Group #14568637 — subgroups

Subgroups — #14568637

Order 2432.

676 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10597320	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597321	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926462	C₂	1	4	yes	maximal, complemented
5	#11926446	C₂	1	2	yes	maximal, complemented
6	#11926445	C₂	1	4	yes	maximal, complemented
7	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₆	C₂²	1	2	yes	—
9	C₂²×D₇₆	C₂²	1	2	yes	—
10	C₂²×D₇₆	C₂²	1	2	yes	—
11	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
16	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
19	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
20	#10597321	—	2	8	no	—
21	#10597320	—	2	4	no	—
22	C₄×Dic₃₈	—	2	4	no	—
23	C₁₉×#95	C₂²	1	2	yes	—
24	C₂³×D₁₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	C₂³	1	2	yes	—
30	C₂²×Dic₁₉	C₂³	1	2	yes	—
31	C₂×D₇₆	—	2	4	no	—
32	C₂×D₇₆	—	2	4	no	—
33	C₂×D₇₆	—	2	4	no	—
34	C₂×D₇₆	—	2	4	no	—
35	C₂×D₇₆	—	2	8	no	—
36	C₂×D₇₆	—	2	4	no	—
37	C₂×D₇₆	—	4	4	no	—
38	C₂×Dic₃₈	—	2	2	no	—
39	C₂×Dic₃₈	—	2	2	no	—
40	C₂×Dic₃₈	D₄	1	4	yes	complemented
41	C₄⋊C₄×C₁₉	—	2	4	no	—
42	C₄²×C₁₉	—	2	4	no	—
43	C₄²×C₁₉	D₄	1	4	yes	—
44	(C₂×D₁₉)⋊C₄	—	2	16	no	—
45	(C₂×D₁₉)⋊C₄	—	4	8	no	—
46	C₄⋊Dic₁₉	—	2	2	no	—
47	Dic₁₉⋊C₄	—	2	4	no	—
48	C₄×Dic₁₉	—	2	4	no	—
49	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
50	C₂²×D₁₉	—	2	4	no	—
51	C₂²×D₁₉	—	2	4	no	—
52	C₂²×D₁₉	—	2	8	no	—
53	C₂²×D₁₉	—	2	4	no	—
54	C₂²×D₁₉	—	2	8	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	4	no	—
57	C₂×C₄×C₁₉	—	2	4	no	—
58	C₂×C₄×C₁₉	—	2	4	no	—
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂×C₄×C₁₉	#41	1	4	yes	—
64	C₂×C₄×C₁₉	#41	1	2	yes	—
65	C₂×Dic₁₉	—	2	2	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	2	4	no	—
69	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
70	D₇₆	—	4	8	no	—
71	D₇₆	—	4	8	no	—
72	D₇₆	—	4	8	no	—
73	Dic₃₈	—	2	8	no	—
74	#2548	—	19	1	no	maximal, Sylow
75	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
76	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
77	C₂²×C₁₉	C₂×#41	1	2	yes	—
78	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
79	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
80	C₂×D₁₉	—	4	4	no	—
81	C₂×D₁₉	—	4	4	no	—
82	C₂×D₁₉	—	4	4	no	—
83	C₂×D₁₉	—	4	8	no	—
84	C₂×D₁₉	—	4	8	no	—
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	4	4	no	—
87	C₄×C₁₉	#121	1	4	yes	—
88	C₄×C₁₉	#124	1	4	yes	complemented
89	Dic₁₉	—	2	4	no	—
90	Dic₁₉	—	4	2	no	—
91	C₂×#127	—	19	1	no	—
92	C₂×#124	—	19	2	no	—
93	C₂×C₄×Q₈	—	19	1	no	—
94	#394	—	19	4	no	—
95	#390	—	19	4	no	—
96	#390	—	19	2	no	—
97	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic, complemented
