Group #18087346 — subgroups

Subgroups — #18087346

Order 4864.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14564459	C₂	1	1	yes	maximal, characteristic
2	#14563776	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562302	C₂	1	2	yes	maximal
4	#14561494	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1281	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	#11926568	C₂²	1	2	yes	—
8	C₂×#10597278	—	2	2	no	—
9	#11926410	C₂²	1	1	yes	characteristic
10	#11926309	—	2	2	no	—
11	#11926287	—	2	4	no	—
12	C₁₉×#431	C₂²	1	2	yes	—
13	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
14	C₂²×D₇₆	—	2	1	no	—
15	C₂²×D₇₆	—	2	2	no	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₄⋊Dic₁₉	—	2	1	no	—
19	C₂×#64520	—	2	2	no	—
20	#10597320	—	2	2	no	—
21	#10597320	—	2	1	no	—
22	#10597320	D₄	1	2	yes	—
23	C₁₉×C₄⋊C₈	—	2	2	no	—
24	C₁₉×C₂²⋊C₈	—	2	2	no	—
25	C₁₉×#97	—	2	2	no	—
26	C₄×C₈×C₁₉	—	2	2	no	—
27	C₁₉⋊#95	—	2	2	no	—
28	#10597278	—	4	4	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₂³×D₁₉	—	4	1	no	—
32	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	#41	1	2	yes	—
34	C₂²×Dic₁₉	—	4	1	no	—
35	C₂×D₇₆	—	2	2	no	—
36	C₂×D₇₆	—	2	4	no	—
37	C₂×D₇₆	—	4	2	no	—
38	C₂×D₇₆	—	4	2	no	—
39	C₂×D₇₆	—	4	1	no	—
40	C₂×D₇₆	—	4	2	no	—
41	C₂×D₇₆	—	8	4	no	—
42	C₂×C₈×C₁₉	—	2	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	4	2	no	—
46	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₁₉	#41	1	2	yes	—
48	C₄²×C₁₉	#41	1	1	yes	characteristic
49	C₄⋊Dic₁₉	—	4	2	no	—
50	#64520	—	4	2	no	—
51	#64520	—	4	2	no	—
52	C₂×C₁₉⋊C₈	—	4	2	no	—
53	#10634	—	19	1	no	maximal, Sylow
54	C₂³×C₁₉	#124	1	1	yes	characteristic
55	C₂²×D₁₉	—	4	2	no	—
56	C₂²×D₁₉	—	8	4	no	—
57	C₂²×D₁₉	—	8	1	no	—
58	C₂²×D₁₉	—	8	1	no	—
59	C₂×C₄×C₁₉	—	4	2	no	—
60	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#123	1	2	yes	—
62	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#126	1	2	yes	—
64	C₂×C₄×C₁₉	#135	1	2	yes	—
65	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
66	C₂×Dic₁₉	—	8	2	no	—
67	C₂×Dic₁₉	—	8	1	no	—
68	D₇₆	—	4	4	no	—
69	D₇₆	—	8	4	no	—
70	D₇₆	—	8	4	no	—
71	D₇₆	—	8	2	no	—
72	C₈×C₁₉	—	4	2	no	—
73	C₈×C₁₉	—	8	2	no	—
74	C₁₉⋊C₈	—	8	2	no	—
75	#1961	—	19	1	no	—
76	#1838	—	19	1	no	—
77	#1545	—	19	2	no	—
78	#1286	—	19	2	no	—
79	#1281	D₁₉	1	1	yes	characteristic, complemented
80	C₂²×C₁₉	—	2	2	no	—
81	C₂²×C₁₉	#397	1	1	yes	characteristic
82	C₂²×C₁₉	#488	1	1	yes	characteristic
83	C₂²×C₁₉	#490	1	1	yes	characteristic
84	C₂×D₁₉	—	8	2	no	—
85	C₂×D₁₉	—	8	4	no	—
86	C₂×D₁₉	—	16	2	no	—
87	C₂×D₁₉	—	16	2	no	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	2	2	no	—
