Group #18069141 — subgroups

Subgroups — #18069141

Order 4864.

352 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14563615	C₂	1	2	yes	maximal
2	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	#11926299	C₄	1	4	yes	—
6	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
8	C₁₉×#336	—	2	2	no	—
9	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	—	2	2	no	—
13	C₂×C₄²×C₁₉	—	4	2	no	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	D₄	1	2	yes	—
16	C₂²×C₁₉⋊C₈	—	2	4	no	—
17	C₁₉×C₂²⋊C₈	—	4	2	no	—
18	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
19	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
20	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
21	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	4	no	—
24	C₂²×C₄×C₁₉	—	4	1	no	—
25	C₂²×C₄×C₁₉	—	4	1	no	—
26	C₂²×C₄×C₁₉	—	4	2	no	—
27	C₂²×C₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
34	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
35	C₂×C₈×C₁₉	—	4	4	no	—
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₄²×C₁₉	—	2	4	no	—
38	C₄²×C₁₉	—	4	2	no	—
39	C₂×C₁₉⋊C₈	—	4	4	no	—
40	C₂×C₁₉⋊C₈	—	4	4	no	—
41	C₂×C₁₉⋊C₈	—	4	4	no	—
42	#7044	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	—	2	1	no	—
44	C₂³×C₁₉	—	2	2	no	—
45	C₂³×C₁₉	—	2	1	no	—
46	C₂³×C₁₉	—	2	2	no	—
47	C₂³×C₁₉	#95	1	1	yes	characteristic
48	C₂³×C₁₉	#106	1	1	yes	characteristic
49	C₂³×C₁₉	#107	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	4	1	no	—
58	C₂×C₄×C₁₉	—	4	2	no	—
59	C₂×C₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	4	4	no	—
61	C₂×C₄×C₁₉	—	4	4	no	—
62	C₂×C₄×C₁₉	#99	1	2	yes	—
63	C₂×C₄×C₁₉	#102	1	2	yes	—
64	C₂×C₄×C₁₉	#103	1	2	yes	—
65	C₂×C₄×C₁₉	#108	1	4	yes	—
66	C₈×C₁₉	—	8	2	no	—
67	C₁₉⋊C₈	—	8	4	no	—
68	#1817	D₁₉	1	1	yes	characteristic
69	#1797	—	19	2	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	—	2	2	no	—
74	C₂²×C₁₉	—	4	2	no	—
75	C₂²×C₁₉	—	4	1	no	—
76	C₂²×C₁₉	—	4	1	no	—
77	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
78	C₂²×C₁₉	#340	1	1	yes	characteristic
79	C₂²×C₁₉	#341	1	2	yes	—
80	C₂²×C₁₉	#342	1	1	yes	characteristic
81	C₂²×C₁₉	#344	1	2	yes	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	2	2	no	—
84	C₄×C₁₉	—	2	4	no	—
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
88	C₂×C₄⋊C₈	—	38	2	no	—
89	C₂×C₂²⋊C₈	—	38	2	no	—
90	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
91	#336	—	2	2	no	—
92	#336	—	19	4	no	—
93	C₂×C₁₉	—	4	1	no	—
94	C₂×C₁₉	—	4	1	no	—
95	C₂×C₁₉	#1287	1	2	yes	—
96	C₂×C₁₉	#1289	1	1	yes	characteristic
97	C₂×C₁₉	#1298	1	1	yes	characteristic
98	C₂×C₁₉	#1301	1	2	yes	—
99	C₂×C₁₉	#1306	1	1	yes	characteristic
100	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
101	C₂³×C₄	D₇₆	1	1	yes	characteristic
102	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
103	C₂²×C₈	—	2	2	no	—
104	C₂²×C₈	—	38	4	no	—
105	C₂×C₄²	—	4	2	no	—
106	C₂×C₄²	C₄×D₁₉	1	2	yes	—
107	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
108	C₄⋊C₈	—	76	4	no	—
109	C₂²⋊C₈	—	4	2	no	—
110	C₂²⋊C₈	—	76	2	no	—
111	C₂²⋊C₈	—	76	2	no	—
112	C₁₉	#7044	1	1	yes	characteristic, complemented, Sylow
113	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
114	C₂²×C₄	—	2	4	no	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	—	4	1	no	—
117	C₂²×C₄	—	4	1	no	—
118	C₂²×C₄	—	4	1	no	—
119	C₂²×C₄	—	4	2	no	—
120	C₂²×C₄	#64516	1	2	yes	—
121	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
122	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
123	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
124	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
125	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
126	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₂×C₈	—	4	4	no	—
128	C₂×C₈	—	4	2	no	—
129	C₂×C₈	—	76	4	no	—
130	C₂×C₈	—	76	4	no	—
131	C₂×C₈	—	76	4	no	—
132	C₄²	—	2	4	no	—
133	C₄²	—	4	2	no	—
134	C₂³	—	2	1	no	—
135	C₂³	—	2	2	no	—
136	C₂³	—	2	1	no	—
137	C₂³	—	2	2	no	—
138	C₂³	#10597274	1	1	yes	characteristic
139	C₂³	#10597275	1	1	yes	characteristic
140	C₂³	C₁₉⋊#95	1	1	yes	characteristic
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	—	4	1	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	—	4	4	no	—
152	C₂×C₄	—	4	4	no	—
153	C₂×C₄	#10597273	1	2	yes	—
154	C₂×C₄	#10597278	1	2	yes	—
155	C₂×C₄	#10597279	1	4	yes	—
156	C₂×C₄	#10597291	1	2	yes	—
157	C₈	—	8	2	no	—
158	C₈	—	152	4	no	—
159	C₂²	—	2	1	no	—
160	C₂²	—	2	1	no	—
161	C₂²	—	2	2	no	—
162	C₂²	—	2	2	no	—
163	C₂²	—	4	1	no	—
164	C₂²	—	4	2	no	—
165	C₂²	—	4	1	no	—
166	C₂²	#11926301	1	1	yes	characteristic
167	C₂²	#11926307	1	1	yes	characteristic
168	C₂²	#11926308	1	2	yes	—
169	C₂²	#11926311	1	1	yes	characteristic
170	C₂²	#11926314	1	2	yes	—
171	C₄	—	2	2	no	—
172	C₄	—	2	2	no	—
173	C₄	—	2	2	no	—
174	C₄	—	2	4	no	—
175	C₄	—	4	1	no	—
176	C₂	—	4	1	no	—
177	C₂	—	4	1	no	—
178	C₂	#14561498	1	2	yes	—
179	C₂	#14561503	1	1	yes	characteristic
180	C₂	#14561522	1	1	yes	characteristic
181	C₂	#14561531	1	2	yes	—
182	C₂	#14561543	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563615

