Group #18075560 — subgroups

Subgroups — #18075560

Order 4864.

336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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	#14572565	C₂	1	1	yes	maximal, characteristic
2	#14562390	C₂	1	2	yes	maximal
3	#14562372	C₂	1	2	yes	maximal
4	C₁₉⋊#1309	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1309	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926671	—	2	2	no	—
8	#11926668	—	2	2	no	—
9	#11926572	C₄	1	2	yes	—
10	#11926568	C₂²	1	2	yes	—
11	#11926502	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926294	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926291	—	2	2	no	—
16	#11926289	—	2	2	no	—
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₁₉×#423	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₁₉	—	2	2	no	—
20	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	#10597372	C₂×C₄	1	2	yes	—
23	#10597370	—	2	2	no	—
24	C₂×#64520	—	2	2	no	—
25	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
27	#10597316	Q₈	1	2	yes	—
28	#10597315	D₄	1	2	yes	—
29	C₄×Dic₃₈	—	2	2	no	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	#10597272	—	2	2	no	—
34	Dic₁₉⋊C₈	—	2	4	no	—
35	C₈×Dic₁₉	—	2	2	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	#41	1	2	yes	—
42	C₂×Dic₃₈	—	2	2	no	—
43	M₁₆×C₁₉	—	4	2	no	—
44	M₁₆×C₁₉	—	8	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	4	2	no	—
47	C₄²×C₁₉	C₂×D₄	1	2	yes	—
48	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₂²⋊Dic₁₉	—	2	2	no	—
51	C₄⋊Dic₁₉	—	2	2	no	—
52	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
53	Dic₁₉⋊C₄	—	2	4	no	—
54	C₄×Dic₁₉	—	2	2	no	—
55	#64520	—	8	2	no	—
56	C₂×C₁₉⋊C₈	—	2	2	no	—
57	C₂×C₁₉⋊C₈	—	4	1	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
60	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
62	#8637	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	#117	1	1	yes	characteristic
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#121	1	2	yes	—
71	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
72	C₂×Dic₁₉	—	2	4	no	—
73	Dic₃₈	—	4	2	no	—
74	Dic₃₈	—	4	2	no	—
75	C₈×C₁₉	—	4	2	no	—
76	C₈×C₁₉	—	8	2	no	—
77	C₁₉⋊C₈	—	2	1	no	—
78	C₁₉⋊C₈	—	2	2	no	—
79	C₁₉⋊C₈	—	8	2	no	—
80	C₁₉⋊C₈	#101	1	2	yes	—
81	#2960	—	19	1	no	—
82	#1566	—	19	2	no	—
83	#1561	—	19	2	no	—
84	#1309	—	19	1	no	—
85	#1309	D₁₉	1	1	yes	characteristic
86	C₂²×C₁₉	—	2	1	no	—
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	#380	1	1	yes	characteristic
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
92	C₄×C₁₉	#413	1	1	yes	characteristic
93	C₄×C₁₉	#471	1	2	yes	—
94	C₄×C₁₉	#471	1	2	yes	—
95	Dic₁₉	—	4	4	no	—
96	#533	—	19	1	no	—
97	#446	—	38	2	no	—
98	C₈×Q₈	—	38	2	no	—
99	#424	—	19	2	no	—
100	#423	—	19	2	no	—
101	#423	C₂×D₁₉	1	2	yes	—
102	#423	C₂×D₁₉	1	1	yes	characteristic
103	#405	—	19	2	no	—
104	C₂×C₄×C₈	—	19	1	no	—
105	#334	—	38	2	no	—
106	#334	—	38	2	no	—
107	#332	—	38	2	no	—
108	#332	—	38	2	no	—
109	C₂×C₁₉	—	4	1	no	—
110	C₂×C₁₉	#1801	1	1	yes	characteristic
111	C₂×C₁₉	#1815	1	2	yes	—
112	C₂×M₁₆	—	2	2	no	—
113	C₂×M₁₆	—	38	2	no	—
114	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
115	C₂²×C₈	—	19	1	no	—
116	C₂²×C₈	—	19	1	no	—
117	C₄⋊Q₈	—	19	2	no	—
118	#125	—	19	2	no	—
119	C₂²⋊Q₈	—	38	2	no	—
120	C₄×Q₈	—	38	2	no	—
121	#117	—	19	2	no	—
122	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
123	C₄⋊C₈	—	2	2	no	—
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	—	2	2	no	—
126	C₄⋊C₈	—	38	4	no	—
127	C₄⋊C₈	—	38	2	no	—
128	C₄⋊C₈	—	38	2	no	—
129	#97	—	38	2	no	—
130	C₄×C₈	—	19	2	no	—
131	C₄×C₈	—	19	2	no	—
132	C₄×C₈	—	38	2	no	—
133	C₁₉	#8637	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₈	—	38	2	no	—
135	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
136	C₂²×C₄	#64541	1	2	yes	—
137	M₁₆	—	4	2	no	—
138	M₁₆	—	8	2	no	—
139	M₁₆	—	152	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	4	2	no	—
142	C₂×C₈	—	19	1	no	—
143	C₂×C₈	—	19	1	no	—
144	C₂×C₈	—	19	2	no	—
145	C₂×C₈	—	38	2	no	—
146	C₂×C₈	—	76	1	no	—
147	C₂×C₈	—	76	2	no	—
148	C₄⋊C₄	—	19	4	no	—
149	C₄⋊C₄	—	38	2	no	—
150	C₄⋊C₄	—	38	4	no	—
151	C₂²⋊C₄	—	38	2	no	—
152	C₄²	—	38	2	no	—
153	C₄²	D₄×D₁₉	1	2	yes	—
154	C₄²	D₄×D₁₉	1	1	yes	characteristic
155	C₄²	Q₈×D₁₉	1	1	yes	characteristic
156	C₂³	#10597318	1	1	yes	characteristic
157	Q₈	—	76	2	no	—
158	Q₈	—	76	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	38	4	no	—
164	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
165	C₂×C₄	#10597330	1	2	yes	—
166	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
167	C₂×C₄	#10597342	1	2	yes	—
168	C₈	—	4	2	no	—
169	C₈	—	8	2	no	—
170	C₈	—	19	2	no	—
171	C₈	—	38	1	no	—
172	C₈	—	38	2	no	—
173	C₈	—	152	2	no	—
174	C₂²	—	2	1	no	—
175	C₂²	—	2	2	no	—
176	C₂²	#11926403	1	1	yes	characteristic
177	C₄	—	2	1	no	—
178	C₄	—	2	2	no	—
179	C₄	—	76	4	no	—
180	C₄	#101×D₁₉	1	1	yes	characteristic
181	C₄	#11926525	1	1	yes	characteristic
182	C₄	#11926806	1	2	yes	—
183	C₄	#11926810	1	2	yes	—
184	C₂	—	4	1	no	—
185	C₂	#14563630	1	1	yes	characteristic
186	C₂	#14563693	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572565