98	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
99	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
100	C₂×C₁₉	#535	1	1	yes	characteristic
101	C₂×C₁₉	#550	1	2	yes	—
102	C₂×C₁₉	#559	1	2	yes	—
103	D₁₉	—	8	4	no	—
104	C₂²×Q₈	—	19	1	no	—
105	C₂²×D₄	—	19	2	no	—
106	C₂²×D₄	—	19	2	no	—
107	C₂²×D₄	—	19	2	no	—
108	#127	—	38	4	no	—
109	#124	—	38	8	no	—
110	C₄×Q₈	—	38	4	no	—
111	C₂×C₄⋊C₄	—	19	1	no	—
112	C₂×C₄⋊C₄	—	19	2	no	—
113	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
114	C₂×C₂²⋊C₄	—	19	8	no	—
115	C₂×C₂²⋊C₄	—	19	8	no	—
116	C₂×C₄²	—	19	2	no	—
117	C₂×C₄²	C₂×D₁₉	1	2	yes	—
118	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
119	#95	C₂×D₁₉	1	2	yes	—
120	C₁₉	#2548	1	1	yes	characteristic, complemented, Sylow
121	C₂⁴	—	19	4	no	—
122	C₂×Q₈	—	19	4	no	—
123	C₂×Q₈	—	38	2	no	—
124	C₂×Q₈	—	38	2	no	—
125	C₂×D₄	—	38	4	no	—
126	C₂×D₄	—	38	4	no	—
127	C₂×D₄	—	38	4	no	—
128	C₂×D₄	—	38	8	no	—
129	C₂×D₄	—	38	4	no	—
130	C₂×D₄	—	38	4	no	—
131	C₂×D₄	—	76	4	no	—
132	C₂²×C₄	—	19	2	no	—
133	C₂²×C₄	—	19	2	no	—
134	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
135	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
136	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
137	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
138	C₄⋊C₄	—	2	4	no	—
139	C₄⋊C₄	—	38	4	no	—
140	C₄⋊C₄	—	38	2	no	—
141	C₂²⋊C₄	—	38	16	no	—
142	C₂²⋊C₄	—	76	8	no	—
143	C₄²	—	2	4	no	—
144	C₄²	—	38	4	no	—
145	C₄²	D₇₆	1	4	yes	—
146	C₂³	—	38	4	no	—
147	C₂³	—	38	8	no	—
148	C₂³	—	38	4	no	—
149	C₂³	—	38	4	no	—
150	C₂³	—	38	8	no	—
151	C₂³	C₂³×D₁₉	1	1	yes	characteristic
152	Q₈	—	38	8	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	4	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	19	4	no	—
161	C₂×C₄	—	38	2	no	—
162	C₂×C₄	—	38	2	no	—
163	C₂×C₄	—	38	2	no	—
164	C₂×C₄	—	38	4	no	—
165	C₂×C₄	C₂×D₇₆	1	2	yes	—
166	C₂×C₄	C₂×D₇₆	1	2	yes	—
167	C₂×C₄	C₂×D₇₆	1	2	yes	—
168	C₂×C₄	#64541	1	4	yes	—
169	C₂×C₄	D₄×D₁₉	1	2	yes	—
170	C₂×C₄	#64545	1	2	yes	—
171	C₂²	—	76	4	no	—
172	C₂²	—	76	4	no	—
173	C₂²	—	76	8	no	—
174	C₂²	—	76	8	no	—
175	C₂²	—	76	4	no	—
176	C₂²	C₂²×D₇₆	1	1	yes	characteristic
177	C₂²	C₂×#64541	1	2	yes	—
178	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
179	C₂²	C₂×#64545	1	1	yes	characteristic
180	C₂²	#10597435	1	2	yes	—
181	C₄	—	2	2	no	—
182	C₄	—	4	4	no	—
183	C₄	—	38	4	no	—
184	C₄	—	76	2	no	—
185	C₄	#10597321	1	4	yes	complemented
186	C₄	#10597341	1	4	yes	—
187	C₂	—	152	4	no	—
188	C₂	C₂×#10597341	1	1	yes	characteristic
189	C₂	C₂×#10597321	1	1	yes	characteristic
190	C₂	#11927113	1	1	yes	characteristic
191	C₂	#11927215	1	2	yes	—
192	C₂	#11927279	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

