Group #18069613 — subgroups

Subgroups — #18069613

Order 4864.

314 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14563664	C₂	1	2	yes	maximal
2	C₂×C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597275	—	2	2	no	—
4	#11926404	—	2	2	no	—
5	#11926307	C₄	1	4	yes	complemented
6	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₁₆×C₁₉	C₄	1	2	yes	complemented
8	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
9	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	—	4	2	no	—
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₉	D₄	1	2	yes	—
14	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
15	C₂×C₂²⋊Dic₁₉	—	4	2	no	—
16	C₂×C₄⋊Dic₁₉	—	2	4	no	—
17	C₂×C₁₆×C₁₉	—	2	2	no	—
18	C₂×C₁₆×C₁₉	—	4	2	no	—
19	C₁₉⋊#95	—	4	2	no	—
20	#10597275	—	4	4	no	—
21	C₂⁴×C₁₉	D₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
27	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	4	4	no	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	—	2	4	no	—
31	C₂×C₈×C₁₉	—	4	2	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
36	C₂²⋊Dic₁₉	—	8	2	no	—
37	C₂²⋊Dic₁₉	—	8	2	no	—
38	C₄⋊Dic₁₉	—	4	4	no	—
39	C₄⋊Dic₁₉	—	4	4	no	—
40	C₁₆×C₁₉	—	4	2	no	—
41	#7230	—	19	1	no	maximal, Sylow
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	—	4	1	no	—
44	C₂³×C₁₉	#102	1	2	yes	—
45	C₂³×C₁₉	#107	1	1	yes	characteristic
46	C₂³×C₁₉	D₁₆	1	1	yes	characteristic
47	C₂³×C₁₉	SD₃₂	1	2	yes	—
48	C₂³×C₁₉	Q₃₂	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#103	1	2	yes	—
57	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
58	C₂×Dic₁₉	—	8	4	no	—
59	C₂×Dic₁₉	—	8	4	no	—
60	C₂×Dic₁₉	—	8	4	no	—
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	2	no	—
63	C₈×C₁₉	#99	1	2	yes	—
64	C₂×C₂²⋊C₁₆	D₁₉	1	1	yes	characteristic
65	#1808	—	19	2	no	—
66	C₂²×C₁₉	—	2	2	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	4	1	no	—
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	#340	1	1	yes	characteristic
74	C₂²×C₁₉	#357	1	2	yes	—
75	C₂²×C₁₉	#358	1	2	yes	—
76	C₂²×C₁₉	#366	1	1	yes	characteristic
77	C₂²×C₁₉	#367	1	1	yes	characteristic
78	C₄×C₁₉	—	2	2	no	—
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
81	C₄×C₁₉	#342	1	1	yes	characteristic
82	Dic₁₉	—	16	4	no	—
83	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
84	C₂²×C₁₆	Dic₁₉	1	2	yes	complemented
85	C₂×#107	—	38	2	no	—
86	#380	—	38	2	no	—
87	C₂²⋊C₁₆	—	2	2	no	—
88	#340	—	19	4	no	—
89	C₂×C₁₉	—	2	2	no	—
90	C₂×C₁₉	—	2	2	no	—
91	C₂×C₁₉	—	2	1	no	—
92	C₂×C₁₉	—	2	1	no	—
93	C₂×C₁₉	#1289	1	1	yes	characteristic
94	C₂×C₁₉	#1380	1	1	yes	characteristic
95	C₂×C₁₉	#1384	1	1	yes	characteristic
96	C₂³×C₄	D₇₆	1	1	yes	characteristic
97	C₂²×C₈	—	4	2	no	—
98	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
99	C₂²×C₈	C₄×D₁₉	1	2	yes	—
100	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
101	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
102	C₂×C₄⋊C₄	—	38	4	no	—
103	C₂×C₂²⋊C₄	—	76	2	no	—
104	C₂×C₁₆	—	2	2	no	—
105	C₂×C₁₆	—	4	2	no	—
106	#107	—	76	4	no	—
107	#95	—	76	2	no	—
108	C₁₉	#7230	1	1	yes	characteristic, complemented, Sylow
109	C₂⁴	D₁₅₂	1	1	yes	characteristic
110	C₂²×C₄	—	4	1	no	—
111	C₂²×C₄	—	4	1	no	—
112	C₂²×C₄	—	76	4	no	—
113	C₂²×C₄	#64516	1	2	yes	—
114	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
115	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
116	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
117	C₂×C₈	—	2	4	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	4	1	no	—
120	C₂×C₈	—	4	2	no	—
121	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
122	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
123	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
124	C₄⋊C₄	—	76	4	no	—
125	C₄⋊C₄	—	76	4	no	—
126	C₂²⋊C₄	—	152	2	no	—
127	C₂²⋊C₄	—	152	2	no	—
128	C₁₆	—	4	2	no	—
129	C₂³	—	4	1	no	—
130	C₂³	—	4	1	no	—
131	C₂³	D₃₀₄	1	1	yes	characteristic
132	C₂³	#10597257	1	2	yes	—
133	C₂³	Dic₁₅₂	1	1	yes	characteristic
134	C₂³	#10597275	1	1	yes	characteristic
135	C₂³	#10597278	1	2	yes	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	4	2	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	—	152	4	no	—
143	C₂×C₄	—	152	4	no	—
144	C₂×C₄	—	152	4	no	—
145	C₂×C₄	#10597273	1	2	yes	—
146	C₂×C₄	#10597274	1	1	yes	characteristic
147	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
148	C₈	—	2	1	no	—
149	C₈	—	2	2	no	—
150	C₈	#10597291	1	2	yes	—
151	C₂²	—	2	2	no	—
152	C₂²	—	2	1	no	—
153	C₂²	—	2	2	no	—
154	C₂²	—	2	1	no	—
155	C₂²	—	4	1	no	—
156	C₂²	—	4	2	no	—
157	C₂²	—	4	1	no	—
158	C₂²	#11926307	1	1	yes	characteristic
159	C₂²	#11926346	1	2	yes	—
160	C₂²	#11926349	1	2	yes	—
161	C₂²	#11926370	1	1	yes	characteristic
162	C₂²	#11926372	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	2	1	no	—
165	C₄	—	304	4	no	—
166	C₄	#11926301	1	1	yes	characteristic
167	C₄	#11926311	1	1	yes	characteristic
168	C₂	—	2	2	no	—
169	C₂	—	2	2	no	—
170	C₂	—	2	1	no	—
171	C₂	—	2	1	no	—
172	C₂	#14561503	1	1	yes	characteristic
173	C₂	#14561727	1	1	yes	characteristic
174	C₂	#14561737	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563664

