Group #18076301 — subgroups

Subgroups — #18076301

Order 4864.

382 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 163 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	#14563752	C₂	1	1	yes	maximal, characteristic
2	#14563381	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926296	C₂	1	2	yes	maximal
4	C₂×#11926294	C₂	1	2	yes	maximal
5	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
9	#11926299	—	2	2	no	—
10	#11926299	C₄	1	2	yes	—
11	#11926299	C₄	1	2	yes	—
12	#11926296	—	2	4	no	—
13	#11926294	—	2	4	no	—
14	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	—	2	2	no	—
18	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	D₄	1	2	yes	—
21	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×C₁₉⋊C₈	—	2	1	no	—
24	C₂²×C₁₉⋊C₈	—	2	1	no	—
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₁₉×C₄⋊C₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	4	4	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
32	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
33	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₈×C₁₉	—	4	2	no	—
39	C₂×C₈×C₁₉	—	4	4	no	—
40	C₄²×C₁₉	—	2	4	no	—
41	C₄²×C₁₉	—	2	2	no	—
42	C₄²×C₁₉	—	2	2	no	—
43	C₄²×C₁₉	—	2	2	no	—
44	C₄²×C₁₉	—	2	2	no	—
45	C₄²×C₁₉	C₂×D₄	1	2	yes	—
46	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
47	C₂×C₁₉⋊C₈	—	2	4	no	—
48	C₂×C₁₉⋊C₈	—	2	4	no	—
49	C₂×C₁₉⋊C₈	—	4	1	no	—
50	C₂×C₁₉⋊C₈	—	4	1	no	—
51	C₂×C₁₉⋊C₈	—	4	2	no	—
52	C₂×C₁₉⋊C₈	—	4	2	no	—
53	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	—
54	#8812	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	#108	1	4	yes	—
63	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
64	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
67	C₂×C₄×C₁₉	#131	1	2	yes	—
68	C₂×C₄×C₁₉	#131	1	2	yes	—
69	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
70	C₂×C₄×C₁₉	#137	1	2	yes	—
71	C₈×C₁₉	—	8	2	no	—
72	C₁₉⋊C₈	—	2	8	no	—
73	C₁₉⋊C₈	—	8	1	no	—
74	C₁₉⋊C₈	—	8	1	no	—
75	#1842	D₁₉	1	1	yes	characteristic
76	#1831	—	19	1	no	—
77	#1744	—	19	1	no	—
78	C₂×#335	—	19	2	no	—
79	C₂×#334	—	19	2	no	—
80	C₂²×C₁₉	#384	1	1	yes	characteristic
81	C₂²×C₁₉	#424	1	1	yes	characteristic
82	C₂²×C₁₉	#424	1	1	yes	characteristic
83	C₂²×C₁₉	#428	1	2	yes	—
84	C₂²×C₁₉	C₂×#108	1	2	yes	—
85	C₄×C₁₉	—	2	4	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	4	2	no	—
88	C₄×C₁₉	#424	1	4	yes	—
89	C₄×C₁₉	#496	1	1	yes	characteristic
90	C₄×C₁₉	#497	1	1	yes	characteristic
91	C₄×C₁₉	#501	1	2	yes	—
92	C₂×C₄⋊C₈	—	2	2	no	—
93	C₂×C₄⋊C₈	—	19	1	no	—
94	C₂×C₄⋊C₈	—	19	1	no	—
95	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
96	C₂×C₄×C₈	—	19	2	no	—
97	C₄³	C₂×D₁₉	1	1	yes	characteristic
98	#336	—	19	2	no	—
99	#336	—	19	2	no	—
100	#336	—	38	2	no	—
101	#335	—	38	4	no	—
102	#334	—	38	4	no	—
103	C₂×C₁₉	#1573	1	2	yes	—
104	C₂×C₁₉	#1574	1	2	yes	—
105	C₂×C₁₉	#1843	1	1	yes	characteristic
106	C₂×C₁₉	#1847	1	1	yes	characteristic
107	C₂×C₁₉	#1848	1	1	yes	characteristic
108	C₂²×C₈	—	2	2	no	—
109	C₂²×C₈	—	19	4	no	—
110	C₂²×C₈	—	38	1	no	—
111	C₂²×C₈	—	38	1	no	—
112	C₂×C₄²	Dic₃₈	1	2	yes	—
113	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
114	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
115	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
116	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
117	C₄⋊C₈	—	2	2	no	—
118	C₄⋊C₈	—	2	2	no	—
119	C₄⋊C₈	—	4	4	no	—
120	C₄⋊C₈	—	38	2	no	—
121	C₄⋊C₈	—	38	2	no	—
122	C₄×C₈	—	19	4	no	—
123	C₄×C₈	—	19	4	no	—
124	C₁₉	#8812	1	1	yes	characteristic, complemented, Sylow
125	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
126	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
127	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
128	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
129	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
130	C₂×C₈	—	4	4	no	—
131	C₂×C₈	—	4	2	no	—
132	C₂×C₈	—	19	8	no	—
133	C₂×C₈	—	38	4	no	—
134	C₂×C₈	—	38	4	no	—
135	C₂×C₈	—	76	2	no	—
136	C₂×C₈	—	76	1	no	—
137	C₂×C₈	—	76	1	no	—
138	C₂×C₈	—	76	2	no	—
139	C₄²	—	2	2	no	—
140	C₄²	—	2	2	no	—
141	C₄²	—	2	4	no	—
142	C₄²	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	D₄×D₁₉	1	2	yes	—
145	C₄²	Q₈×D₁₉	1	2	yes	—
146	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	#10597279	1	4	yes	—
154	C₂×C₄	#10597334	1	2	yes	—
155	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
156	C₂×C₄	#10597347	1	2	yes	—
157	C₂×C₄	#10597353	1	2	yes	—
158	C₂×C₄	#10597378	1	2	yes	—
159	C₂×C₄	#10597386	1	1	yes	characteristic
160	C₂×C₄	#10597388	1	2	yes	—
161	C₂×C₄	#10597390	1	1	yes	characteristic
162	C₈	—	8	2	no	—
163	C₈	—	38	8	no	—
164	C₈	—	152	1	no	—
165	C₈	—	152	1	no	—
166	C₂²	#11926413	1	1	yes	characteristic
167	C₂²	#11926570	1	1	yes	characteristic
168	C₂²	#11926572	1	1	yes	characteristic
169	C₂²	#11926584	1	2	yes	—
170	C₂²	C₂×#10597279	1	2	yes	—
171	C₄	—	2	4	no	—
172	C₄	—	2	2	no	—
173	C₄	—	4	2	no	—
174	C₄	#11926569	1	4	yes	—
175	C₄	#11926931	1	1	yes	characteristic
176	C₄	#11926936	1	1	yes	characteristic
177	C₄	#11926950	1	2	yes	—
178	C₂	#14562418	1	2	yes	—
179	C₂	#14562426	1	2	yes	—
180	C₂	#14563788	1	1	yes	characteristic
181	C₂	#14563801	1	1	yes	characteristic
182	C₂	#14563806	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563752

