Group #18069254 — subgroups

Subgroups — #18069254

Order 4864.

212 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14561575	C₂	1	1	yes	maximal, characteristic
2	#14561510	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2056	C₂	1	1	yes	maximal, characteristic
4	#11926568	—	2	1	no	—
5	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
6	C₂²×Q₁₆×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×#103	—	2	1	no	—
9	C₁₉×#391	—	2	1	no	—
10	C₁₉×#340	C₄	1	1	yes	characteristic
11	C₂²×Q₈×C₁₉	—	2	1	no	—
12	C₂×Q₁₆×C₁₉	—	4	1	no	—
13	C₂×Q₁₆×C₁₉	—	4	2	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	1	no	—
17	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
18	C₂×#64520	—	4	1	no	—
19	C₁₉×C₄⋊C₈	—	4	1	no	—
20	C₁₉×#103	—	4	2	no	—
21	C₁₉×#95	—	4	1	no	—
22	C₁₉×#95	—	4	1	no	—
23	C₂×C₁₉⋊C₁₆	—	4	1	no	—
24	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
26	C₂×Q₈×C₁₉	—	2	2	no	—
27	C₂×Q₈×C₁₉	—	4	1	no	—
28	C₂×Q₈×C₁₉	—	4	1	no	—
29	C₂×Q₈×C₁₉	—	4	1	no	—
30	C₂×Q₈×C₁₉	—	4	1	no	—
31	C₂×Q₈×C₁₉	—	4	1	no	—
32	C₂²×C₄×C₁₉	—	4	1	no	—
33	C₂²×C₄×C₁₉	—	4	1	no	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
37	Q₁₆×C₁₉	—	4	2	no	—
38	Q₁₆×C₁₉	—	4	2	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	—	2	1	no	—
41	C₂×C₈×C₁₉	—	4	1	no	—
42	C₂×C₈×C₁₉	—	4	1	no	—
43	C₄⋊C₄×C₁₉	—	4	1	no	—
44	C₄⋊C₄×C₁₉	—	4	1	no	—
45	C₄²×C₁₉	—	2	1	no	—
46	C₄²×C₁₉	—	2	1	no	—
47	#64520	—	8	1	no	—
48	#64520	—	8	1	no	—
49	C₂×C₁₉⋊C₈	—	4	2	no	—
50	C₁₉⋊C₁₆	—	8	1	no	—
51	#7090	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	#102	1	1	yes	characteristic
53	Q₈×C₁₉	—	4	2	no	—
54	Q₈×C₁₉	—	4	2	no	—
55	Q₈×C₁₉	—	8	1	no	—
56	Q₈×C₁₉	—	8	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	4	1	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	8	1	no	—
65	C₂×C₄×C₁₉	—	8	1	no	—
66	C₂×C₄×C₁₉	—	8	1	no	—
67	C₂×C₄×C₁₉	—	8	1	no	—
68	C₂×C₄×C₁₉	—	8	1	no	—
69	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
71	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
72	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
73	C₈×C₁₉	—	4	1	no	—
74	C₈×C₁₉	—	4	1	no	—
75	C₁₉⋊C₈	—	8	2	no	—
76	#2056	D₁₉	1	1	yes	characteristic
77	#1322	—	19	1	no	—
78	#1292	—	19	1	no	—
79	C₂²×C₁₉	—	2	1	no	—
80	C₂²×C₁₉	—	2	1	no	—
81	C₂²×C₁₉	#327	1	1	yes	characteristic
82	C₂²×C₁₉	#358	1	1	yes	characteristic
83	C₂²×C₁₉	#360	1	1	yes	characteristic
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	2	1	no	—
87	C₄×C₁₉	—	4	1	no	—
88	C₄×C₁₉	—	8	2	no	—
89	C₄×C₁₉	—	16	1	no	—
90	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
91	C₄×C₁₉	#355	1	1	yes	characteristic
