Group #18069293 — subgroups

Subgroups — #18069293

Order 4864.

294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14561717	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1957	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597269	—	2	2	no	—
4	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#102	—	2	2	no	—
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#384	C₄	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	—	2	1	no	—
9	C₂²×D₄×C₁₉	—	4	1	no	—
10	C₂²×C₈×C₁₉	D₄	1	2	yes	—
11	C₁₉×#127	—	2	1	no	—
12	C₁₉×#127	—	4	1	no	—
13	C₁₉×#127	C₈	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
15	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×#102	—	4	2	no	—
18	C₁₉×#102	—	4	2	no	—
19	C₄×C₈×C₁₉	—	4	1	no	—
20	#10597269	—	2	4	no	—
21	#10597269	—	4	2	no	—
22	C₂×C₁₉⋊C₁₆	—	4	2	no	—
23	C₂⁴×C₁₉	—	4	1	no	—
24	C₂×D₄×C₁₉	—	2	2	no	—
25	C₂×D₄×C₁₉	—	4	2	no	—
26	C₂×D₄×C₁₉	—	4	2	no	—
27	C₂×D₄×C₁₉	—	4	1	no	—
28	C₂×D₄×C₁₉	—	4	2	no	—
29	C₂×D₄×C₁₉	—	4	2	no	—
30	C₂×D₄×C₁₉	—	8	2	no	—
31	C₂×D₄×C₁₉	—	8	2	no	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	—	4	1	no	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	D₈	1	2	yes	—
38	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
39	C₄⋊C₄×C₁₉	—	4	2	no	—
40	C₄⋊C₄×C₁₉	—	8	2	no	—
41	C₄²×C₁₉	—	2	1	no	—
42	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
43	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
44	C₁₉⋊C₁₆	—	4	4	no	—
45	#7107	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	—	4	2	no	—
47	C₂³×C₁₉	—	8	2	no	—
48	C₂³×C₁₉	—	8	2	no	—
49	C₂³×C₁₉	—	8	1	no	—
50	C₂³×C₁₉	—	8	1	no	—
51	C₂³×C₁₉	#100	1	1	yes	characteristic
52	D₄×C₁₉	—	4	4	no	—
53	D₄×C₁₉	—	8	4	no	—
54	D₄×C₁₉	—	8	4	no	—
55	D₄×C₁₉	—	8	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	8	2	no	—
61	C₂×C₄×C₁₉	—	8	1	no	—
62	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#102	1	2	yes	—
65	C₂×C₄×C₁₉	#104	1	2	yes	—
66	C₈×C₁₉	—	2	2	no	—
67	C₈×C₁₉	—	2	2	no	—
68	#1957	D₁₉	1	1	yes	characteristic
69	#1376	—	19	2	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	8	4	no	—
73	C₂²×C₁₉	—	8	2	no	—
74	C₂²×C₁₉	—	16	2	no	—
75	C₂²×C₁₉	—	16	1	no	—
76	C₂²×C₁₉	—	16	1	no	—
77	C₂²×C₁₉	#323	1	1	yes	characteristic
78	C₂²×C₁₉	#329	1	1	yes	characteristic
79	C₂²×C₁₉	#331	1	1	yes	characteristic
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	—	16	1	no	—
83	C₄×C₁₉	D₄⋊C₈	1	2	yes	—
84	C₄×C₁₉	#327	1	2	yes	—
85	C₂×#127	Dic₁₉	1	1	yes	characteristic
86	C₂×M₃₂	—	38	2	no	—
87	C₂×#102	—	2	2	no	—
88	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
89	#384	Dic₁₉	1	1	yes	characteristic
90	C₂×C₁₉	—	2	1	no	—
91	C₂×C₁₉	—	2	1	no	—
92	C₂×C₁₉	—	16	2	no	—
93	C₂×C₁₉	#1270	1	1	yes	characteristic
94	C₂×C₁₉	#1357	1	1	yes	characteristic
95	C₂×C₁₉	#1359	1	1	yes	characteristic
96	C₂²×D₄	—	2	1	no	—
97	C₂²×D₄	—	4	1	no	—
98	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
99	#127	—	2	1	no	—
100	#127	—	4	1	no	—
101	#127	C₁₉⋊C₈	1	2	yes	—
102	C₂×C₄⋊C₄	—	2	1	no	—
103	C₂×C₄⋊C₄	—	4	1	no	—
104	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
105	M₃₂	—	38	4	no	—
106	M₃₂	—	76	2	no	—
107	C₂×C₁₆	—	76	2	no	—
108	#102	—	4	2	no	—
109	#102	—	4	2	no	—
110	C₄×C₈	—	4	1	no	—
111	C₁₉	#7107	1	1	yes	characteristic, complemented, Sylow
112	C₂⁴	—	4	1	no	—
113	C₂×D₄	—	2	2	no	—
114	C₂×D₄	—	4	2	no	—
115	C₂×D₄	—	4	2	no	—
116	C₂×D₄	—	4	2	no	—
117	C₂×D₄	—	4	1	no	—
118	C₂×D₄	—	4	2	no	—
119	C₂×D₄	—	8	2	no	—
120	C₂×D₄	—	8	2	no	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	4	1	no	—
123	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	#64525	1	2	yes	—
127	C₂×C₈	#64526	1	2	yes	—
128	C₄⋊C₄	—	4	2	no	—
129	C₄⋊C₄	—	8	2	no	—
130	C₄²	—	2	1	no	—
131	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
132	C₄²	#64520	1	1	yes	characteristic
133	C₁₆	—	76	4	no	—
134	C₂³	—	4	2	no	—
135	C₂³	—	8	2	no	—
136	C₂³	—	8	2	no	—
137	C₂³	—	8	1	no	—
138	C₂³	—	8	1	no	—
139	C₂³	#10597290	1	1	yes	characteristic
140	D₄	—	4	4	no	—
141	D₄	—	8	4	no	—
142	D₄	—	8	4	no	—
143	D₄	—	8	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	8	2	no	—
149	C₂×C₄	—	8	1	no	—
150	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
151	C₂×C₄	#10597289	1	2	yes	—
152	C₂×C₄	#10597291	1	1	yes	characteristic
153	C₂×C₄	#10597294	1	2	yes	—
154	C₈	—	2	2	no	—
155	C₈	—	2	2	no	—
156	C₂²	—	2	1	no	—
157	C₂²	—	2	1	no	—
158	C₂²	—	8	4	no	—
159	C₂²	—	8	2	no	—
160	C₂²	—	16	2	no	—
161	C₂²	—	16	1	no	—
162	C₂²	—	16	1	no	—
163	C₂²	#11926268	1	1	yes	characteristic
164	C₂²	#11926284	1	1	yes	characteristic
165	C₂²	#11926288	1	1	yes	characteristic
166	C₄	—	2	2	no	—
167	C₄	—	2	2	no	—
168	C₄	—	16	1	no	—
169	C₄	D₄⋊(C₁₉⋊C₈)	1	2	yes	—
170	C₄	#11926278	1	2	yes	—
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	—	16	2	no	—
174	C₂	#14561456	1	1	yes	characteristic
175	C₂	#14561672	1	1	yes	characteristic
176	C₂	#14561676	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561717

