Group #18069253 — subgroups

Subgroups — #18069253

Order 4864.

212 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14564958	C₂	1	1	yes	maximal, characteristic
2	#14561575	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1292	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₇₆	C₄	1	1	yes	characteristic
5	C₂×#10597273	—	2	1	no	—
6	#11926450	—	2	1	no	—
7	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
8	#11926307	C₄	1	1	yes	characteristic
9	C₁₉×#423	—	2	1	no	—
10	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₈	—	2	1	no	—
12	C₂×M₁₆×C₁₉	—	4	1	no	—
13	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₉	—	2	1	no	—
17	C₂×Dic₇₆	—	4	1	no	—
18	C₂×Dic₇₆	—	4	2	no	—
19	C₁₉×C₄⋊C₈	—	2	2	no	—
20	C₁₉×C₄⋊C₈	—	4	1	no	—
21	C₁₉×C₄⋊C₈	—	4	1	no	—
22	C₁₉⋊#95	—	4	1	no	—
23	C₁₉⋊#95	—	4	1	no	—
24	#10597273	—	4	2	no	—
25	C₂×C₁₉⋊C₁₆	—	4	1	no	—
26	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	4	1	no	—
30	C₂²×Dic₁₉	—	4	1	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	—	4	1	no	—
33	C₂×Dic₃₈	—	4	1	no	—
34	C₂×Dic₃₈	—	4	1	no	—
35	C₂×Dic₃₈	—	4	1	no	—
36	C₂×Dic₃₈	—	4	1	no	—
37	M₁₆×C₁₉	—	8	1	no	—
38	M₁₆×C₁₉	—	8	1	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	C₂×C₈×C₁₉	—	4	2	no	—
44	C₄²×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	2	1	no	—
46	C₄⋊Dic₁₉	—	4	1	no	—
47	C₄⋊Dic₁₉	—	4	1	no	—
48	Dic₇₆	—	4	2	no	—
49	Dic₇₆	—	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	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
61	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
62	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
63	C₂×Dic₁₉	—	4	2	no	—
64	C₂×Dic₁₉	—	8	1	no	—
65	C₂×Dic₁₉	—	8	1	no	—
66	C₂×Dic₁₉	—	8	1	no	—
67	C₂×Dic₁₉	—	8	1	no	—
68	C₂×Dic₁₉	—	8	1	no	—
69	Dic₃₈	—	4	2	no	—
70	Dic₃₈	—	4	2	no	—
71	Dic₃₈	—	8	1	no	—
72	Dic₃₈	—	8	1	no	—
73	C₈×C₁₉	—	4	1	no	—
74	C₈×C₁₉	—	4	1	no	—
75	C₈×C₁₉	—	8	2	no	—
76	#2056	—	19	1	no	—
77	#1322	—	19	1	no	—
78	#1292	D₁₉	1	1	yes	characteristic
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	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
89	C₄×C₁₉	#355	1	1	yes	characteristic
90	Dic₁₉	—	8	2	no	—
91	Dic₁₉	—	16	1	no	—
92	C₂²×Q₁₆	—	19	1	no	—
93	#423	—	2	1	no	—
94	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
95	C₂×#103	—	38	1	no	—
96	#391	—	38	1	no	—
97	C₂²⋊C₁₆	—	38	1	no	—
98	#340	—	19	1	no	—
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	—	38	1	no	—
105	C₂×Q₁₆	—	76	1	no	—
106	C₂×Q₁₆	—	76	2	no	—
107	C₂×M₁₆	—	4	1	no	—
108	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
109	C₂²×C₈	D₇₆	1	1	yes	characteristic
110	C₂×C₄⋊C₄	—	38	1	no	—
111	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₂×C₁₆	—	76	1	no	—
113	C₄⋊C₈	—	2	2	no	—
114	C₄⋊C₈	—	4	1	no	—
115	C₄⋊C₈	—	4	1	no	—
116	#103	—	76	2	no	—
117	#95	—	76	1	no	—
118	#95	—	76	1	no	—
119	C₁₉	#7090	1	1	yes	characteristic, complemented, Sylow
120	C₂×Q₈	—	38	2	no	—
121	C₂×Q₈	—	76	1	no	—
122	C₂×Q₈	—	76	1	no	—
123	C₂×Q₈	—	76	1	no	—
124	C₂×Q₈	—	76	1	no	—
125	C₂×Q₈	—	76	1	no	—
126	C₂²×C₄	—	76	1	no	—
127	C₂²×C₄	—	76	1	no	—
128	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
129	C₂²×C₄	#64525	1	1	yes	characteristic
130	C₂²×C₄	#64527	1	1	yes	characteristic
131	Q₁₆	—	76	2	no	—
132	Q₁₆	—	76	2	no	—
133	M₁₆	—	8	1	no	—
134	M₁₆	—	8	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	—	4	2	no	—
140	C₄⋊C₄	—	76	1	no	—
141	C₄⋊C₄	—	76	1	no	—
142	C₄²	—	2	1	no	—
143	C₄²	—	2	1	no	—
144	C₁₆	—	152	1	no	—
145	C₂³	#10597266	1	1	yes	characteristic
146	Q₈	—	76	2	no	—
147	Q₈	—	76	2	no	—
148	Q₈	—	152	1	no	—
149	Q₈	—	152	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	—	76	2	no	—
157	C₂×C₄	—	152	1	no	—
158	C₂×C₄	—	152	1	no	—
159	C₂×C₄	—	152	1	no	—
160	C₂×C₄	—	152	1	no	—
161	C₂×C₄	—	152	1	no	—
162	C₂×C₄	#10597262	1	1	yes	characteristic
163	C₂×C₄	#10597263	1	1	yes	characteristic
164	C₂×C₄	#10597284	1	1	yes	characteristic
165	C₂×C₄	#10597286	1	1	yes	characteristic
166	C₈	—	4	1	no	—
167	C₈	—	4	1	no	—
168	C₈	—	8	2	no	—
169	C₂²	—	2	1	no	—
170	C₂²	—	2	1	no	—
171	C₂²	#11926277	1	1	yes	characteristic
172	C₂²	#11926347	1	1	yes	characteristic
173	C₂²	#11926353	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	—	304	1	no	—
179	C₄	—	152	2	no	—
180	C₄	#11926332	1	1	yes	characteristic
181	C₄	#11926340	1	1	yes	characteristic
182	C₂	—	2	1	no	—
183	C₂	—	2	1	no	—
184	C₂	#14561628	1	1	yes	characteristic
185	C₂	#14561637	1	1	yes	characteristic
186	C₂	#14561646	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564958