C₂×#10597321

C₂

yes

maximal, complemented

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic, complemented

#11926462

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal, complemented

#11926445

C₂

yes

maximal, complemented

C₄×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597321

—

#10597320

—

C₄×Dic₃₈

—

C₁₉×#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

complemented

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

#2548

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#124

yes

complemented

Dic₁₉

—

Dic₁₉

—

C₂×#127

—

C₂×#124

—

C₂×C₄×Q₈

—

#394

—

#390

—

#390

—

C₄×C₄⋊C₄

D₁₉

yes

characteristic, complemented

C₂×C₁₉

yes

C₂×C₁₉

yes

100

C₂×C₁₉

#535

yes

characteristic

101

C₂×C₁₉

#550

yes

—

102

C₂×C₁₉

#559

yes

—

103

D₁₉

—

104

C₂²×Q₈

—

105

C₂²×D₄

—

106

C₂²×D₄

—

107

C₂²×D₄

—

108

#127

—

109

#124

—

110

C₄×Q₈

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

114

C₂×C₂²⋊C₄

—

115

C₂×C₂²⋊C₄

—

116

C₂×C₄²

—

117

C₂×C₄²

C₂×D₁₉

yes

—

118

C₂×C₄²

C₂×D₁₉

yes

characteristic

119

#95

C₂×D₁₉

yes

—

120

C₁₉

#2548

yes

characteristic, complemented, Sylow

121

C₂⁴

—

122

C₂×Q₈

—

123

C₂×Q₈

—

124

C₂×Q₈

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

C₂²×D₁₉

yes

—

135

C₂²×C₄

C₂²×D₁₉

yes

characteristic

136

C₂²×C₄

C₂²×D₁₉

yes

characteristic

137

C₂²×C₄

C₂²×D₁₉

yes

characteristic

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₂²⋊C₄

—

142

C₂²⋊C₄

—

143

C₄²

—

144

C₄²

—

145

C₄²

D₇₆

yes

—

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

C₂×D₇₆

yes

—

166

C₂×C₄

C₂×D₇₆

yes

—

167

C₂×C₄

C₂×D₇₆

yes

—

168

C₂×C₄

#64541

yes

—

169

C₂×C₄

D₄×D₁₉

yes

—

170

C₂×C₄

#64545

yes

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

C₂²×D₇₆

yes

characteristic

177

C₂²

C₂×#64541

yes

—

178

C₂²

C₂×D₄×D₁₉

yes

characteristic

179

C₂²

C₂×#64545

yes

characteristic

180

C₂²

#10597435

yes

—

181

C₄

—

182

C₄

—

183

C₄

—

184

C₄

—

185

C₄

#10597321

yes

complemented

186

C₄

#10597341

yes

—

187

C₂

—

152

—

188

C₂

C₂×#10597341

yes

characteristic

189

C₂

C₂×#10597321

yes

characteristic

190

C₂

#11927113

yes

characteristic

191

C₂

#11927215

yes

—

192

C₂

#11927279

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
prime radical	C₂×#10597320	C₂
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#2548
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₄×C₄⋊C₄×C₁₉

C₂

prime radical

C₂×#10597320

C₂

hypercenter

C₄×C₄⋊C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
2. C₂×#10597321	C₂	semidirect
3. C₂×C₄×Dic₃₈	C₂	semidirect
4. #11926462	C₂	semidirect
5. #11926446	C₂	semidirect
6. #11926445	C₂	semidirect
7. C₄×C₄⋊C₄×C₁₉	C₂	semidirect
40. C₂×Dic₃₈	D₄	semidirect
88. C₄×C₁₉	#124	semidirect
97. C₄×C₄⋊C₄	D₁₉	semidirect
120. C₁₉	#2548	semidirect
185. C₄	#10597321	semidirect

H ≅ G/N

type

2. C₂×#10597321

C₂

semidirect

3. C₂×C₄×Dic₃₈

C₂

semidirect

4. #11926462

C₂

semidirect

5. #11926446

C₂

semidirect

6. #11926445

C₂

semidirect

7. C₄×C₄⋊C₄×C₁₉

C₂

semidirect

40. C₂×Dic₃₈

D₄

semidirect

88. C₄×C₁₉

#124

semidirect

97. C₄×C₄⋊C₄

D₁₉

semidirect

120. C₁₉

#2548

semidirect

185. C₄

#10597321

semidirect

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

subgroup	index
C₂×#10597320	2
C₂×#10597321	2
C₂×C₄×Dic₃₈	2
#11926462	2
#11926446	2
#11926445	2
C₄×C₄⋊C₄×C₁₉	2
#2548	19

subgroup

index

C₂×C₄×Dic₃₈

C₄×C₄⋊C₄×C₁₉

Subgroups — #14568637

Conjugacy classes of subgroups

Complements

Maximal subgroups