Group #18075463 — subgroups

Subgroups — #18075463

Order 4864.

398 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14563631	C₂	1	2	yes	maximal
2	#14562391	C₂	1	2	yes	maximal
3	#14561510	C₂	1	2	yes	maximal
4	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#11926568	C₂²	1	4	yes	—
6	C₂×#10597293	—	2	2	no	—
7	#11926313	—	2	2	no	—
8	#11926295	—	2	2	no	—
9	#11926295	—	2	2	no	—
10	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₈×Q₈×C₁₉	—	2	2	no	—
12	C₈×Q₈×C₁₉	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×#64520	—	2	4	no	—
28	C₁₉×C₄⋊C₈	—	2	4	no	—
29	C₁₉×C₄⋊C₈	—	2	2	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	C₄×C₈×C₁₉	—	2	2	no	—
32	C₄×C₈×C₁₉	D₄	1	2	yes	—
33	C₄×C₈×C₁₉	D₄	1	2	yes	—
34	#10597293	—	4	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	2	2	no	—
39	C₂×Q₈×C₁₉	SD₁₆	1	4	yes	—
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	4	1	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₄²×C₁₉	—	2	2	no	—
55	C₄²×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	C₂×D₄	1	2	yes	—
57	C₄²×C₁₉	#41	1	2	yes	—
58	#64520	—	4	4	no	—
59	#64520	—	4	4	no	—
60	C₂×C₁₉⋊C₈	—	4	4	no	—
61	#8615	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
63	Q₈×C₁₉	—	2	8	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	4	1	no	—
70	C₂×C₄×C₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	#106	1	4	yes	—
72	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#121	1	2	yes	—
75	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
76	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
77	C₂×C₄×C₁₉	#135	1	2	yes	—
78	C₈×C₁₉	—	2	1	no	—
79	C₈×C₁₉	—	2	2	no	—
80	C₈×C₁₉	—	4	2	no	—
81	C₈×C₁₉	#101	1	2	yes	complemented
82	C₁₉⋊C₈	—	8	4	no	—
83	C₂×C₈×Q₈	D₁₉	1	1	yes	characteristic
84	#1801	—	19	2	no	—
85	#1566	—	19	2	no	—
86	#1292	—	19	2	no	—
87	C₂²×C₁₉	—	2	1	no	—
88	C₂²×C₁₉	—	2	1	no	—
89	C₂²×C₁₉	#380	1	1	yes	characteristic
90	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
91	C₂²×C₁₉	#427	1	1	yes	characteristic
92	C₄×C₁₉	—	2	1	no	—
93	C₄×C₁₉	—	2	4	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	4	2	no	—
96	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
97	C₄×C₁₉	#413	1	1	yes	characteristic
98	C₄×C₁₉	#465	1	4	yes	—
99	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
100	C₈×Q₈	—	2	2	no	—
101	C₈×Q₈	—	2	2	no	—
102	#423	—	19	4	no	—
103	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
104	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
105	C₂×#101	—	38	2	no	—
106	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
107	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
108	#343	—	38	2	no	—
109	#334	—	38	2	no	—
110	#334	—	38	2	no	—
111	C₂×C₁₉	—	2	1	no	—
112	C₂×C₁₉	—	2	1	no	—
113	C₂×C₁₉	#1801	1	1	yes	characteristic
114	C₂×C₁₉	#1807	1	1	yes	characteristic
115	C₂×C₁₉	#1813	1	1	yes	characteristic
116	C₂²×Q₈	D₇₆	1	1	yes	characteristic
117	C₂×M₁₆	—	38	4	no	—
118	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
119	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
120	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
121	C₄×Q₈	—	2	2	no	—
122	C₄×Q₈	—	2	2	no	—
123	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
124	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
125	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
126	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
127	C₄⋊C₈	—	2	4	no	—
128	C₄⋊C₈	—	2	2	no	—
129	C₄⋊C₈	—	38	4	no	—
130	C₄⋊C₈	—	38	4	no	—
131	#101	—	76	4	no	—
132	C₄×C₈	—	2	2	no	—
133	C₄×C₈	—	2	2	no	—
134	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
135	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
136	C₁₉	#8615	1	1	yes	characteristic, complemented, Sylow
137	C₂×Q₈	—	2	2	no	—
138	C₂×Q₈	—	2	2	no	—
139	C₂×Q₈	#64516	1	4	yes	—
140	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
141	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
142	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
143	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
144	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
145	M₁₆	—	76	4	no	—
146	M₁₆	—	76	4	no	—
147	C₂×C₈	—	2	2	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	4	1	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	—	76	4	no	—
152	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
153	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
154	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
155	C₄⋊C₄	—	2	2	no	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄²	—	2	2	no	—
158	C₄²	—	2	2	no	—
159	C₄²	#64541	1	2	yes	—
160	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
161	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
162	Q₈	—	2	8	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	4	1	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	#10597274	1	4	yes	—
171	C₂×C₄	C₂×#64516	1	2	yes	—
172	C₂×C₄	#10597350	1	2	yes	—
173	C₂×C₄	#10597370	1	2	yes	—
174	C₂×C₄	#10597372	1	1	yes	characteristic
175	C₂×C₄	#10597376	1	2	yes	—
176	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
177	C₈	—	2	2	no	—
178	C₈	—	2	1	no	—
179	C₈	—	4	2	no	—
180	C₈	—	152	4	no	—
181	C₈	#10597293	1	2	yes	complemented
182	C₂²	—	2	1	no	—
183	C₂²	—	2	1	no	—
184	C₂²	#11926404	1	1	yes	characteristic
185	C₂²	C₂×#10597274	1	1	yes	characteristic
186	C₂²	#11926582	1	1	yes	characteristic
187	C₄	—	2	1	no	—
188	C₄	—	2	4	no	—
189	C₄	—	2	2	no	—
190	C₄	—	4	2	no	—
191	C₄	C₂×#10597293	1	1	yes	characteristic
192	C₄	#11926528	1	1	yes	characteristic
193	C₄	#11926773	1	4	yes	—
194	C₂	—	2	1	no	—
195	C₂	—	2	1	no	—
196	C₂	#14563631	1	1	yes	characteristic
197	C₂	#14563660	1	1	yes	characteristic
198	C₂	#14563685	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563631

