Group #18076344 — subgroups

Subgroups — #18076344

Order 4864.

322 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14563773	C₂	1	1	yes	maximal, characteristic
2	#14562393	C₂	1	2	yes	maximal
3	#14562390	C₂	1	2	yes	maximal
4	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1837	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	#11926309	—	2	2	no	—
10	#11926296	—	2	4	no	—
11	#11926294	—	2	4	no	—
12	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
15	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
16	C₁₉×#423	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#341	—	2	2	no	—
19	C₂×M₁₆×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	D₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×#64520	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
24	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
25	C₁₉×C₄⋊C₈	—	2	2	no	—
26	C₁₉×C₄⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₉	Q₈	1	2	yes	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
37	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	M₁₆×C₁₉	—	4	4	no	—
42	C₂×C₈×C₁₉	—	2	4	no	—
43	C₂×C₈×C₁₉	—	4	2	no	—
44	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
46	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	#64520	—	4	4	no	—
51	C₂×C₁₉⋊C₈	—	2	4	no	—
52	C₂×C₁₉⋊C₈	—	2	4	no	—
53	C₂×C₁₉⋊C₈	—	4	2	no	—
54	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
55	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
56	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
57	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
58	#8824	—	19	1	no	maximal, Sylow
59	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₄×C₁₉	#135	1	4	yes	—
69	C₈×C₁₉	—	2	2	no	—
70	C₈×C₁₉	—	2	2	no	—
71	C₈×C₁₉	—	8	2	no	—
72	C₁₉⋊C₈	—	2	2	no	—
73	C₁₉⋊C₈	—	2	2	no	—
74	C₁₉⋊C₈	—	8	2	no	—
75	C₁₉⋊C₈	#108	1	4	yes	—
76	C₁₉⋊C₈	#108	1	4	yes	—
77	#1837	—	19	1	no	—
78	#1837	D₁₉	1	1	yes	characteristic
79	#1567	—	19	2	no	—
80	#1566	—	19	2	no	—
81	C₂×C₈²	—	19	1	no	—
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	—	2	1	no	—
84	C₂²×C₁₉	#384	1	1	yes	characteristic
85	C₂²×C₁₉	#499	1	2	yes	—
86	C₄×C₁₉	—	2	1	no	—
87	C₄×C₁₉	—	2	1	no	—
88	C₄×C₁₉	#427	1	2	yes	—
89	C₄×C₁₉	C₂×#108	1	2	yes	—
90	C₄×C₁₉	C₂×#108	1	2	yes	—
91	C₄×C₁₉	#495	1	2	yes	—
92	#423	—	19	2	no	—
93	#423	C₂×D₁₉	1	2	yes	—
94	C₂×C₄×C₈	—	19	1	no	—
95	C₂×C₄×C₈	—	19	1	no	—
96	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
97	#341	—	2	2	no	—
98	#341	—	38	2	no	—
99	#335	—	38	4	no	—
100	#334	—	38	4	no	—
101	C₈²	—	19	1	no	—
102	C₈²	—	19	1	no	—
103	C₈²	—	19	1	no	—
104	C₈²	—	19	1	no	—
105	C₂×C₁₉	—	2	2	no	—
106	C₂×C₁₉	#1846	1	1	yes	characteristic
107	C₂×C₁₉	#1848	1	1	yes	characteristic
108	C₂×C₁₉	#1848	1	1	yes	characteristic
109	C₂×M₁₆	—	2	2	no	—
110	C₂×M₁₆	—	38	2	no	—
111	C₂²×C₈	—	19	2	no	—
112	C₂²×C₈	—	19	2	no	—
113	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
114	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
115	C₄⋊C₈	—	2	2	no	—
116	C₄⋊C₈	—	2	2	no	—
117	C₄⋊C₈	—	38	2	no	—
118	C₄⋊C₈	—	38	2	no	—
119	C₄×C₈	—	19	1	no	—
120	C₄×C₈	—	19	1	no	—
121	C₄×C₈	—	19	1	no	—
122	C₄×C₈	—	19	1	no	—
123	C₄×C₈	—	19	2	no	—
124	C₄×C₈	—	19	2	no	—
125	C₄×C₈	Dic₃₈	1	2	yes	—
126	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
127	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
128	C₁₉	#8824	1	1	yes	characteristic, complemented, Sylow
129	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
130	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
131	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
132	M₁₆	—	4	4	no	—
133	M₁₆	—	76	4	no	—
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	4	2	no	—
136	C₂×C₈	—	19	2	no	—
137	C₂×C₈	—	19	2	no	—
138	C₂×C₈	—	19	2	no	—
139	C₂×C₈	—	19	2	no	—
140	C₂×C₈	—	38	4	no	—
141	C₂×C₈	—	38	4	no	—
142	C₂×C₈	—	76	2	no	—
143	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
144	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
145	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
146	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
147	C₄²	D₄×D₁₉	1	1	yes	characteristic
148	C₄²	D₄×D₁₉	1	1	yes	characteristic
149	C₂³	#10597390	1	1	yes	characteristic
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	#10597334	1	1	yes	characteristic
153	C₂×C₄	#10597334	1	1	yes	characteristic
154	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
155	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
156	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
157	C₂×C₄	#10597386	1	1	yes	characteristic
158	C₂×C₄	#10597396	1	4	yes	—
159	C₈	—	2	2	no	—
160	C₈	—	2	2	no	—
161	C₈	—	8	2	no	—
162	C₈	—	19	4	no	—
163	C₈	—	19	4	no	—
164	C₈	—	38	2	no	—
165	C₈	—	38	2	no	—
166	C₈	—	152	2	no	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	1	no	—
169	C₂²	#11926413	1	1	yes	characteristic
170	C₂²	#11926943	1	2	yes	—
171	C₄	—	2	1	no	—
172	C₄	—	2	1	no	—
173	C₄	#11926580	1	2	yes	—
174	C₄	#108×D₁₉	1	2	yes	—
175	C₄	#108×D₁₉	1	2	yes	—
176	C₄	#11926926	1	2	yes	—
177	C₂	—	2	2	no	—
178	C₂	#14563797	1	1	yes	characteristic
179	C₂	#14563805	1	1	yes	characteristic
180	C₂	#14563805	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563773

