Group #18082570 — subgroups

Subgroups — #18082570

Order 4864.

486 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 159 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	C₄×#10597316	C₂	1	1	yes	maximal, characteristic
2	#14563787	C₂	1	1	yes	maximal, characteristic
3	#14561475	C₂	1	4	yes	maximal
4	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597316	C₄	1	1	yes	characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	#11926442	C₄	1	2	yes	—
9	#11926428	—	2	2	no	—
10	#11926410	C₄	1	1	yes	characteristic
11	C₄×Dic₁₉⋊C₄	—	2	2	no	—
12	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×#97	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	D₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
24	C₂×Dic₁₉⋊C₄	—	2	2	no	—
25	C₂×Dic₁₉⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	#10597316	—	2	4	no	—
29	C₁₉×#97	—	2	8	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	C₄×C₈×C₁₉	Q₈	1	4	yes	—
32	C₁₉⋊#95	—	2	2	no	—
33	C₁₉⋊#95	—	2	2	no	—
34	C₁₉⋊#95	—	2	2	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	2	2	no	—
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	8	no	—
45	C₂×C₈×C₁₉	—	2	4	no	—
46	C₄²×C₁₉	—	2	4	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	—	2	2	no	—
50	C₄²×C₁₉	—	2	2	no	—
51	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
52	C₄²×C₁₉	#41	1	2	yes	—
53	C₄⋊Dic₁₉	—	2	2	no	—
54	C₄⋊Dic₁₉	—	2	4	no	—
55	C₄⋊Dic₁₉	M₁₆	1	4	yes	—
56	Dic₁₉⋊C₄	—	2	8	no	—
57	Dic₁₉⋊C₄	—	4	4	no	—
58	C₄×Dic₁₉	—	4	2	no	—
59	C₄×Dic₁₉	—	4	2	no	—
60	C₂×C₁₉⋊C₈	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	#9876	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	#104	1	4	yes	—
71	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
72	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
73	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
76	C₂×C₄×C₁₉	#131	1	2	yes	—
77	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
78	C₂×C₄×C₁₉	#137	1	2	yes	—
79	C₂×Dic₁₉	—	2	4	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	—	4	2	no	—
82	C₂×Dic₁₉	—	4	2	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	—	4	2	no	—
85	C₈×C₁₉	—	2	8	no	—
86	C₁₉⋊C₈	—	8	2	no	—
87	C₄×#125	—	19	1	no	—
88	#1842	—	19	1	no	—
89	C₄×#97	D₁₉	1	1	yes	characteristic
90	#1279	—	19	4	no	—
91	C₂²×C₁₉	#391	1	1	yes	characteristic
92	C₂²×C₁₉	#407	1	1	yes	characteristic
93	C₂²×C₁₉	#408	1	1	yes	characteristic
94	C₂²×C₁₉	#417	1	2	yes	—
95	C₂²×C₁₉	C₂×#104	1	2	yes	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	4	no	—
98	C₄×C₁₉	—	4	2	no	—
99	C₄×C₁₉	#446	1	4	yes	—
100	C₄×C₁₉	#490	1	1	yes	characteristic
101	C₄×C₁₉	#491	1	1	yes	characteristic
102	C₄×C₁₉	#501	1	2	yes	—
103	Dic₁₉	—	4	4	no	—
104	Dic₁₉	—	8	2	no	—
105	C₂×#125	—	19	1	no	—
106	C₂×C₄⋊C₈	—	19	2	no	—
107	C₂×C₄⋊C₈	—	38	2	no	—
108	C₂×#97	—	2	2	no	—
109	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
110	#389	—	19	2	no	—
111	#387	—	38	2	no	—