C₂

yes

maximal

#14562391

C₂

yes

maximal

#14561510

C₂

yes

maximal

C₂×C₈×Q₈×C₁₉

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

—

—

—

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₈×Q₈×C₁₉

—

C₈×Q₈×C₁₉

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597293

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#8615

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

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

#106

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#101

yes

complemented

C₁₉⋊C₈

—

C₂×C₈×Q₈

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

100

C₈×Q₈

—

101

C₈×Q₈

—

102

#423

—

103

C₂×C₄⋊C₈

Dic₁₉

yes

—

104

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

105

C₂×#101

—

106

C₂×C₄×C₈

Dic₁₉

yes

—

107

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

108

#343

—

109

#334

—

110

#334

—

111

C₂×C₁₉

—

112

C₂×C₁₉

—

113

C₂×C₁₉

#1801

yes

characteristic

114

C₂×C₁₉

#1807

yes

characteristic

115

C₂×C₁₉

#1813

yes

characteristic

116

C₂²×Q₈

D₇₆

yes

characteristic

117

C₂×M₁₆

—

118

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

119

C₂²×C₈

C₂×Dic₁₉

yes

—

120

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

121

C₄×Q₈

—

122

C₄×Q₈

—

123

C₂×C₄⋊C₄

Dic₃₈

yes

—

124

C₂×C₄⋊C₄

D₇₆

yes

characteristic

125

C₂×C₄²

C₂×Dic₁₉

yes

—

126

C₂×C₄²

C₂²×D₁₉

yes

characteristic

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

C₄⋊C₈

—

130

C₄⋊C₈

—

131

#101

—

132

C₄×C₈

—

133

C₄×C₈

—

134

C₄×C₈

C₂²⋊D₁₉

yes

—

135

C₄×C₈

C₂²⋊D₁₉

yes

—

136

C₁₉

#8615

yes

characteristic, complemented, Sylow

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

#64516

yes

—

140

C₂²×C₄

C₄⋊Dic₁₉

yes

—

141

C₂²×C₄

C₄⋊Dic₁₉

yes

—

142

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

143

C₂²×C₄

C₂×D₇₆

yes

characteristic

144

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

145

M₁₆

—

146

M₁₆

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

153

C₂×C₈

C₂²⋊Dic₁₉

yes

—

154

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄²

—

158

C₄²

—

159

C₄²

#64541

yes

—

160

C₄²

C₂×C₂²⋊D₁₉

yes

—

161

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

162

Q₈

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

#10597274

yes

—

171

C₂×C₄

C₂×#64516

yes

—

172

C₂×C₄

#10597350

yes

—

173

C₂×C₄

#10597370

yes

—

174

C₂×C₄

#10597372

yes

characteristic

175

C₂×C₄

#10597376

yes

—

176

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

152

—

181

C₈

#10597293

yes

complemented

182

C₂²

—

183

C₂²

—

184

C₂²

#11926404

yes

characteristic

185

C₂²

C₂×#10597274

yes

characteristic

186

C₂²

#11926582

yes

characteristic

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

C₂×#10597293

yes

characteristic

192

C₄

#11926528

yes

characteristic

193

C₄

#11926773

yes

—

194

C₂

—

195

C₂

—

196

C₂

#14563631

yes

characteristic

197

C₂

#14563660

yes

characteristic

198

C₂

#14563685

yes

characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈×Q₈	D₁₉
hypocenter	C₁₉	#8615
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×Q₈

subgroup

G/H

center

C₂²

#11926404

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₈×Q₈×C₁₉

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₂×C₈×Q₈

D₁₉

hypocenter

C₁₉

#8615

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×Q₈

N	H ≅ G/N	type
81. C₈×C₁₉	#101	semidirect
136. C₁₉	#8615	semidirect
181. C₈	#10597293	semidirect

H ≅ G/N

type

81. C₈×C₁₉

#101

semidirect

136. C₁₉

#8615

semidirect

181. C₈

#10597293

semidirect

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

subgroup	index
#14563631	2
#14562391	2
#14561510	2
C₂×C₈×Q₈×C₁₉	2
#8615	19

subgroup

index

C₂×C₈×Q₈×C₁₉

Subgroups — #18075463

Conjugacy classes of subgroups

Complements

Maximal subgroups