Group #14565038 — subgroups

Subgroups — #14565038

Order 2432.

274 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 89 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×#10597289	C₂	1	2	yes	maximal
2	#11926414	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926306	C₂	1	2	yes	maximal, complemented
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
9	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	—	2	1	no	—
12	C₂×C₄⋊Dic₁₉	—	2	1	no	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597289	—	2	4	no	—
16	C₂⁴×C₁₉	—	2	1	no	—
17	C₂×D₄×C₁₉	—	2	2	no	—
18	C₂×D₄×C₁₉	—	2	2	no	—
19	C₂×D₄×C₁₉	—	2	1	no	—
20	C₂×D₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂²⋊C₄×C₁₉	—	4	2	no	—
28	C₂²⋊C₄×C₁₉	—	4	2	no	—
29	C₄²×C₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	4	2	no	—
33	C₄⋊Dic₁₉	—	4	2	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂³×C₁₉	—	2	2	no	—
38	C₂³×C₁₉	—	4	1	no	—
39	C₂³×C₁₉	—	4	1	no	—
40	C₂³×C₁₉	—	4	1	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	—	4	1	no	—
44	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
45	D₄×C₁₉	—	2	4	no	—
46	D₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	D₈	1	2	yes	—
55	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	2	yes	—
59	C₂×C₄×C₁₉	#41	1	2	yes	—
60	C₂×Dic₁₉	—	4	2	no	—
61	C₂×Dic₁₉	—	4	2	no	—
62	C₂×Dic₁₉	—	4	2	no	—
63	C₁₉⋊C₈	—	4	2	no	—
64	#2071	—	19	1	no	maximal, Sylow
65	C₂²×C₁₉	—	4	2	no	—
66	C₂²×C₁₉	—	4	2	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	8	1	no	—
69	C₂²×C₁₉	—	8	1	no	—
70	C₂²×C₁₉	—	8	1	no	—
71	C₂²×C₁₉	—	8	1	no	—
72	C₂²×C₁₉	#121	1	1	yes	characteristic
73	C₂²×C₁₉	#123	1	1	yes	characteristic
74	C₂²×C₁₉	#124	1	1	yes	characteristic
75	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
76	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
77	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
78	C₂²×C₁₉	#137	1	1	yes	characteristic
79	C₄×C₁₉	—	2	2	no	—
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	8	1	no	—
82	C₄×C₁₉	#123	1	2	yes	—
83	C₄×C₁₉	#126	1	2	yes	—
84	Dic₁₉	—	8	2	no	—
85	C₂×#102	—	19	2	no	—
86	#390	D₁₉	1	1	yes	characteristic
87	#384	—	19	1	no	—
88	#340	—	19	2	no	—
89	#336	—	19	1	no	—
90	C₂×C₁₉	—	8	2	no	—
91	C₂×C₁₉	#397	1	1	yes	characteristic
92	C₂×C₁₉	#459	1	1	yes	characteristic
93	C₂×C₁₉	#461	1	1	yes	characteristic
94	C₂×C₁₉	#480	1	1	yes	characteristic
95	C₂×C₁₉	#481	1	1	yes	characteristic
96	C₂×C₁₉	#486	1	1	yes	characteristic
97	C₂×C₁₉	#489	1	1	yes	characteristic
98	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
99	C₂²×C₈	—	19	2	no	—
100	C₂×C₄⋊C₄	—	19	2	no	—
101	C₂×C₄⋊C₄	—	38	1	no	—
102	C₂×C₄⋊C₄	—	38	1	no	—
103	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
104	C₂×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
107	#102	—	38	4	no	—
108	C₁₉	#2071	1	1	yes	characteristic, complemented, Sylow
109	C₂⁴	—	2	1	no	—
110	C₂×D₄	—	2	1	no	—
111	C₂×D₄	—	2	2	no	—
112	C₂×D₄	—	2	2	no	—
113	C₂×D₄	D₇₆	1	2	yes	—
114	C₂²×C₄	—	2	1	no	—
115	C₂²×C₄	—	38	2	no	—
116	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
117	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
118	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
119	C₂×C₈	—	38	2	no	—
120	C₂×C₈	—	38	2	no	—
121	C₂×C₈	—	38	2	no	—
122	C₄⋊C₄	—	2	2	no	—
123	C₄⋊C₄	—	38	2	no	—
124	C₄⋊C₄	—	38	2	no	—
125	C₄⋊C₄	—	76	2	no	—
126	C₄⋊C₄	—	76	2	no	—
127	C₂²⋊C₄	—	4	2	no	—
128	C₂²⋊C₄	—	4	2	no	—
129	C₄²	—	2	2	no	—
130	C₂³	—	2	2	no	—
131	C₂³	—	4	1	no	—
132	C₂³	—	4	1	no	—
133	C₂³	—	4	1	no	—
134	C₂³	—	4	1	no	—
135	C₂³	—	4	1	no	—
136	C₂³	—	4	1	no	—
137	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
138	D₄	—	2	4	no	—
139	D₄	—	4	2	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	4	1	no	—
145	C₂×C₄	—	4	1	no	—
146	C₂×C₄	—	4	1	no	—
147	C₂×C₄	—	76	2	no	—
148	C₂×C₄	—	76	2	no	—
149	C₂×C₄	—	76	2	no	—
150	C₂×C₄	#64525	1	2	yes	—
151	C₂×C₄	#64526	1	2	yes	—
152	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
153	C₂×C₄	#64541	1	1	yes	characteristic
154	C₂×C₄	#64543	1	2	yes	—
155	C₂×C₄	#64543	1	2	yes	—
156	C₈	—	76	2	no	—
157	C₂²	—	4	2	no	—
158	C₂²	—	4	2	no	—
159	C₂²	—	4	2	no	—
160	C₂²	—	8	1	no	—
161	C₂²	—	8	1	no	—
162	C₂²	—	8	1	no	—
163	C₂²	—	8	1	no	—
164	C₂²	#10597376	1	1	yes	characteristic
165	C₂²	C₂×#64525	1	1	yes	characteristic
166	C₂²	C₂×#64526	1	1	yes	characteristic
167	C₂²	#10597381	1	1	yes	characteristic
168	C₂²	#10597382	1	1	yes	characteristic
169	C₂²	#10597395	1	1	yes	characteristic
170	C₂²	#10597397	1	1	yes	characteristic
171	C₄	—	2	2	no	—
172	C₄	—	2	2	no	—
173	C₄	—	8	1	no	—
174	C₄	—	152	2	no	—
175	C₄	#10597325	1	2	yes	—
176	C₄	#10597332	1	2	yes	—
177	C₂	—	8	2	no	—
178	C₂	#11926469	1	1	yes	characteristic
179	C₂	#11926739	1	1	yes	characteristic
180	C₂	#11926749	1	1	yes	characteristic
181	C₂	#11926855	1	1	yes	characteristic
182	C₂	#11926860	1	1	yes	characteristic
183	C₂	#11926890	1	1	yes	characteristic
184	C₂	#11926903	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597289

