Group #18069632 — subgroups

Subgroups — #18069632

Order 4864.

280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14563631	C₂	1	2	yes	maximal
2	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic
3	#11926568	—	2	2	no	—
4	C₂×#10597293	—	2	2	no	—
5	#11926313	C₄	1	4	yes	—
6	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
9	C₁₉×#336	—	2	2	no	—
10	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	—	2	1	no	—
13	C₄×Q₈×C₁₉	—	4	1	no	—
14	C₄×Q₈×C₁₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	2	yes	—
19	C₂×#64520	—	2	4	no	—
20	C₁₉×C₄⋊C₈	—	4	1	no	—
21	C₄×C₈×C₁₉	—	4	1	no	—
22	#10597293	—	4	2	no	—
23	#10597293	—	4	2	no	—
24	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
25	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
26	C₂×Q₈×C₁₉	—	4	1	no	—
27	C₂×Q₈×C₁₉	—	4	1	no	—
28	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
29	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
30	C₂×Q₈×C₁₉	Q₁₆	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	—	4	1	no	—
38	C₂×C₈×C₁₉	—	4	1	no	—
39	C₂×C₈×C₁₉	—	4	2	no	—
40	C₂×C₈×C₁₉	—	4	1	no	—
41	C₄⋊C₄×C₁₉	—	4	2	no	—
42	C₄⋊C₄×C₁₉	—	4	1	no	—
43	C₄²×C₁₉	—	2	1	no	—
44	C₄²×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	2	2	no	—
47	#64520	—	4	4	no	—
48	#64520	—	4	4	no	—
49	C₂×C₁₉⋊C₈	—	4	4	no	—
50	#7238	—	19	1	no	maximal, Sylow
51	C₂³×C₁₉	#95	1	1	yes	characteristic
52	Q₈×C₁₉	—	4	1	no	—
53	Q₈×C₁₉	—	4	2	no	—
54	Q₈×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	2	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	—	2	2	no	—
63	C₂×C₄×C₁₉	—	4	1	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#102	1	2	yes	—
68	C₂×C₄×C₁₉	#103	1	2	yes	—
69	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
70	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
71	C₈×C₁₉	—	4	2	no	—
72	C₈×C₁₉	—	8	1	no	—
73	C₁₉⋊C₈	—	8	4	no	—
74	#1984	D₁₉	1	1	yes	characteristic
75	#1801	—	19	2	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	—	2	1	no	—
78	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
79	C₂²×C₁₉	#340	1	1	yes	characteristic
80	C₂²×C₁₉	#342	1	1	yes	characteristic
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	2	1	no	—
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	4	1	no	—
87	C₄×C₁₉	—	4	2	no	—
88	C₄×C₁₉	#355	1	1	yes	characteristic
89	C₄×C₁₉	#356	1	1	yes	characteristic
90	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
91	#423	—	38	2	no	—
92	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
93	C₂×#101	—	38	2	no	—
94	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
95	#343	—	19	4	no	—
96	#336	—	2	2	no	—
97	C₂×C₁₉	—	2	1	no	—
98	C₂×C₁₉	—	2	1	no	—
99	C₂×C₁₉	#1289	1	1	yes	characteristic
100	C₂×C₁₉	#1392	1	1	yes	characteristic
101	C₂×C₁₉	#1394	1	1	yes	characteristic
102	C₂²×Q₈	D₇₆	1	1	yes	characteristic
103	C₂×M₁₆	—	38	4	no	—
104	C₂²×C₈	—	2	1	no	—
105	C₂²×C₈	—	2	1	no	—
106	C₄×Q₈	—	4	1	no	—
107	C₄×Q₈	—	4	1	no	—
108	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
109	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
110	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
111	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
112	C₄⋊C₈	—	4	1	no	—
113	C₄⋊C₈	—	76	2	no	—
114	C₄⋊C₈	—	76	2	no	—
115	#101	—	76	2	no	—
116	#101	—	76	2	no	—
117	C₄×C₈	—	4	1	no	—
118	C₁₉	#7238	1	1	yes	characteristic, complemented, Sylow
119	C₂×Q₈	—	4	1	no	—
120	C₂×Q₈	—	4	1	no	—
121	C₂×Q₈	#64516	1	2	yes	—
122	C₂×Q₈	D₁₅₂	1	1	yes	characteristic
123	C₂×Q₈	Dic₇₆	1	1	yes	characteristic
124	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
125	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
126	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
127	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
128	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
129	M₁₆	—	76	4	no	—
130	M₁₆	—	76	4	no	—
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	4	1	no	—
133	C₂×C₈	—	4	1	no	—
134	C₂×C₈	—	4	2	no	—
135	C₂×C₈	—	4	1	no	—
136	C₂×C₈	—	76	4	no	—
137	C₄⋊C₄	—	4	1	no	—
138	C₄⋊C₄	—	4	2	no	—
139	C₄²	—	2	1	no	—
140	C₄²	—	2	1	no	—
141	C₄²	—	2	2	no	—
142	C₄²	—	2	2	no	—
143	C₂³	C₁₉⋊#95	1	1	yes	characteristic
144	Q₈	—	4	2	no	—
145	Q₈	—	4	1	no	—
146	Q₈	—	4	1	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	2	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	2	no	—
155	C₂×C₄	—	4	1	no	—
156	C₂×C₄	—	4	2	no	—
157	C₂×C₄	#10597273	1	2	yes	—
158	C₂×C₄	#10597274	1	1	yes	characteristic
159	C₂×C₄	#10597275	1	1	yes	characteristic
160	C₂×C₄	#10597278	1	2	yes	—
161	C₂×C₄	#10597291	1	1	yes	characteristic
162	C₂×C₄	#10597291	1	1	yes	characteristic
163	C₈	—	4	2	no	—
164	C₈	—	8	1	no	—
165	C₈	—	152	4	no	—
166	C₂²	—	2	1	no	—
167	C₂²	—	2	1	no	—
168	C₂²	#11926301	1	1	yes	characteristic
169	C₂²	#11926307	1	1	yes	characteristic
170	C₂²	#11926311	1	1	yes	characteristic
171	C₄	—	2	2	no	—
172	C₄	—	2	2	no	—
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	2	1	no	—
176	C₄	—	4	1	no	—
177	C₄	—	4	2	no	—
178	C₄	#11926341	1	1	yes	characteristic
179	C₄	#11926343	1	1	yes	characteristic
180	C₂	—	2	1	no	—
181	C₂	—	2	1	no	—
182	C₂	#14561503	1	1	yes	characteristic
183	C₂	#14561758	1	1	yes	characteristic
184	C₂	#14561762	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563631