112	#382	—	19	1	no	—
113	C₄×C₄⋊C₄	—	19	2	no	—
114	C₄×C₄⋊C₄	—	38	2	no	—
115	C₄³	C₂×D₁₉	1	1	yes	characteristic
116	C₂×C₁₉	#1483	1	2	yes	—
117	C₂×C₁₉	#1489	1	2	yes	—
118	C₂×C₁₉	#1985	1	1	yes	characteristic
119	C₂×C₁₉	#1992	1	1	yes	characteristic
120	C₂×C₁₉	#1994	1	1	yes	characteristic
121	C₂²×C₈	—	2	2	no	—
122	C₂²×C₈	—	38	2	no	—
123	#125	—	38	4	no	—
124	C₂×C₄⋊C₄	—	19	2	no	—
125	C₂×C₄⋊C₄	—	19	2	no	—
126	C₂×C₄⋊C₄	—	38	2	no	—
127	C₂×C₄⋊C₄	—	38	2	no	—
128	C₂×C₄²	—	38	2	no	—
129	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
131	C₂×C₄²	D₇₆	1	2	yes	—
132	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
133	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
134	C₄⋊C₈	—	38	4	no	—
135	C₄⋊C₈	—	76	4	no	—
136	#97	—	2	8	no	—
137	C₄×C₈	—	2	2	no	—
138	C₄×C₈	Dic₃₈	1	4	yes	—
139	#95	—	38	2	no	—
140	#95	—	38	2	no	—
141	#95	—	38	2	no	—
142	C₁₉	#9876	1	1	yes	characteristic, complemented, Sylow
143	C₂²×C₄	—	38	2	no	—
144	C₂²×C₄	—	38	2	no	—
145	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
146	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
147	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
148	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
149	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
150	C₂×C₈	—	2	8	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	76	2	no	—
153	C₂×C₈	—	76	4	no	—
154	C₄⋊C₄	—	19	4	no	—
155	C₄⋊C₄	—	38	8	no	—
156	C₄⋊C₄	—	38	2	no	—
157	C₄⋊C₄	—	38	4	no	—
158	C₄⋊C₄	—	76	4	no	—
159	C₄²	—	2	4	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	2	2	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	2	2	no	—
164	C₄²	—	76	2	no	—
165	C₄²	—	76	2	no	—
166	C₄²	C₂×Dic₃₈	1	2	yes	—
167	C₄²	#64541	1	2	yes	—
168	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	38	4	no	—
176	C₂×C₄	—	76	2	no	—
177	C₂×C₄	—	76	2	no	—
178	C₂×C₄	—	76	2	no	—
179	C₂×C₄	—	76	2	no	—
180	C₂×C₄	—	76	2	no	—
181	C₂×C₄	#10597262	1	4	yes	—
182	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
183	C₂×C₄	#10597315	1	1	yes	characteristic
184	C₂×C₄	#10597321	1	1	yes	characteristic
185	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
186	C₂×C₄	#10597353	1	2	yes	—
187	C₂×C₄	#10597354	1	2	yes	—
188	C₂×C₄	#10597355	1	2	yes	—
189	C₂×C₄	#10597370	1	2	yes	—
190	C₈	—	2	8	no	—
191	C₈	—	152	2	no	—
192	C₂²	#11926450	1	1	yes	characteristic
193	C₂²	#11926507	1	1	yes	characteristic
194	C₂²	#11926512	1	1	yes	characteristic
195	C₂²	#11926546	1	2	yes	—
196	C₂²	C₂×#10597262	1	2	yes	—
197	C₄	—	2	4	no	—
198	C₄	—	2	2	no	—
199	C₄	—	4	2	no	—
200	C₄	—	76	4	no	—
201	C₄	—	152	2	no	—
202	C₄	#11926672	1	4	yes	—
203	C₄	#11926909	1	1	yes	characteristic
204	C₄	#11926913	1	1	yes	characteristic
205	C₄	#11926953	1	2	yes	—
206	C₂	#14562049	1	2	yes	—
207	C₂	#14562075	1	2	yes	—
208	C₂	#14564575	1	1	yes	characteristic
209	C₂	#14564604	1	1	yes	characteristic
210	C₂	#14564612	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597316

