Group #18069464 — subgroups

Subgroups — #18069464

Order 4864.

262 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 123 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	C₄×#10597269	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	#11926597	—	2	1	no	—
6	#11926320	—	2	1	no	—
7	C₄×C₁₉⋊C₁₆	C₄	1	2	yes	complemented
8	#11926297	—	2	1	no	—
9	#11926295	C₄	1	2	yes	complemented
10	C₂×C₁₉×#106	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₁₉×#340	—	2	1	no	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄²×C₁₉	—	4	1	no	—
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₁₉×#106	—	2	2	no	—
20	C₁₉×#106	C₈	1	4	yes	complemented
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
25	C₁₉×#95	—	4	1	no	—
26	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
27	#10597269	—	2	4	no	—
28	C₂×C₁₉⋊C₁₆	—	2	2	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄×C₁₉⋊C₈	—	4	1	no	—
31	C₂²×C₄×C₁₉	—	4	2	no	—
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
42	C₄⋊C₄×C₁₉	—	2	4	no	—
43	C₄⋊C₄×C₁₉	—	4	2	no	—
44	C₄²×C₁₉	—	8	2	no	—
45	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
47	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
48	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
49	C₂×C₁₉⋊C₈	—	4	2	no	—
50	C₁₉⋊C₁₆	—	2	4	no	—
51	#7174	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	#102	1	1	yes	characteristic
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	—	8	2	no	—
57	C₂×C₄×C₁₉	—	8	2	no	—
58	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
60	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#104	1	2	yes	—
64	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
66	C₈×C₁₉	—	2	1	no	—
67	C₈×C₁₉	—	2	1	no	—
68	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
69	C₈×C₁₉	#97	1	1	yes	characteristic
70	C₈×C₁₉	C₄⋊C₈	1	2	yes	—
71	C₁₉⋊C₈	—	8	2	no	—
72	C₄×M₃₂	—	19	1	no	—
73	C₄×#106	D₁₉	1	1	yes	characteristic
74	#1564	—	19	1	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	D₄⋊C₈	1	2	yes	—
78	C₂²×C₁₉	#340	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	—	8	4	no	—
83	C₄×C₁₉	Q₈⋊C₈	1	2	yes	—
84	C₄×C₁₉	#336	1	1	yes	characteristic
85	C₄×C₁₉	#339	1	1	yes	characteristic
86	C₄×C₁₉	#365	1	2	yes	—
87	C₂×M₃₂	—	38	1	no	—
88	#431	—	38	1	no	—
89	C₂×#106	Dic₁₉	1	2	yes	—
90	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
91	C₄×C₄⋊C₄	—	2	1	no	—
92	#346	—	38	1	no	—
93	C₄×C₁₆	—	19	2	no	—
94	#340	—	2	1	no	—
95	#335	—	38	1	no	—
96	#334	—	19	2	no	—
97	C₂×C₁₉	—	2	2	no	—
98	C₂×C₁₉	#1279	1	1	yes	characteristic
99	C₂×C₁₉	#1383	1	1	yes	characteristic
100	C₂×C₁₉	#1384	1	1	yes	characteristic
101	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
102	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
103	C₂×C₄⋊C₄	—	2	2	no	—
104	C₂×C₄²	—	4	1	no	—
105	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
106	M₃₂	—	38	4	no	—
107	C₂×C₁₆	—	38	2	no	—
108	#106	—	2	2	no	—
109	#106	C₁₉⋊C₈	1	4	yes	complemented
110	C₄⋊C₈	—	38	2	no	—
111	C₂²⋊C₈	—	76	1	no	—
112	C₄×C₈	—	76	1	no	—
113	C₄×C₈	Dic₃₈	1	1	yes	characteristic
114	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
115	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
116	C₄×C₈	D₇₆	1	1	yes	characteristic
117	#95	—	4	1	no	—
118	C₁₉	#7174	1	1	yes	characteristic, complemented, Sylow
119	C₂²×C₄	—	4	2	no	—
120	C₂²×C₄	#64525	1	1	yes	characteristic
121	C₂²×C₄	#64526	1	1	yes	characteristic
122	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
123	C₂×C₈	—	2	2	no	—
124	C₂×C₈	—	76	2	no	—
125	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
126	C₂×C₈	#64520	1	2	yes	—
127	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
128	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
129	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
130	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
131	C₄⋊C₄	—	2	4	no	—
132	C₄⋊C₄	—	4	2	no	—
133	C₄²	—	8	2	no	—
134	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
135	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
136	C₄²	#64527	1	1	yes	characteristic
137	C₄²	#64528	1	1	yes	characteristic
138	C₁₆	—	38	4	no	—
139	C₂³	#10597289	1	1	yes	characteristic
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	—	4	4	no	—
143	C₂×C₄	—	8	2	no	—
144	C₂×C₄	—	8	2	no	—
145	C₂×C₄	#10597264	1	1	yes	characteristic
146	C₂×C₄	#10597265	1	1	yes	characteristic
147	C₂×C₄	#10597266	1	1	yes	characteristic
148	C₂×C₄	#10597267	1	1	yes	characteristic
149	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
150	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
151	C₂×C₄	#10597292	1	1	yes	characteristic
152	C₂×C₄	#10597294	1	2	yes	—
153	C₈	—	2	1	no	—
154	C₈	—	2	1	no	—
155	C₈	—	152	2	no	—
156	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
157	C₈	#10597260	1	1	yes	characteristic
158	C₈	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
159	C₂²	—	2	1	no	—
160	C₂²	—	2	1	no	—
161	C₂²	D₄⋊(C₁₉⋊C₈)	1	2	yes	—
162	C₂²	#11926306	1	1	yes	characteristic
163	C₄	—	2	1	no	—
164	C₄	—	2	1	no	—
165	C₄	—	2	1	no	—
166	C₄	—	8	4	no	—
167	C₄	Q₈⋊(C₁₉⋊C₈)	1	2	yes	—
168	C₄	#11926299	1	1	yes	characteristic
169	C₄	#11926303	1	1	yes	characteristic
170	C₄	#11926366	1	2	yes	—
171	C₂	—	2	2	no	—
172	C₂	#14561476	1	1	yes	characteristic
173	C₂	#14561733	1	1	yes	characteristic
174	C₂	#14561736	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597269