C₂

yes

maximal, characteristic

#14562393

C₂

yes

maximal

#14562390

C₂

yes

maximal

C₂×C₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₁₉×#1837

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₈×C₁₉⋊C₈

C₄

yes

characteristic

C₈×C₁₉⋊C₈

C₄

yes

characteristic

C₈×C₁₉⋊C₈

C₄

yes

characteristic

C₈×C₁₉⋊C₈

C₄

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#341

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₁₉⋊C₈

Q₈

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

#8824

—

maximal, Sylow

C₂³×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#108

yes

—

C₁₉⋊C₈

#108

yes

—

#1837

—

#1837

D₁₉

yes

characteristic

#1567

—

#1566

—

C₂×C₈²

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#499

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#427

yes

—

C₄×C₁₉

C₂×#108

yes

—

C₄×C₁₉

C₂×#108

yes

—

C₄×C₁₉

#495

yes

—

#423

—

#423

C₂×D₁₉

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

100

#334

—

101

C₈²

—

102

C₈²

—

103

C₈²

—

104

C₈²

—

105

C₂×C₁₉

—

106

C₂×C₁₉

#1846

yes

characteristic

107

C₂×C₁₉

#1848

yes

characteristic

108

C₂×C₁₉

#1848

yes

characteristic

109

C₂×M₁₆

—

110

C₂×M₁₆

—

111

C₂²×C₈

—

112

C₂²×C₈

—

113

C₂²×C₈

C₂²⋊D₁₉

yes

—

114

C₂×C₄²

C₂²×D₁₉

yes

characteristic

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

C₄⋊C₈

—

119

C₄×C₈

—

120

C₄×C₈

—

121

C₄×C₈

—

122

C₄×C₈

—

123

C₄×C₈

—

124

C₄×C₈

—

125

C₄×C₈

Dic₃₈

yes

—

126

C₄×C₈

C₄×D₁₉

yes

characteristic

127

C₄×C₈

C₄×D₁₉

yes

characteristic

128

C₁₉

#8824

yes

characteristic, complemented, Sylow

129

C₂²×C₄

Q₈×D₁₉

yes

characteristic

130

C₂²×C₄

Q₈×D₁₉

yes

characteristic

131

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

132

M₁₆

—

133

M₁₆

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

Dic₁₉⋊C₄

yes

—

144

C₂×C₈

Dic₁₉⋊C₄

yes

—

145

C₄²

C₂×Dic₃₈

yes

characteristic

146

C₄²

C₂×C₄×D₁₉

yes

characteristic

147

C₄²

D₄×D₁₉

yes

characteristic

148

C₄²

D₄×D₁₉

yes

characteristic

149

C₂³

#10597390

yes

characteristic

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

#10597334

yes

characteristic

153

C₂×C₄

#10597334

yes

characteristic

154

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

155

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

156

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

157

C₂×C₄

#10597386

yes

characteristic

158

C₂×C₄

#10597396

yes

—

159

C₈

—

160

C₈

—

161

C₈

—

162

C₈

—

163

C₈

—

164

C₈

—

165

C₈

—

166

C₈

—

152

—

167

C₂²

—

168

C₂²

—

169

C₂²

#11926413

yes

characteristic

170

C₂²

#11926943

yes

—

171

C₄

—

172

C₄

—

173

C₄

#11926580

yes

—

174

C₄

#108×D₁₉

yes

—

175

C₄

#108×D₁₉

yes

—

176

C₄

#11926926

yes

—

177

C₂

—

178

C₂

#14563797

yes

characteristic

179

C₂

#14563805

yes

characteristic

180

C₂

#14563805

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1837	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1837	D₁₉
hypocenter	C₁₉	#8824
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1837

C₂

socle

C₂²×C₁₉

#384

prime radical

C₂³×C₁₉

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
128. C₁₉	#8824	semidirect

H ≅ G/N

type

128. C₁₉

#8824

semidirect

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

subgroup	index
#14563773	2
#14562393	2
#14562390	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1837	2
#8824	19

subgroup

index

#14563773

#14562393

#14562390

C₂×C₈×C₁₉⋊C₈

C₁₉×#1837

#8824

Subgroups — #18076344

Conjugacy classes of subgroups

Complements

Maximal subgroups