Group #18073547 — subgroups

Subgroups — #18073547

Order 4864.

384 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 143 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	#14562300	C₂	1	1	yes	maximal, characteristic
2	#14562230	C₂	1	1	yes	maximal, characteristic
3	C₈×#64520	C₂	1	2	yes	maximal
4	#14561524	C₂	1	2	yes	maximal
5	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₄×#64520	C₂²	1	2	yes	—
8	#11926290	C₄	1	4	yes	—
9	#11926286	C₄	1	4	yes	—
10	#11926266	—	2	2	no	—
11	C₈×C₁₉⋊C₈	—	2	2	no	—
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#446	—	2	2	no	—
14	C₈×Q₈×C₁₉	—	2	2	no	—
15	C₁₉×#424	C₄	1	2	yes	—
16	C₁₉×#423	C₂²	1	1	yes	characteristic
17	C₁₉×#405	C₄	1	2	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
23	C₁₉×#125	C₂×C₄	1	2	yes	—
24	C₁₉×C₂²⋊Q₈	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₁₉×#117	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×#64520	—	2	2	no	—
29	C₁₉×C₄⋊C₈	—	2	4	no	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×#97	—	2	2	no	—
32	C₄×C₈×C₁₉	—	2	2	no	—
33	C₄×C₈×C₁₉	D₄	1	2	yes	—
34	C₄×C₈×C₁₉	D₄	1	2	yes	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
37	#10597260	C₂×C₄	1	4	yes	—
38	C₄×C₁₉⋊C₈	—	2	2	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₂×Q₈×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	2	yes	—
43	M₁₆×C₁₉	—	4	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	4	1	no	—
47	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₄⋊C₄×C₁₉	C₄²	1	4	yes	—
53	C₂²⋊C₄×C₁₉	—	2	2	no	—
54	C₄²×C₁₉	—	2	2	no	—
55	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×D₄	1	2	yes	—
58	#64520	—	2	8	no	—
59	C₂×C₁₉⋊C₈	—	2	4	no	—
60	C₂×C₁₉⋊C₈	—	2	4	no	—
61	#8242	—	19	1	no	maximal, Sylow
62	C₂³×C₁₉	#117	1	1	yes	characteristic
63	Q₈×C₁₉	—	4	4	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	4	no	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
71	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
72	C₈×C₁₉	—	2	1	no	—
73	C₈×C₁₉	—	2	2	no	—
74	C₈×C₁₉	—	4	2	no	—
75	C₈×C₁₉	#101	1	2	yes	—
76	C₁₉⋊C₈	—	2	8	no	—
77	C₁₉⋊C₈	—	4	4	no	—
78	#2960	D₁₉	1	1	yes	characteristic
79	#1544	—	19	1	no	—
80	#1526	—	19	1	no	—
81	C₈×M₁₆	—	19	2	no	—
82	#1299	—	19	2	no	—
83	C₂²×C₁₉	—	2	1	no	—
84	C₂²×C₁₉	—	2	2	no	—
85	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
86	C₄×C₁₉	—	2	1	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	4	4	no	—
89	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
90	C₄×C₁₉	#413	1	1	yes	characteristic
91	C₄×C₁₉	#443	1	4	yes	—
92	#533	C₂×D₁₉	1	1	yes	characteristic
93	#446	—	2	2	no	—
94	C₈×Q₈	—	2	2	no	—
95	#431	—	19	2	no	—
96	#424	Dic₁₉	1	2	yes	—
97	#423	C₂×D₁₉	1	1	yes	characteristic
98	#405	Dic₁₉	1	2	yes	—
99	C₄×M₁₆	—	19	2	no	—
100	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
101	#332	—	19	4	no	—
102	#330	—	19	4	no	—
103	#322	—	38	2	no	—
104	C₈²	—	38	2	no	—
105	C₂×C₁₉	—	4	1	no	—
106	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
107	C₂×C₁₉	#1764	1	2	yes	—
108	C₂×M₁₆	—	38	2	no	—
109	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
110	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
111	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
112	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
113	#125	C₄×D₁₉	1	2	yes	—
114	C₂²⋊Q₈	—	2	2	no	—
115	C₄×Q₈	—	2	2	no	—
116	#117	C₂×Dic₁₉	1	2	yes	—
117	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
118	C₄⋊C₈	—	2	4	no	—
119	C₄⋊C₈	—	2	2	no	—
120	C₄⋊C₈	—	19	4	no	—
121	C₂²⋊C₈	—	38	2	no	—
122	#97	—	2	2	no	—
123	#97	—	19	4	no	—
124	C₄×C₈	—	2	2	no	—
125	C₄×C₈	—	38	2	no	—
126	C₄×C₈	—	38	2	no	—
127	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
128	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
129	C₁₉	#8242	1	1	yes	characteristic, complemented, Sylow
130	C₂×Q₈	—	2	2	no	—
131	C₂²×C₄	#64541	1	2	yes	—
132	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
133	M₁₆	—	4	2	no	—
134	M₁₆	—	38	8	no	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	4	1	no	—
138	C₂×C₈	—	38	4	no	—
139	C₂×C₈	—	38	4	no	—
140	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
141	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
142	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
143	C₄⋊C₄	—	2	4	no	—
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	C₄×Dic₁₉	1	4	yes	—
146	C₂²⋊C₄	—	2	2	no	—
147	C₄²	—	2	2	no	—
148	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
149	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
150	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
151	C₂³	#10597372	1	1	yes	characteristic
152	Q₈	—	4	4	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
158	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
159	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
160	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
161	C₈	—	2	2	no	—
162	C₈	—	2	1	no	—
163	C₈	—	4	2	no	—
164	C₈	—	38	8	no	—
165	C₈	—	76	4	no	—
166	C₈	#10597293	1	2	yes	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	2	no	—
169	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	2	no	—
172	C₄	—	4	4	no	—
173	C₄	C₂×#10597293	1	1	yes	characteristic
174	C₄	#11926528	1	1	yes	characteristic
175	C₄	#11926659	1	4	yes	—
176	C₂	—	4	1	no	—
177	C₂	C₄×#10597293	1	1	yes	characteristic
178	C₂	#14563470	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562300