C₂

yes

maximal, complemented

C₁₉×#1957

C₂

yes

maximal, characteristic

C₂×#10597269

—

C₂×C₁₉×#127

C₄

yes

characteristic

C₂×C₁₉×#102

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

C₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#102

—

C₁₉×#102

—

C₄×C₈×C₁₉

—

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7107

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1957

D₁₉

yes

characteristic

#1376

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

—

C₄×C₁₉

#327

yes

—

C₂×#127

Dic₁₉

yes

characteristic

C₂×M₃₂

—

C₂×#102

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

Dic₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

#127

—

100

#127

—

101

#127

C₁₉⋊C₈

yes

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

105

M₃₂

—

106

M₃₂

—

107

C₂×C₁₆

—

108

#102

—

109

#102

—

110

C₄×C₈

—

111

C₁₉

#7107

yes

characteristic, complemented, Sylow

112

C₂⁴

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂×D₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

#64525

yes

—

127

C₂×C₈

#64526

yes

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄²

—

131

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

132

C₄²

#64520

yes

characteristic

133

C₁₆

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

—

139

C₂³

#10597290

yes

characteristic

140

D₄

—

141

D₄

—

142

D₄

—

143

D₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

151

C₂×C₄

#10597289

yes

—

152

C₂×C₄

#10597291

yes

characteristic

153

C₂×C₄

#10597294

yes

—

154

C₈

—

155

C₈

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

#11926268

yes

characteristic

164

C₂²

#11926284

yes

characteristic

165

C₂²

#11926288

yes

characteristic

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

D₄⋊(C₁₉⋊C₈)

yes

—

170

C₄

#11926278

yes

—

171

C₂

—

172

C₂

—

173

C₂

—

174

C₂

#14561456

yes

characteristic

175

C₂

#14561672

yes

characteristic

176

C₂

#14561676

yes

characteristic

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄²×C₁₉	C₂×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1957	C₂
socle	C₂²×C₁₉	#331
prime radical	C₂×C₁₉×#127	C₄
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1957	D₁₉
hypocenter	C₁₉	#7107
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1957

subgroup

G/H

center

C₂²

#11926288

commutator

C₄²×C₁₉

C₂×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#1957

C₂

socle

C₂²×C₁₉

#331

prime radical

C₂×C₁₉×#127

C₄

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1957

N	H ≅ G/N	type
1. #14561717	C₂	semidirect
111. C₁₉	#7107	semidirect

H ≅ G/N

type

1. #14561717

C₂

semidirect

111. C₁₉

#7107

semidirect

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

subgroup	index
#14561717	2
C₁₉×#1957	2
#7107	19

subgroup

index

#14561717

C₁₉×#1957

#7107

Subgroups — #18069293

Conjugacy classes of subgroups

Complements

Maximal subgroups