C₂

yes

maximal

C₁₉×#1817

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926299

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₄

yes

—

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7044

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

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

#99

yes

—

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1817

D₁₉

yes

characteristic

#1797

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#342

yes

characteristic

C₂²×C₁₉

#344

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

Dic₁₉

yes

—

#336

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1287

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#1306

yes

characteristic

100

C₂³×C₄

Dic₃₈

yes

characteristic

101

C₂³×C₄

D₇₆

yes

characteristic

102

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

103

C₂²×C₈

—

104

C₂²×C₈

—

105

C₂×C₄²

—

106

C₂×C₄²

C₄×D₁₉

yes

—

107

C₂×C₄²

C₂²⋊D₁₉

yes

—

108

C₄⋊C₈

—

109

C₂²⋊C₈

—

110

C₂²⋊C₈

—

111

C₂²⋊C₈

—

112

C₁₉

#7044

yes

characteristic, complemented, Sylow

113

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

#64516

yes

—

121

C₂²×C₄

D₁₅₂

yes

characteristic

122

C₂²×C₄

Dic₇₆

yes

characteristic

123

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

124

C₂²×C₄

Dic₁₉⋊C₄

yes

—

125

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

126

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₄²

—

133

C₄²

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

—

138

C₂³

#10597274

yes

characteristic

139

C₂³

#10597275

yes

characteristic

140

C₂³

C₁₉⋊#95

yes

characteristic

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

#10597273

yes

—

154

C₂×C₄

#10597278

yes

—

155

C₂×C₄

#10597279

yes

—

156

C₂×C₄

#10597291

yes

—

157

C₈

—

158

C₈

—

152

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

#11926301

yes

characteristic

167

C₂²

#11926307

yes

characteristic

168

C₂²

#11926308

yes

—

169

C₂²

#11926311

yes

characteristic

170

C₂²

#11926314

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₂

—

177

C₂

—

178

C₂

#14561498

yes

—

179

C₂

#14561503

yes

characteristic

180

C₂

#14561522

yes

characteristic

181

C₂

#14561531

yes

—

182

C₂

#14561543

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂²×C₄²	C₂×D₁₉
Fitting	C₁₉×#1817	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂²×C₄²×C₁₉	C₂²
hypercenter	#1817	D₁₉
hypocenter	C₁₉	#7044
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1817

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂²×C₄²

C₂×D₁₉

Fitting

C₁₉×#1817

C₂

socle

C₂³×C₁₉

#95

prime radical

C₂⁴×C₁₉

C₄⋊C₄

cosocle

C₂²×C₄²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1817

N	H ≅ G/N	type
112. C₁₉	#7044	semidirect

H ≅ G/N

type

112. C₁₉

#7044

semidirect

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

subgroup	index
#14563615	2
C₁₉×#1817	2
#7044	19

subgroup

index

#14563615

C₁₉×#1817

#7044

Subgroups — #18069141

Conjugacy classes of subgroups

Complements

Maximal subgroups