Group #18069163 — subgroups

Subgroups — #18069163

Order 4864.

196 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14564570	C₂	1	1	yes	maximal, characteristic
2	#14561575	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Dic₃₈	C₄	1	1	yes	characteristic
5	C₂×C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	#11926298	—	2	1	no	—
8	#11926298	—	2	1	no	—
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
11	C₂²×Dic₃₈	C₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	C₈	1	1	yes	characteristic
16	C₂×Dic₁₉⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₁₉	—	2	1	no	—
18	C₂²×C₁₉⋊C₈	—	2	1	no	—
19	C₄×Dic₃₈	—	4	1	no	—
20	C₄×Dic₃₈	—	4	1	no	—
21	C₂×C₁₆×C₁₉	—	4	1	no	—
22	C₁₉×C₄⋊C₈	—	4	1	no	—
23	C₂×C₁₉⋊C₁₆	—	4	1	no	—
24	C₄×C₁₉⋊C₈	—	4	1	no	—
25	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	2	1	no	—
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂×Dic₃₈	—	2	1	no	—
31	C₂×Dic₃₈	—	4	1	no	—
32	C₂×Dic₃₈	—	4	1	no	—
33	C₂×Dic₃₈	C₁₆	1	2	yes	complemented
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	4	1	no	—
37	C₂×C₈×C₁₉	—	4	1	no	—
38	C₄²×C₁₉	—	2	1	no	—
39	C₄²×C₁₉	—	2	1	no	—
40	C₄⋊Dic₁₉	—	4	1	no	—
41	Dic₁₉⋊C₄	—	4	2	no	—
42	C₄×Dic₁₉	—	4	1	no	—
43	C₄×Dic₁₉	—	4	1	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	4	1	no	—
46	C₂×C₁₉⋊C₈	—	4	1	no	—
47	C₁₆×C₁₉	—	8	1	no	—
48	C₁₉⋊C₁₆	—	8	1	no	—
49	#7057	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
60	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
61	C₂×Dic₁₉	—	2	2	no	—
62	C₂×Dic₁₉	—	4	1	no	—
63	C₂×Dic₁₉	—	4	1	no	—
64	C₂×Dic₁₉	—	4	2	no	—
65	C₂×Dic₁₉	—	4	1	no	—
66	Dic₃₈	—	4	2	no	—
67	Dic₃₈	—	4	2	no	—
68	C₈×C₁₉	—	4	1	no	—
69	C₈×C₁₉	—	4	1	no	—
70	C₁₉⋊C₈	—	4	2	no	—
71	#1984	—	19	1	no	—
72	#1322	—	19	1	no	—
73	#1322	D₁₉	1	1	yes	characteristic
74	C₂²×C₁₉	—	2	1	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	#323	1	1	yes	characteristic
77	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
78	C₂²×C₁₉	#349	1	1	yes	characteristic
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	2	1	no	—
81	C₄×C₁₉	—	2	1	no	—
82	C₄×C₁₉	—	4	1	no	—
83	C₄×C₁₉	#354	1	1	yes	characteristic
84	C₄×C₁₉	#356	1	1	yes	characteristic
85	Dic₁₉	—	4	2	no	—
86	Dic₁₉	—	8	1	no	—
87	C₂×C₄×Q₈	—	19	1	no	—
88	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
89	C₂×C₄×C₈	—	19	1	no	—
90	C₂²⋊C₁₆	—	2	1	no	—
91	C₂²⋊C₁₆	—	38	1	no	—
92	#336	—	38	1	no	—
93	#336	—	38	1	no	—
94	C₂×C₁₉	—	2	1	no	—
95	C₂×C₁₉	—	2	1	no	—
96	C₂×C₁₉	#1314	1	1	yes	characteristic
97	C₂×C₁₉	#1319	1	1	yes	characteristic
98	C₂×C₁₉	#1321	1	1	yes	characteristic
99	C₂²×Q₈	—	19	1	no	—
100	C₂²×C₈	—	38	1	no	—
101	C₂²×C₈	D₇₆	1	1	yes	characteristic
102	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
103	C₄×Q₈	—	76	1	no	—
104	C₄×Q₈	—	76	1	no	—
105	C₂×C₄⋊C₄	—	19	1	no	—
106	C₂×C₄⋊C₄	—	38	1	no	—
107	C₂×C₄²	—	38	1	no	—
108	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
109	C₂×C₁₆	—	4	1	no	—
110	C₂×C₁₆	—	76	1	no	—
111	C₄⋊C₈	—	4	1	no	—
112	C₄×C₈	—	76	1	no	—
113	C₁₉	#7057	1	1	yes	characteristic, complemented, Sylow
114	C₂×Q₈	—	19	2	no	—
115	C₂×Q₈	—	38	1	no	—
116	C₂×Q₈	—	76	1	no	—
117	C₂×Q₈	—	76	1	no	—
118	C₂²×C₄	—	38	1	no	—
119	C₂²×C₄	—	38	1	no	—
120	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
121	C₂²×C₄	#64515	1	1	yes	characteristic
122	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
123	C₂×C₈	—	2	1	no	—
124	C₂×C₈	—	2	1	no	—
125	C₂×C₈	—	4	1	no	—
126	C₂×C₈	—	4	1	no	—
127	C₂×C₈	—	38	2	no	—
128	C₂×C₈	—	76	1	no	—
129	C₂×C₈	—	76	1	no	—
130	C₄⋊C₄	—	76	1	no	—
131	C₄⋊C₄	—	76	2	no	—
132	C₄²	—	2	1	no	—
133	C₄²	—	2	1	no	—
134	C₄²	—	76	1	no	—
135	C₄²	—	76	1	no	—
136	C₁₆	—	8	1	no	—
137	C₁₆	—	152	1	no	—
138	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
139	Q₈	—	76	2	no	—
140	Q₈	—	76	2	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	4	1	no	—
147	C₂×C₄	—	38	2	no	—
148	C₂×C₄	—	76	1	no	—
149	C₂×C₄	—	76	1	no	—
150	C₂×C₄	—	76	2	no	—
151	C₂×C₄	—	76	1	no	—
152	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
153	C₂×C₄	#10597255	1	1	yes	characteristic
154	C₂×C₄	#10597263	1	1	yes	characteristic
155	C₂×C₄	#10597280	1	1	yes	characteristic
156	C₈	—	4	1	no	—
157	C₈	—	4	1	no	—
158	C₈	—	76	2	no	—
159	C₂²	—	2	1	no	—
160	C₂²	—	2	1	no	—
161	C₂²	#11926267	1	1	yes	characteristic
162	C₂²	(C₂×D₁₉)⋊C₁₆	1	1	yes	characteristic
163	C₂²	#11926325	1	1	yes	characteristic
164	C₄	—	2	1	no	—
165	C₄	—	2	1	no	—
166	C₄	—	2	1	no	—
167	C₄	—	4	1	no	—
168	C₄	—	76	2	no	—
169	C₄	—	152	1	no	—
170	C₄	#11926338	1	1	yes	characteristic
171	C₄	#11926342	1	1	yes	characteristic
172	C₂	—	2	1	no	—
173	C₂	—	2	1	no	—
174	C₂	#14561558	1	1	yes	characteristic
175	C₂	#14561568	1	1	yes	characteristic
176	C₂	#14561572	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564570

