	—
120	C₁₉	#2063	1	1	yes	characteristic, complemented, Sylow
121	C₂⁴	—	2	1	no	—
122	C₂×D₄	—	2	1	no	—
123	C₂×D₄	—	2	1	no	—
124	C₂×D₄	—	2	1	no	—
125	C₂×D₄	—	2	1	no	—
126	C₂×D₄	—	2	1	no	—
127	C₂×D₄	Dic₃₈	1	2	yes	—
128	C₂²×C₄	—	38	1	no	—
129	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
130	M₁₆	—	2	1	no	—
131	M₁₆	—	2	1	no	—
132	M₁₆	—	2	1	no	—
133	M₁₆	—	38	1	no	—
134	M₁₆	—	38	1	no	—
135	M₁₆	C₂²⋊D₁₉	1	2	yes	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	19	2	no	—
139	C₂×C₈	—	38	1	no	—
140	C₂×C₈	—	38	1	no	—
141	C₂×C₈	—	38	1	no	—
142	C₄⋊C₄	—	19	1	no	—
143	C₄⋊C₄	—	19	1	no	—
144	C₄⋊C₄	—	38	1	no	—
145	C₄⋊C₄	—	38	1	no	—
146	C₂²⋊C₄	—	38	1	no	—
147	C₄²	—	38	1	no	—
148	C₂³	—	2	2	no	—
149	C₂³	—	4	1	no	—
150	C₂³	—	4	1	no	—
151	C₂³	—	8	1	no	—
152	C₂³	—	8	1	no	—
153	C₂³	#64541	1	1	yes	characteristic
154	D₄	—	2	2	no	—
155	D₄	—	2	2	no	—
156	D₄	—	4	1	no	—
157	D₄	—	4	1	no	—
158	C₂×C₄	—	38	1	no	—
159	C₂×C₄	—	38	1	no	—
160	C₂×C₄	—	76	1	no	—
161	C₂×C₄	—	152	1	no	—
162	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
163	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
164	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
165	C₂×C₄	#64543	1	1	yes	characteristic
166	C₂×C₄	#64543	1	1	yes	characteristic
167	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	C₈	—	2	2	no	—
169	C₈	—	4	1	no	—
170	C₈	—	38	2	no	—
171	C₈	—	76	1	no	—
172	C₂²	—	2	1	no	—
173	C₂²	—	2	1	no	—
174	C₂²	—	4	2	no	—
175	C₂²	—	8	2	no	—
176	C₂²	—	8	2	no	—
177	C₂²	—	8	1	no	—
178	C₂²	—	8	1	no	—
179	C₂²	#10597325	1	1	yes	characteristic
180	C₂²	#10597330	1	1	yes	characteristic
181	C₂²	#10597370	1	1	yes	characteristic
182	C₄	—	76	1	no	—
183	C₄	—	76	1	no	—
184	C₄	—	152	1	no	—
185	C₄	#10597324	1	1	yes	characteristic
186	C₄	#10597324	1	1	yes	characteristic
187	C₄	#10597384	1	1	yes	characteristic
188	C₄	#10597385	1	1	yes	characteristic
189	C₂	—	2	1	no	—
190	C₂	—	2	1	no	—
191	C₂	—	8	2	no	—
192	C₂	#11926467	1	1	yes	characteristic
193	C₂	#11926806	1	1	yes	characteristic
194	C₂	#11926813	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597279

C₂

yes

maximal, characteristic, complemented

#11926586

C₂

yes

maximal, characteristic, complemented

#11926572

C₂

yes

maximal, characteristic, complemented

#11926549

C₂

yes

maximal, characteristic

C₂×#10597289

C₂

yes

maximal, characteristic

#11926312

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#100

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#100

—

—

—

—

—

—

—

Dic₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#41

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

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

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2063

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

#343

—

C₂×C₁₉

—

100

C₂×C₁₉

—

101

C₂×C₁₉

—

102

C₂×C₁₉

#396

yes

characteristic

103

C₂×C₁₉

#471

yes

characteristic

104

C₂×C₁₉

#472

yes

characteristic

105

C₂²×D₄

C₂×D₁₉

yes

characteristic

106

C₂×M₁₆

—

107

C₂×M₁₆

C₂×D₁₉

yes

characteristic

108

C₂×M₁₆

C₂×D₁₉

yes

characteristic

109

C₂²×C₈

—

110

#117

—

111

C₂×C₄⋊C₄

—

112

#108

—

113

#107

—

114

#106

—

115

C₄⋊C₈

—

116

#102

—

117

#102

—

118

#102

—

119

#100

—

120

C₁₉

#2063

yes

characteristic, complemented, Sylow

121

C₂⁴

—

122

C₂×D₄

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

Dic₃₈

yes

—

128

C₂²×C₄

—

129

C₂²×C₄

C₂²×D₁₉

yes

characteristic

130

M₁₆

—

131

M₁₆

—

132

M₁₆

—

133

M₁₆

—

134

M₁₆

—

135

M₁₆

C₂²⋊D₁₉

yes

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₂²⋊C₄

—

147

C₄²

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

#64541

yes

characteristic

154

D₄

—

155

D₄

—

156

D₄

—

157

D₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

152

—

162

C₂×C₄

C₂×Dic₃₈

yes

characteristic

163

C₂×C₄

D₄×D₁₉

yes

characteristic

164

C₂×C₄

D₄×D₁₉

yes

characteristic

165

C₂×C₄

#64543

yes

characteristic

166

C₂×C₄

#64543

yes

characteristic

167

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

168

C₈

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

179

C₂²

#10597325

yes

characteristic

180

C₂²

#10597330

yes

characteristic

181

C₂²

#10597370

yes

characteristic

182

C₄

—

183

C₄

—

184

C₄

—

152

—

185

C₄

#10597324

yes

characteristic

186

C₄

#10597324

yes

characteristic

187

C₄

#10597384

yes

characteristic

188

C₄

#10597385

yes

characteristic

189

C₂

—

190

C₂

—

191

C₂

—

192

C₂

#11926467

yes

characteristic

193

C₂

#11926806

yes

characteristic

194

C₂

#11926813

yes

characteristic

	subgroup	G/H
center	C₂²	#10597330
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#100	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×#100	D₁₉
hypocenter	C₁₉	#2063
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

subgroup

G/H

center

C₂²

#10597330

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#100

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

N	H ≅ G/N	type
1. C₂×#10597279	C₂	semidirect
2. #11926586	C₂	semidirect
3. #11926572	C₂	semidirect
6. #11926312	C₂	semidirect
120. C₁₉	#2063	semidirect

H ≅ G/N

type

1. C₂×#10597279

C₂

semidirect

2. #11926586

C₂

semidirect

3. #11926572

C₂

semidirect

6. #11926312

C₂

semidirect

120. C₁₉

#2063

semidirect

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

subgroup	index
C₂×#10597279	2
#11926586	2
#11926572	2
#11926549	2
C₂×#10597289	2
#11926312	2
C₂×C₁₉×#100	2
#2063	19

subgroup

index

C₂×C₁₉×#100

Subgroups — #14564991

Conjugacy classes of subgroups

Complements

Maximal subgroups