C₂

yes

maximal, characteristic

#14563381

C₂

yes

maximal, characteristic

C₂×#11926296

C₂

yes

maximal

C₂×#11926294

C₂

yes

maximal

C₁₉×#1842

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926299

—

#11926299

C₄

yes

—

#11926299

C₄

yes

—

#11926296

—

#11926294

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

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

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

Q₈

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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

#8812

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#108

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1842

D₁₉

yes

—

—

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×#108

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

C₂×C₄×C₈

—

C₄³

C₂×D₁₉

yes

characteristic

#336

—

#336

—

100

#336

—

101

#335

—

102

#334

—

103

C₂×C₁₉

#1573

yes

—

104

C₂×C₁₉

#1574

yes

—

105

C₂×C₁₉

#1843

yes

characteristic

106

C₂×C₁₉

#1847

yes

characteristic

107

C₂×C₁₉

#1848

yes

characteristic

108

C₂²×C₈

—

109

C₂²×C₈

—

110

C₂²×C₈

—

111

C₂²×C₈

—

112

C₂×C₄²

Dic₃₈

yes

—

113

C₂×C₄²

C₄×D₁₉

yes

characteristic

114

C₂×C₄²

C₄×D₁₉

yes

characteristic

115

C₂×C₄²

C₂²⋊D₁₉

yes

—

116

C₂×C₄²

C₂²×D₁₉

yes

characteristic

117

C₄⋊C₈

—

118

C₄⋊C₈

—

119

C₄⋊C₈

—

120

C₄⋊C₈

—

121

C₄⋊C₈

—

122

C₄×C₈

—

123

C₄×C₈

—

124

C₁₉

#8812

yes

characteristic, complemented, Sylow

125

C₂²×C₄

Dic₁₉⋊C₄

yes

—

126

C₂²×C₄

Dic₁₉⋊C₄

yes

—

127

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

128

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

129

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₄²

—

144

C₄²

D₄×D₁₉

yes

—

145

C₄²

Q₈×D₁₉

yes

—

146

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

#10597279

yes

—

154

C₂×C₄

#10597334

yes

—

155

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

156

C₂×C₄

#10597347

yes

—

157

C₂×C₄

#10597353

yes

—

158

C₂×C₄

#10597378

yes

—

159

C₂×C₄

#10597386

yes

characteristic

160

C₂×C₄

#10597388

yes

—

161

C₂×C₄

#10597390

yes

characteristic

162

C₈

—

163

C₈

—

164

C₈

—

152

—

165

C₈

—

152

—

166

C₂²

#11926413

yes

characteristic

167

C₂²

#11926570

yes

characteristic

168

C₂²

#11926572

yes

characteristic

169

C₂²

#11926584

yes

—

170

C₂²

C₂×#10597279

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

#11926569

yes

—

175

C₄

#11926931

yes

characteristic

176

C₄

#11926936

yes

characteristic

177

C₄

#11926950

yes

—

178

C₂

#14562418

yes

—

179

C₂

#14562426

yes

—

180

C₂

#14563788

yes

characteristic

181

C₂

#14563801

yes

characteristic

182

C₂

#14563806

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#8812
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1842

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
124. C₁₉	#8812	semidirect

H ≅ G/N

type

124. C₁₉

#8812

semidirect

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

subgroup	index
#14563752	2
#14563381	2
C₂×#11926296	2
C₂×#11926294	2
C₁₉×#1842	2
#8812	19

subgroup

index

C₁₉×#1842

Subgroups — #18076301

Conjugacy classes of subgroups

Complements

Maximal subgroups