90	C₄×C₁₉	#463	1	2	yes	—
91	C₄×C₁₉	#482	1	2	yes	—
92	Dic₁₉	—	16	1	no	—
93	C₂×#127	—	19	1	no	—
94	#431	C₂×D₁₉	1	2	yes	—
95	#423	—	19	2	no	—
96	C₂×#102	—	38	2	no	—
97	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
98	#382	—	19	1	no	—
99	#341	—	38	2	no	—
100	#331	—	38	4	no	—
101	C₂×C₁₉	—	2	1	no	—
102	C₂×C₁₉	—	2	1	no	—
103	C₂×C₁₉	#2073	1	1	yes	characteristic
104	C₂×C₁₉	#2081	1	2	yes	—
105	D₁₉	—	16	2	no	—
106	C₂²×D₄	—	38	1	no	—
107	C₂²×D₄	—	38	2	no	—
108	C₂×M₁₆	—	38	2	no	—
109	C₂²×C₈	D₇₆	1	2	yes	—
110	#127	—	19	2	no	—
111	#127	—	38	2	no	—
112	#127	—	38	1	no	—
113	C₂×C₄⋊C₄	—	38	1	no	—
114	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
115	C₄⋊C₈	—	2	2	no	—
116	C₄⋊C₈	—	38	2	no	—
117	C₄⋊C₈	—	38	2	no	—
118	#102	—	76	4	no	—
119	C₂²⋊C₈	—	2	2	no	—
120	#97	—	2	2	no	—
121	C₄×C₈	—	2	2	no	—
122	#95	—	38	2	no	—
123	C₁₉	#10634	1	1	yes	characteristic, complemented, Sylow
124	C₂⁴	—	76	1	no	—
125	C₂×D₄	—	38	4	no	—
126	C₂×D₄	—	38	2	no	—
127	C₂×D₄	—	76	1	no	—
128	C₂×D₄	—	76	2	no	—
129	C₂×D₄	—	76	2	no	—
130	C₂×D₄	—	76	2	no	—
131	C₂×D₄	—	152	4	no	—
132	C₂²×C₄	—	76	1	no	—
133	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
134	C₂²×C₄	#64541	1	2	yes	—
135	M₁₆	—	76	2	no	—
136	M₁₆	—	76	2	no	—
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	4	2	no	—
141	C₂×C₈	—	76	2	no	—
142	C₄⋊C₄	—	76	2	no	—
143	C₄²	D₄×D₁₉	1	1	yes	characteristic
144	C₄²	#64543	1	2	yes	—
145	C₄²	#64545	1	1	yes	characteristic
146	C₂³	—	76	2	no	—
147	C₂³	—	152	4	no	—
148	C₂³	—	152	1	no	—
149	C₂³	—	152	1	no	—
150	C₂³	#10597321	1	1	yes	characteristic
151	D₄	—	76	4	no	—
152	D₄	—	152	4	no	—
153	D₄	—	152	4	no	—
154	D₄	—	152	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	—	152	2	no	—
157	C₂×C₄	—	152	1	no	—
158	C₂×C₄	#10597329	1	2	yes	—
159	C₂×C₄	#10597332	1	1	yes	characteristic
160	C₂×C₄	#10597341	1	1	yes	characteristic
161	C₂×C₄	#10597344	1	2	yes	—
162	C₂×C₄	#10597350	1	2	yes	—
163	C₂×C₄	#10597354	1	2	yes	—
164	C₈	—	4	2	no	—
165	C₈	—	8	2	no	—
166	C₈	—	152	2	no	—
167	C₂²	—	2	2	no	—
168	C₂²	—	304	2	no	—
169	C₂²	—	304	2	no	—
170	C₂²	—	152	2	no	—
171	C₂²	—	152	4	no	—
172	C₂²	#11926471	1	1	yes	characteristic
173	C₂²	#11926899	1	1	yes	characteristic
174	C₂²	#11926909	1	1	yes	characteristic
175	C₄	—	2	2	no	—
176	C₄	—	2	2	no	—
177	C₄	—	304	1	no	—
178	C₄	#11926760	1	2	yes	—
179	C₄	#11926869	1	2	yes	—
180	C₂	—	2	1	no	—
181	C₂	—	2	1	no	—
182	C₂	—	304	2	no	—
183	C₂	#14565050	1	1	yes	characteristic
184	C₂	#14565094	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564459