C₂

yes

maximal

#11926414

C₂

yes

maximal, characteristic, complemented

#11926306

C₂

yes

maximal, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597289

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×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

D₈

yes

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2071

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#126

yes

—

Dic₁₉

—

C₂×#102

—

#390

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

104

C₂×C₂²⋊C₄

—

105

C₂×C₂²⋊C₄

—

106

C₂×C₄²

C₂×D₁₉

yes

characteristic

107

#102

—

108

C₁₉

#2071

yes

characteristic, complemented, Sylow

109

C₂⁴

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

D₇₆

yes

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

117

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

118

C₂²×C₄

C₂²×D₁₉

yes

characteristic

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₂²⋊C₄

—

128

C₂²⋊C₄

—

129

C₄²

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

138

D₄

—

139

D₄

—

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

#64525

yes

—

151

C₂×C₄

#64526

yes

—

152

C₂×C₄

C₂×D₇₆

yes

characteristic

153

C₂×C₄

#64541

yes

characteristic

154

C₂×C₄

#64543

yes

—

155

C₂×C₄

#64543

yes

—

156

C₈

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

—

164

C₂²

#10597376

yes

characteristic

165

C₂²

C₂×#64525

yes

characteristic

166

C₂²

C₂×#64526

yes

characteristic

167

C₂²

#10597381

yes

characteristic

168

C₂²

#10597382

yes

characteristic

169

C₂²

#10597395

yes

characteristic

170

C₂²

#10597397

yes

characteristic

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

152

—

175

C₄

#10597325

yes

—

176

C₄

#10597332

yes

—

177

C₂

—

178

C₂

#11926469

yes

characteristic

179

C₂

#11926739

yes

characteristic

180

C₂

#11926749

yes

characteristic

181

C₂

#11926855

yes

characteristic

182

C₂

#11926860

yes

characteristic

183

C₂

#11926890

yes

characteristic

184

C₂

#11926903

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#390	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2071
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#390

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
2. #11926414	C₂	semidirect
3. #11926306	C₂	semidirect
4. #11926299	C₂	semidirect
108. C₁₉	#2071	semidirect

H ≅ G/N

type

2. #11926414

C₂

semidirect

3. #11926306

C₂

semidirect

4. #11926299

C₂

semidirect

108. C₁₉

#2071

semidirect

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

subgroup	index
C₂×#10597289	2
#11926414	2
#11926306	2
#11926299	2
C₁₉×#390	2
#2071	19

subgroup

index

C₁₉×#390

Subgroups — #14565038

Conjugacy classes of subgroups

Complements

Maximal subgroups