C₂

yes

maximal, characteristic

#14561575

C₂

yes

maximal, characteristic

C₁₉×#1322

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₄

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

#11926298

—

#11926298

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₂²×Dic₃₈

C₈

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

C₈

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₂×C₁₉⋊C₁₆

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₁₆

yes

complemented

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7057

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1984

—

#1322

—

#1322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₂²×C₁₉

#349

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×C₄×Q₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

#336

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

100

C₂²×C₈

—

101

C₂²×C₈

D₇₆

yes

characteristic

102

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

103

C₄×Q₈

—

104

C₄×Q₈

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄²

—

108

C₂×C₄²

C₄×D₁₉

yes

characteristic

109

C₂×C₁₆

—

110

C₂×C₁₆

—

111

C₄⋊C₈

—

112

C₄×C₈

—

113

C₁₉

#7057

yes

characteristic, complemented, Sylow

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

C₈×D₁₉

yes

characteristic

121

C₂²×C₄

#64515

yes

characteristic

122

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄²

—

133

C₄²

—

134

C₄²

—

135

C₄²

—

136

C₁₆

—

137

C₁₆

—

152

—

138

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

139

Q₈

—

140

Q₈

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

C₁₆×D₁₉

yes

characteristic

153

C₂×C₄

#10597255

yes

characteristic

154

C₂×C₄

#10597263

yes

characteristic

155

C₂×C₄

#10597280

yes

characteristic

156

C₈

—

157

C₈

—

158

C₈

—

159

C₂²

—

160

C₂²

—

161

C₂²

#11926267

yes

characteristic

162

C₂²

(C₂×D₁₉)⋊C₁₆

yes

characteristic

163

C₂²

#11926325

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

—

152

—

170

C₄

#11926338

yes

characteristic

171

C₄

#11926342

yes

characteristic

172

C₂

—

173

C₂

—

174

C₂

#14561558

yes

characteristic

175

C₂

#14561568

yes

characteristic

176

C₂

#14561572

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂×C₄×C₁₉	C₂×C₁₆
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1322	C₂
socle	C₂²×C₁₉	#323
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1322	D₁₉
hypocenter	C₁₉	#7057
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂×C₄×C₁₉

C₂×C₁₆

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1322

C₂

socle

C₂²×C₁₉

#323

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

N	H ≅ G/N	type
33. C₂×Dic₃₈	C₁₆	semidirect
113. C₁₉	#7057	semidirect

H ≅ G/N

type

33. C₂×Dic₃₈

C₁₆

semidirect

113. C₁₉

#7057

semidirect

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

subgroup	index
#14564570	2
#14561575	2
C₁₉×#1322	2
#7057	19

subgroup

index

#14564570

#14561575

C₁₉×#1322

#7057

Subgroups — #18069163

Conjugacy classes of subgroups

Complements

Maximal subgroups