92	C₂²×Q₁₆	Dic₁₉	1	1	yes	characteristic
93	#423	—	38	1	no	—
94	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
95	C₂×#103	—	2	1	no	—
96	#391	—	2	1	no	—
97	C₂²⋊C₁₆	—	38	1	no	—
98	#340	Dic₁₉	1	1	yes	characteristic
99	C₂×C₁₉	—	2	1	no	—
100	C₂×C₁₉	—	2	1	no	—
101	C₂×C₁₉	#1342	1	1	yes	characteristic
102	C₂×C₁₉	#1345	1	1	yes	characteristic
103	C₂×C₁₉	#1348	1	1	yes	characteristic
104	C₂²×Q₈	—	2	1	no	—
105	C₂×Q₁₆	—	4	1	no	—
106	C₂×Q₁₆	—	4	2	no	—
107	C₂×M₁₆	—	76	1	no	—
108	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
109	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂×C₄⋊C₄	—	2	1	no	—
111	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₂×C₁₆	—	76	1	no	—
113	C₄⋊C₈	—	4	1	no	—
114	C₄⋊C₈	—	38	2	no	—
115	C₄⋊C₈	—	76	1	no	—
116	#103	—	4	2	no	—
117	#95	—	4	1	no	—
118	#95	—	4	1	no	—
119	C₁₉	#7090	1	1	yes	characteristic, complemented, Sylow
120	C₂×Q₈	—	2	2	no	—
121	C₂×Q₈	—	4	1	no	—
122	C₂×Q₈	—	4	1	no	—
123	C₂×Q₈	—	4	1	no	—
124	C₂×Q₈	—	4	1	no	—
125	C₂×Q₈	—	4	1	no	—
126	C₂²×C₄	—	4	1	no	—
127	C₂²×C₄	—	4	1	no	—
128	C₂²×C₄	#64525	1	1	yes	characteristic
129	C₂²×C₄	#64526	1	1	yes	characteristic
130	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	Q₁₆	—	4	2	no	—
132	Q₁₆	—	4	2	no	—
133	M₁₆	—	152	1	no	—
134	M₁₆	—	152	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	4	1	no	—
138	C₂×C₈	—	4	1	no	—
139	C₂×C₈	—	76	2	no	—
140	C₄⋊C₄	—	4	1	no	—
141	C₄⋊C₄	—	4	1	no	—
142	C₄²	—	2	1	no	—
143	C₄²	—	2	1	no	—
144	C₁₆	—	152	1	no	—
145	C₂³	#10597289	1	1	yes	characteristic
146	Q₈	—	4	2	no	—
147	Q₈	—	4	2	no	—
148	Q₈	—	8	1	no	—
149	Q₈	—	8	1	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	4	1	no	—
156	C₂×C₄	—	4	2	no	—
157	C₂×C₄	—	8	1	no	—
158	C₂×C₄	—	8	1	no	—
159	C₂×C₄	—	8	1	no	—
160	C₂×C₄	—	8	1	no	—
161	C₂×C₄	—	8	1	no	—
162	C₂×C₄	#10597285	1	1	yes	characteristic
163	C₂×C₄	#10597286	1	1	yes	characteristic
164	C₂×C₄	#10597291	1	1	yes	characteristic
165	C₂×C₄	#10597294	1	1	yes	characteristic
166	C₈	—	4	1	no	—
167	C₈	—	4	1	no	—
168	C₈	—	152	2	no	—
169	C₂²	—	2	1	no	—
170	C₂²	—	2	1	no	—
171	C₂²	#11926278	1	1	yes	characteristic
172	C₂²	#11926348	1	1	yes	characteristic
173	C₂²	#11926354	1	1	yes	characteristic
174	C₄	—	2	1	no	—
175	C₄	—	2	1	no	—
176	C₄	—	2	1	no	—
177	C₄	—	4	1	no	—
178	C₄	—	8	2	no	—
179	C₄	—	16	1	no	—
180	C₄	#11926331	1	1	yes	characteristic
181	C₄	#11926341	1	1	yes	characteristic
182	C₂	—	2	1	no	—
183	C₂	—	2	1	no	—
184	C₂	#14561629	1	1	yes	characteristic
185	C₂	#14561638	1	1	yes	characteristic
186	C₂	#14561647	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561575