C₂

yes

maximal, characteristic

#14561575

C₂

yes

maximal, characteristic

C₁₉×#1292

C₂

yes

maximal, characteristic

C₂²×Dic₇₆

C₄

yes

characteristic

C₂×#10597273

—

#11926450

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926307

C₄

yes

characteristic

C₁₉×#423

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597273

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

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

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#2056

—

#1322

—

#1292

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₄×C₁₉

#355

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂²×Q₁₆

—

#423

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₂×#103

—

#391

—

C₂²⋊C₁₆

—

#340

—

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

C₄×D₁₉

yes

characteristic

109

C₂²×C₈

D₇₆

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

(C₂×D₁₉)⋊C₄

yes

characteristic

129

C₂²×C₄

#64525

yes

characteristic

130

C₂²×C₄

#64527

yes

characteristic

131

Q₁₆

—

132

Q₁₆

—

133

M₁₆

—

134

M₁₆

—

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

#10597266

yes

characteristic

146

Q₈

—

147

Q₈

—

148

Q₈

—

152

—

149

Q₈

—

152

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

152

—

158

C₂×C₄

—

152

—

159

C₂×C₄

—

152

—

160

C₂×C₄

—

152

—

161

C₂×C₄

—

152

—

162

C₂×C₄

#10597262

yes

characteristic

163

C₂×C₄

#10597263

yes

characteristic

164

C₂×C₄

#10597284

yes

characteristic

165

C₂×C₄

#10597286

yes

characteristic

166

C₈

—

167

C₈

—

168

C₈

—

169

C₂²

—

170

C₂²

—

171

C₂²

#11926277

yes

characteristic

172

C₂²

#11926347

yes

characteristic

173

C₂²

#11926353

yes

characteristic

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

304

—

179

C₄

—

152

—

180

C₄

#11926332

yes

characteristic

181

C₄

#11926340

yes

characteristic

182

C₂

—

183

C₂

—

184

C₂

#14561628

yes

characteristic

185

C₂

#14561637

yes

characteristic

186

C₂

#14561646

yes

characteristic

	subgroup	G/H
center	C₂²	#11926277
commutator	C₂²×C₈×C₁₉	C₂×C₄
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1292	C₂
socle	C₂²×C₁₉	#327
prime radical	C₂³×C₁₉	#102
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1292	D₁₉
hypocenter	C₁₉	#7090
LCS	G ▷ C₂²×C₈×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1292

subgroup

G/H

center

C₂²

#11926277

commutator

C₂²×C₈×C₁₉

C₂×C₄

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1292

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 ◁ #1292

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
#14564958	2
#14561575	2
C₁₉×#1292	2
#7090	19

subgroup

index

#14564958

#14561575

C₁₉×#1292

#7090

Subgroups — #18069253

Conjugacy classes of subgroups

Complements

Maximal subgroups