C₂

yes

maximal, characteristic

#14562390

C₂

yes

maximal

#14562372

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal, characteristic

C₁₉×#1309

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

—

C₄

yes

—

#11926568

C₂²

yes

—

#11926502

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

C₂×C₄

yes

—

#10597370

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

#10597316

Q₈

yes

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

#10597272

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#101

yes

—

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#380

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#471

yes

—

Dic₁₉

—

#533

—

#446

—

C₈×Q₈

—

#424

—

100

#423

—

101

#423

C₂×D₁₉

yes

—

102

#423

C₂×D₁₉

yes

characteristic

103

#405

—

104

C₂×C₄×C₈

—

105

#334

—

106

#334

—

107

#332

—

108

#332

—

109

C₂×C₁₉

—

110

C₂×C₁₉

#1801

yes

characteristic

111

C₂×C₁₉

#1815

yes

—

112

C₂×M₁₆

—

113

C₂×M₁₆

—

114

C₂×M₁₆

C₄×D₁₉

yes

—

115

C₂²×C₈

—

116

C₂²×C₈

—

117

C₄⋊Q₈

—

118

#125

—

119

C₂²⋊Q₈

—

120

C₄×Q₈

—

121

#117

—

122

C₂×C₄²

C₂²×D₁₉

yes

characteristic

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

C₄⋊C₈

—

126

C₄⋊C₈

—

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

#97

—

130

C₄×C₈

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₁₉

#8637

yes

characteristic, complemented, Sylow

134

C₂×Q₈

—

135

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

136

C₂²×C₄

#64541

yes

—

137

M₁₆

—

138

M₁₆

—

139

M₁₆

—

152

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₂²⋊C₄

—

152

C₄²

—

153

C₄²

D₄×D₁₉

yes

—

154

C₄²

D₄×D₁₉

yes

characteristic

155

C₄²

Q₈×D₁₉

yes

characteristic

156

C₂³

#10597318

yes

characteristic

157

Q₈

—

158

Q₈

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

165

C₂×C₄

#10597330

yes

—

166

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

167

C₂×C₄

#10597342

yes

—

168

C₈

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₈

—

173

C₈

—

152

—

174

C₂²

—

175

C₂²

—

176

C₂²

#11926403

yes

characteristic

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

#101×D₁₉

yes

characteristic

181

C₄

#11926525

yes

characteristic

182

C₄

#11926806

yes

—

183

C₄

#11926810

yes

—

184

C₂

—

185

C₂

#14563630

yes

characteristic

186

C₂

#14563693

yes

—

	subgroup	G/H
center	C₂²	#11926403
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1309	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1309	D₁₉
hypocenter	C₁₉	#8637
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#11926403

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1309

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
133. C₁₉	#8637	semidirect

H ≅ G/N

type

133. C₁₉

#8637

semidirect

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

subgroup	index
#14572565	2
#14562390	2
#14562372	2
C₁₉⋊#1309	2
C₁₉×#1309	2
#8637	19

subgroup

index

#14572565

#14562390

#14562372

C₁₉⋊#1309

C₁₉×#1309

#8637

Subgroups — #18075560

Conjugacy classes of subgroups

Complements

Maximal subgroups