C₂

yes

maximal

C₁₉×#1984

C₂

yes

maximal, characteristic

#11926568

—

C₂×#10597293

—

#11926313

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#336

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

#10597293

—

#10597293

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

characteristic

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂×Q₈×C₁₉

Q₁₆

yes

characteristic

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1984

D₁₉

yes

characteristic

#1801

—

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

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

#423

—

C₂×C₄⋊C₈

Dic₁₉

yes

characteristic

C₂×#101

—

C₂×C₄×C₈

Dic₁₉

yes

characteristic

#343

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1289

yes

characteristic

100

C₂×C₁₉

#1392

yes

characteristic

101

C₂×C₁₉

#1394

yes

characteristic

102

C₂²×Q₈

D₇₆

yes

characteristic

103

C₂×M₁₆

—

104

C₂²×C₈

—

105

C₂²×C₈

—

106

C₄×Q₈

—

107

C₄×Q₈

—

108

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

109

C₂×C₄⋊C₄

C₄×D₁₉

yes

—

110

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

111

C₂×C₄²

C₂²⋊D₁₉

yes

—

112

C₄⋊C₈

—

113

C₄⋊C₈

—

114

C₄⋊C₈

—

115

#101

—

116

#101

—

117

C₄×C₈

—

118

C₁₉

#7238

yes

characteristic, complemented, Sylow

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

#64516

yes

—

122

C₂×Q₈

D₁₅₂

yes

characteristic

123

C₂×Q₈

Dic₇₆

yes

characteristic

124

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

125

C₂²×C₄

Dic₁₉⋊C₄

yes

—

126

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

127

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

128

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

129

M₁₆

—

130

M₁₆

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₂³

C₁₉⋊#95

yes

characteristic

144

Q₈

—

145

Q₈

—

146

Q₈

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

#10597273

yes

—

158

C₂×C₄

#10597274

yes

characteristic

159

C₂×C₄

#10597275

yes

characteristic

160

C₂×C₄

#10597278

yes

—

161

C₂×C₄

#10597291

yes

characteristic

162

C₂×C₄

#10597291

yes

characteristic

163

C₈

—

164

C₈

—

165

C₈

—

152

—

166

C₂²

—

167

C₂²

—

168

C₂²

#11926301

yes

characteristic

169

C₂²

#11926307

yes

characteristic

170

C₂²

#11926311

yes

characteristic

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

#11926341

yes

characteristic

179

C₄

#11926343

yes

characteristic

180

C₂

—

181

C₂

—

182

C₂

#14561503

yes

characteristic

183

C₂

#14561758

yes

characteristic

184

C₂

#14561762

yes

characteristic

	subgroup	G/H
center	C₂²	#11926311
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂×C₄×Q₈	C₂×D₁₉
Fitting	C₁₉×#1984	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂³×C₁₉	#95
cosocle	C₂×C₄×Q₈×C₁₉	C₂²
hypercenter	#1984	D₁₉
hypocenter	C₁₉	#7238
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×Q₈ ◁ #1984

subgroup

G/H

center

C₂²

#11926311

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂×C₄×Q₈

C₂×D₁₉

Fitting

C₁₉×#1984

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×Q₈×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×Q₈ ◁ #1984

N	H ≅ G/N	type
118. C₁₉	#7238	semidirect

H ≅ G/N

type

118. C₁₉

#7238

semidirect

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

subgroup	index
#14563631	2
C₁₉×#1984	2
#7238	19

subgroup

index

#14563631

C₁₉×#1984

#7238

Subgroups — #18069632

Conjugacy classes of subgroups

Complements

Maximal subgroups