C₂

yes

maximal, characteristic

#14562230

C₂

yes

maximal, characteristic

C₈×#64520

C₂

yes

maximal

#14561524

C₂

yes

maximal

C₁₉×#2960

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₄×#64520

C₂²

yes

—

#11926290

C₄

yes

—

#11926286

C₄

yes

—

#11926266

—

C₈×C₁₉⋊C₈

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#446

—

C₈×Q₈×C₁₉

—

C₁₉×#424

C₄

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#405

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

C₂×C₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×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

—

C₄⋊C₄×C₁₉

C₄²

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#101

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2960

D₁₉

yes

characteristic

#1544

—

#1526

—

C₈×M₁₆

—

#1299

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

#533

C₂×D₁₉

yes

characteristic

#446

—

C₈×Q₈

—

#431

—

#424

Dic₁₉

yes

—

#423

C₂×D₁₉

yes

characteristic

#405

Dic₁₉

yes

—

C₄×M₁₆

—

100

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

101

#332

—

102

#330

—

103

#322

—

104

C₈²

—

105

C₂×C₁₉

—

106

C₂×C₁₉

C₄×#101

yes

characteristic

107

C₂×C₁₉

#1764

yes

—

108

C₂×M₁₆

—

109

C₂×M₁₆

C₂×Dic₁₉

yes

—

110

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

111

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

112

C₄⋊Q₈

C₄×D₁₉

yes

—

113

#125

C₄×D₁₉

yes

—

114

C₂²⋊Q₈

—

115

C₄×Q₈

—

116

#117

C₂×Dic₁₉

yes

—

117

C₂×C₄²

C₂²×D₁₉

yes

characteristic

118

C₄⋊C₈

—

119

C₄⋊C₈

—

120

C₄⋊C₈

—

121

C₂²⋊C₈

—

122

#97

—

123

#97

—

124

C₄×C₈

—

125

C₄×C₈

—

126

C₄×C₈

—

127

C₄×C₈

C₂²⋊D₁₉

yes

—

128

C₄×C₈

C₂²⋊D₁₉

yes

—

129

C₁₉

#8242

yes

characteristic, complemented, Sylow

130

C₂×Q₈

—

131

C₂²×C₄

#64541

yes

—

132

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

133

M₁₆

—

134

M₁₆

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

141

C₂×C₈

C₂²⋊Dic₁₉

yes

—

142

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

C₄×Dic₁₉

yes

—

146

C₂²⋊C₄

—

147

C₄²

—

148

C₄²

C₂×C₄×D₁₉

yes

characteristic

149

C₄²

C₂×C₄×D₁₉

yes

characteristic

150

C₄²

C₂×C₂²⋊D₁₉

yes

—

151

C₂³

#10597372

yes

characteristic

152

Q₈

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

158

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

159

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

160

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

161

C₈

—

162

C₈

—

163

C₈

—

164

C₈

—

165

C₈

—

166

C₈

#10597293

yes

—

167

C₂²

—

168

C₂²

—

169

C₂²

C₄×C₂²⋊Dic₁₉

yes

characteristic

170

C₄

—

171

C₄

—

172

C₄

—

173

C₄

C₂×#10597293

yes

characteristic

174

C₄

#11926528

yes

characteristic

175

C₄

#11926659

yes

—

176

C₂

—

177

C₂

C₄×#10597293

yes

characteristic

178

C₂

#14563470

yes

—

	subgroup	G/H
center	C₂×C₈	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2960	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2960	D₁₉
hypocenter	C₁₉	#8242
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

subgroup

G/H

center

C₂×C₈

C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2960

C₂

socle

C₂²×C₁₉

C₄×C₂²⋊C₄

prime radical

C₂³×C₁₉

#117

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

N	H ≅ G/N	type
129. C₁₉	#8242	semidirect

H ≅ G/N

type

129. C₁₉

#8242

semidirect

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

subgroup	index
#14562300	2
#14562230	2
C₈×#64520	2
#14561524	2
C₁₉×#2960	2
#8242	19

subgroup

index

C₁₉×#2960

Subgroups — #18073547

Conjugacy classes of subgroups

Complements

Maximal subgroups