C₂

yes

maximal

C₂×C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂×#10597275

—

#11926404

—

#11926307

C₄

yes

complemented

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₁₆×C₁₉

C₄

yes

complemented

C₁₉×C₂²⋊C₁₆

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₁₉⋊#95

—

#10597275

—

C₂⁴×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₆×C₁₉

—

#7230

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#102

yes

—

C₂³×C₁₉

#107

yes

characteristic

C₂³×C₁₉

D₁₆

yes

characteristic

C₂³×C₁₉

SD₃₂

yes

—

C₂³×C₁₉

Q₃₂

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#106

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#99

yes

—

C₂×C₂²⋊C₁₆

D₁₉

yes

characteristic

#1808

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#340

yes

characteristic

C₂²×C₁₉

#357

yes

—

C₂²×C₁₉

#358

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂³×C₈

C₂×D₁₉

yes

characteristic

C₂²×C₁₆

Dic₁₉

yes

complemented

C₂×#107

—

#380

—

C₂²⋊C₁₆

—

#340

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂³×C₄

D₇₆

yes

characteristic

C₂²×C₈

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₄×D₁₉

yes

—

100

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

101

C₂²×C₈

C₂²⋊D₁₉

yes

—

102

C₂×C₄⋊C₄

—

103

C₂×C₂²⋊C₄

—

104

C₂×C₁₆

—

105

C₂×C₁₆

—

106

#107

—

107

#95

—

108

C₁₉

#7230

yes

characteristic, complemented, Sylow

109

C₂⁴

D₁₅₂

yes

characteristic

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

#64516

yes

—

114

C₂²×C₄

Dic₇₆

yes

characteristic

115

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

116

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

C₄×Dic₁₉

yes

characteristic

122

C₂×C₈

Dic₁₉⋊C₄

yes

—

123

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

152

—

127

C₂²⋊C₄

—

152

—

128

C₁₆

—

129

C₂³

—

130

C₂³

—

131

C₂³

D₃₀₄

yes

characteristic

132

C₂³

#10597257

yes

—

133

C₂³

Dic₁₅₂

yes

characteristic

134

C₂³

#10597275

yes

characteristic

135

C₂³

#10597278

yes

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

152

—

143

C₂×C₄

—

152

—

144

C₂×C₄

—

152

—

145

C₂×C₄

#10597273

yes

—

146

C₂×C₄

#10597274

yes

characteristic

147

C₂×C₄

C₁₉⋊#95

yes

characteristic

148

C₈

—

149

C₈

—

150

C₈

#10597291

yes

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

#11926307

yes

characteristic

159

C₂²

#11926346

yes

—

160

C₂²

#11926349

yes

—

161

C₂²

#11926370

yes

characteristic

162

C₂²

#11926372

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

304

—

166

C₄

#11926301

yes

characteristic

167

C₄

#11926311

yes

characteristic

168

C₂

—

169

C₂

—

170

C₂

—

171

C₂

—

172

C₂

#14561503

yes

characteristic

173

C₂

#14561727

yes

characteristic

174

C₂

#14561737

yes

characteristic

	subgroup	G/H
center	C₂²	#11926307
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂³×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×C₂²⋊C₁₆	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂⁴×C₁₉	D₈
cosocle	C₂³×C₈×C₁₉	C₂²
hypercenter	C₂×C₂²⋊C₁₆	D₁₉
hypocenter	C₁₉	#7230
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×C₂²⋊C₁₆

subgroup

G/H

center

C₂²

#11926307

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂³×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×C₂²⋊C₁₆

C₂

socle

C₂²×C₁₉

#340

prime radical

C₂⁴×C₁₉

D₈

cosocle

C₂³×C₈×C₁₉

C₂²

hypercenter

C₂×C₂²⋊C₁₆

D₁₉

hypocenter

C₁₉

#7230

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×C₂²⋊C₁₆

N	H ≅ G/N	type
5. #11926307	C₄	semidirect
7. C₂²×C₁₆×C₁₉	C₄	semidirect
84. C₂²×C₁₆	Dic₁₉	semidirect
108. C₁₉	#7230	semidirect

H ≅ G/N

type

5. #11926307

C₄

semidirect

7. C₂²×C₁₆×C₁₉

C₄

semidirect

84. C₂²×C₁₆

Dic₁₉

semidirect

108. C₁₉

#7230

semidirect

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

subgroup	index
#14563664	2
C₂×C₁₉×C₂²⋊C₁₆	2
#7230	19

subgroup

index

#14563664

C₂×C₁₉×C₂²⋊C₁₆

#7230

Subgroups — #18069613

Conjugacy classes of subgroups

Complements

Maximal subgroups