C₂

yes

maximal, characteristic

#14562383

C₂

yes

maximal, characteristic

C₄×C₁₉×#106

C₂

yes

maximal, characteristic

C₂×#10597269

—

#11926597

—

#11926320

—

C₄×C₁₉⋊C₁₆

C₄

yes

complemented

#11926297

—

#11926295

C₄

yes

complemented

C₂×C₁₉×#106

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₁₉×#340

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×#106

—

C₁₉×#106

C₈

yes

complemented

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄×C₈

yes

characteristic

C₈×C₁₉

#97

yes

characteristic

C₈×C₁₉

C₄⋊C₈

yes

—

C₁₉⋊C₈

—

C₄×M₃₂

—

C₄×#106

D₁₉

yes

characteristic

#1564

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

D₄⋊C₈

yes

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₈⋊C₈

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×M₃₂

—

#431

—

C₂×#106

Dic₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₄⋊C₄

—

#346

—

C₄×C₁₆

—

#340

—

#335

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

100

C₂×C₁₉

#1384

yes

characteristic

101

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

102

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

103

C₂×C₄⋊C₄

—

104

C₂×C₄²

—

105

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

106

M₃₂

—

107

C₂×C₁₆

—

108

#106

—

109

#106

C₁₉⋊C₈

yes

complemented

110

C₄⋊C₈

—

111

C₂²⋊C₈

—

112

C₄×C₈

—

113

C₄×C₈

Dic₃₈

yes

characteristic

114

C₄×C₈

C₄×D₁₉

yes

characteristic

115

C₄×C₈

C₄×D₁₉

yes

characteristic

116

C₄×C₈

D₇₆

yes

characteristic

117

#95

—

118

C₁₉

#7174

yes

characteristic, complemented, Sylow

119

C₂²×C₄

—

120

C₂²×C₄

#64525

yes

characteristic

121

C₂²×C₄

#64526

yes

characteristic

122

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₂×C₁₉⋊C₈

yes

—

126

C₂×C₈

#64520

yes

—

127

C₂×C₈

C₄×Dic₁₉

yes

characteristic

128

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

129

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

130

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄²

—

134

C₄²

Dic₁₉⋊C₄

yes

characteristic

135

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

136

C₄²

#64527

yes

characteristic

137

C₄²

#64528

yes

characteristic

138

C₁₆

—

139

C₂³

#10597289

yes

characteristic

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

#10597264

yes

characteristic

146

C₂×C₄

#10597265

yes

characteristic

147

C₂×C₄

#10597266

yes

characteristic

148

C₂×C₄

#10597267

yes

characteristic

149

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

150

C₂×C₄

C₁₉⋊#95

yes

characteristic

151

C₂×C₄

#10597292

yes

characteristic

152

C₂×C₄

#10597294

yes

—

153

C₈

—

154

C₈

—

155

C₈

—

152

—

156

C₈

C₄×C₁₉⋊C₈

yes

characteristic

157

C₈

#10597260

yes

characteristic

158

C₈

C₄⋊(C₁₉⋊C₈)

yes

—

159

C₂²

—

160

C₂²

—

161

C₂²

D₄⋊(C₁₉⋊C₈)

yes

—

162

C₂²

#11926306

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

Q₈⋊(C₁₉⋊C₈)

yes

—

168

C₄

#11926299

yes

characteristic

169

C₄

#11926303

yes

characteristic

170

C₄

#11926366

yes

—

171

C₂

—

172

C₂

#14561476

yes

characteristic

173

C₂

#14561733

yes

characteristic

174

C₂

#14561736

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597265
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₄×C₁₉×#106	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₄×#106	D₁₉
hypocenter	C₁₉	#7174
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#106

subgroup

G/H

center

C₂×C₄

#10597265

commutator

C₈×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₄×C₁₉×#106

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#106

N	H ≅ G/N	type
7. C₄×C₁₉⋊C₁₆	C₄	semidirect
9. #11926295	C₄	semidirect
20. C₁₉×#106	C₈	semidirect
109. #106	C₁₉⋊C₈	semidirect
118. C₁₉	#7174	semidirect

H ≅ G/N

type

7. C₄×C₁₉⋊C₁₆

C₄

semidirect

9. #11926295

C₄

semidirect

20. C₁₉×#106

C₈

semidirect

109. #106

C₁₉⋊C₈

semidirect

118. C₁₉

#7174

semidirect

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

subgroup	index
C₄×#10597269	2
#14562383	2
C₄×C₁₉×#106	2
#7174	19

subgroup

index

C₄×#10597269

#14562383

C₄×C₁₉×#106

#7174

Subgroups — #18069464

Conjugacy classes of subgroups

Complements

Maximal subgroups