C₂

yes

maximal, characteristic

#14561510

C₂

yes

maximal, characteristic

C₁₉×#2056

C₂

yes

maximal, characteristic

#11926568

—

C₂²⋊(C₁₉⋊C₁₆)

—

C₂²×Q₁₆×C₁₉

C₄

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₁₉×#391

—

C₁₉×#340

C₄

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉×#95

—

C₁₉×#95

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

SD₃₂

yes

characteristic

C₂×C₄×C₁₉

Q₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2056

D₁₉

yes

characteristic

#1322

—

#1292

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₄×C₁₉

#355

yes

characteristic

C₂²×Q₁₆

Dic₁₉

yes

characteristic

#423

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₂×#103

—

#391

—

C₂²⋊C₁₆

—

#340

Dic₁₉

yes

characteristic

C₂×C₁₉

—

100

C₂×C₁₉

—

101

C₂×C₁₉

#1342

yes

characteristic

102

C₂×C₁₉

#1345

yes

characteristic

103

C₂×C₁₉

#1348

yes

characteristic

104

C₂²×Q₈

—

105

C₂×Q₁₆

—

106

C₂×Q₁₆

—

107

C₂×M₁₆

—

108

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

109

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

110

C₂×C₄⋊C₄

—

111

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

112

C₂×C₁₆

—

113

C₄⋊C₈

—

114

C₄⋊C₈

—

115

C₄⋊C₈

—

116

#103

—

117

#95

—

118

#95

—

119

C₁₉

#7090

yes

characteristic, complemented, Sylow

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂×Q₈

—

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

#64525

yes

characteristic

129

C₂²×C₄

#64526

yes

characteristic

130

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

131

Q₁₆

—

132

Q₁₆

—

133

M₁₆

—

152

—

134

M₁₆

—

152

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄²

—

143

C₄²

—

144

C₁₆

—

152

—

145

C₂³

#10597289

yes

characteristic

146

Q₈

—

147

Q₈

—

148

Q₈

—

149

Q₈

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

#10597285

yes

characteristic

163

C₂×C₄

#10597286

yes

characteristic

164

C₂×C₄

#10597291

yes

characteristic

165

C₂×C₄

#10597294

yes

characteristic

166

C₈

—

167

C₈

—

168

C₈

—

152

—

169

C₂²

—

170

C₂²

—

171

C₂²

#11926278

yes

characteristic

172

C₂²

#11926348

yes

characteristic

173

C₂²

#11926354

yes

characteristic

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

#11926331

yes

characteristic

181

C₄

#11926341

yes

characteristic

182

C₂

—

183

C₂

—

184

C₂

#14561629

yes

characteristic

185

C₂

#14561638

yes

characteristic

186

C₂

#14561647

yes

characteristic

	subgroup	G/H
center	C₂²	#11926278
commutator	C₂²×C₈×C₁₉	C₂×C₄
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#2056	C₂
socle	C₂²×C₁₉	#327
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#2056	D₁₉
hypocenter	C₁₉	#7090
LCS	G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #2056

subgroup

G/H

center

C₂²

#11926278

commutator

C₂²×C₈×C₁₉

C₂×C₄

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#2056

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #2056

N	H ≅ G/N	type
119. C₁₉	#7090	semidirect

H ≅ G/N

type

119. C₁₉

#7090

semidirect

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

subgroup	index
#14561575	2
#14561510	2
C₁₉×#2056	2
#7090	19

subgroup

index

#14561575

#14561510

C₁₉×#2056

#7090

Subgroups — #18069254

Conjugacy classes of subgroups

Complements

Maximal subgroups