C₂

yes

maximal, characteristic

#14563787

C₂

yes

maximal, characteristic

#14561475

C₂

yes

maximal

C₄×C₁₉×#97

C₂

yes

maximal, characteristic

C₂×#10597316

C₄

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926442

C₄

yes

—

#11926428

—

#11926410

C₄

yes

characteristic

C₄×Dic₁₉⋊C₄

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₁₉×#97

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

#10597316

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

Q₈

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

M₁₆

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9876

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₄×Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₄×#125

—

#1842

—

C₄×#97

D₁₉

yes

characteristic

#1279

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×#104

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#446

yes

—

100

C₄×C₁₉

#490

yes

characteristic

101

C₄×C₁₉

#491

yes

characteristic

102

C₄×C₁₉

#501

yes

—

103

Dic₁₉

—

104

Dic₁₉

—

105

C₂×#125

—

106

C₂×C₄⋊C₈

—

107

C₂×C₄⋊C₈

—

108

C₂×#97

—

109

C₂×C₄×C₈

C₂×D₁₉

yes

—

110

#389

—

111

#387

—

112

#382

—

113

C₄×C₄⋊C₄

—

114

C₄×C₄⋊C₄

—

115

C₄³

C₂×D₁₉

yes

characteristic

116

C₂×C₁₉

#1483

yes

—

117

C₂×C₁₉

#1489

yes

—

118

C₂×C₁₉

#1985

yes

characteristic

119

C₂×C₁₉

#1992

yes

characteristic

120

C₂×C₁₉

#1994

yes

characteristic

121

C₂²×C₈

—

122

C₂²×C₈

—

123

#125

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄²

—

129

C₂×C₄²

C₄×D₁₉

yes

characteristic

130

C₂×C₄²

C₄×D₁₉

yes

characteristic

131

C₂×C₄²

D₇₆

yes

—

132

C₂×C₄²

C₂²⋊D₁₉

yes

—

133

C₂×C₄²

C₂²×D₁₉

yes

characteristic

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

#97

—

137

C₄×C₈

—

138

C₄×C₈

Dic₃₈

yes

—

139

#95

—

140

#95

—

141

#95

—

142

C₁₉

#9876

yes

characteristic, complemented, Sylow

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

146

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

147

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

148

C₂²×C₄

C₂×D₇₆

yes

characteristic

149

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄²

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₄²

—

166

C₄²

C₂×Dic₃₈

yes

—

167

C₄²

#64541

yes

—

168

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

#10597262

yes

—

182

C₂×C₄

C₄×Dic₃₈

yes

—

183

C₂×C₄

#10597315

yes

characteristic

184

C₂×C₄

#10597321

yes

characteristic

185

C₂×C₄

M₁₆×D₁₉

yes

—

186

C₂×C₄

#10597353

yes

—

187

C₂×C₄

#10597354

yes

—

188

C₂×C₄

#10597355

yes

—

189

C₂×C₄

#10597370

yes

—

190

C₈

—

191

C₈

—

152

—

192

C₂²

#11926450

yes

characteristic

193

C₂²

#11926507

yes

characteristic

194

C₂²

#11926512

yes

characteristic

195

C₂²

#11926546

yes

—

196

C₂²

C₂×#10597262

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

152

—

202

C₄

#11926672

yes

—

203

C₄

#11926909

yes

characteristic

204

C₄

#11926913

yes

characteristic

205

C₄

#11926953

yes

—

206

C₂

#14562049

yes

—

207

C₂

#14562075

yes

—

208

C₂

#14564575

yes

characteristic

209

C₂

#14564604

yes

characteristic

210

C₂

#14564612

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#9876
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

subgroup

G/H

center

C₂²×C₄

C₂×D₇₆

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#97

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×#97

D₁₉

hypocenter

C₁₉

#9876

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

N	H ≅ G/N	type
142. C₁₉	#9876	semidirect

H ≅ G/N

type

142. C₁₉

#9876

semidirect

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

subgroup	index
C₄×#10597316	2
#14563787	2
#14561475	2
C₄×C₁₉×#97	2
#9876	19

subgroup

index

C₄×C₁₉×#97

Subgroups — #18082570

Conjugacy classes of subgroups

Complements

Maximal subgroups