C₂

yes

maximal, characteristic

#14563776

C₂

yes

maximal, characteristic, complemented

#14562302

C₂

yes

maximal

#14561494

C₂

yes

maximal, complemented

C₁₉×#1281

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

characteristic

#11926568

C₂²

yes

—

C₂×#10597278

—

#11926410

C₂²

yes

characteristic

#11926309

—

#11926287

—

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

—

—

—

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

#10597278

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#463

yes

—

C₄×C₁₉

#482

yes

—

Dic₁₉

—

C₂×#127

—

#431

C₂×D₁₉

yes

—

#423

—

C₂×#102

—

C₂×#97

C₂×D₁₉

yes

characteristic

#382

—

#341

—

100

#331

—

101

C₂×C₁₉

—

102

C₂×C₁₉

—

103

C₂×C₁₉

#2073

yes

characteristic

104

C₂×C₁₉

#2081

yes

—

105

D₁₉

—

106

C₂²×D₄

—

107

C₂²×D₄

—

108

C₂×M₁₆

—

109

C₂²×C₈

D₇₆

yes

—

110

#127

—

111

#127

—

112

#127

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄²

C₂²×D₁₉

yes

characteristic

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

#102

—

119

C₂²⋊C₈

—

120

#97

—

121

C₄×C₈

—

122

#95

—

123

C₁₉

#10634

yes

characteristic, complemented, Sylow

124

C₂⁴

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

152

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂×D₇₆

yes

characteristic

134

C₂²×C₄

#64541

yes

—

135

M₁₆

—

136

M₁₆

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₄⋊C₄

—

143

C₄²

D₄×D₁₉

yes

characteristic

144

C₄²

#64543

yes

—

145

C₄²

#64545

yes

characteristic

146

C₂³

—

147

C₂³

—

152

—

148

C₂³

—

152

—

149

C₂³

—

152

—

150

C₂³

#10597321

yes

characteristic

151

D₄

—

152

D₄

—

152

—

153

D₄

—

152

—

154

D₄

—

152

—

155

C₂×C₄

—

156

C₂×C₄

—

152

—

157

C₂×C₄

—

152

—

158

C₂×C₄

#10597329

yes

—

159

C₂×C₄

#10597332

yes

characteristic

160

C₂×C₄

#10597341

yes

characteristic

161

C₂×C₄

#10597344

yes

—

162

C₂×C₄

#10597350

yes

—

163

C₂×C₄

#10597354

yes

—

164

C₈

—

165

C₈

—

166

C₈

—

152

—

167

C₂²

—

168

C₂²

—

304

—

169

C₂²

—

304

—

170

C₂²

—

152

—

171

C₂²

—

152

—

172

C₂²

#11926471

yes

characteristic

173

C₂²

#11926899

yes

characteristic

174

C₂²

#11926909

yes

characteristic

175

C₄

—

176

C₄

—

177

C₄

—

304

—

178

C₄

#11926760

yes

—

179

C₄

#11926869

yes

—

180

C₂

—

181

C₂

—

182

C₂

—

304

—

183

C₂

#14565050

yes

characteristic

184

C₂

#14565094

yes

—

	subgroup	G/H
center	C₂²	#11926471
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1281	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂×#10597320	C₂²
hypercenter	#1281	D₁₉
hypocenter	C₁₉	#10634
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂²

#11926471

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1281

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
2. #14563776	C₂	semidirect
4. #14561494	C₂	semidirect
5. C₁₉×#1281	C₂	semidirect
79. #1281	D₁₉	semidirect
123. C₁₉	#10634	semidirect

H ≅ G/N

type

2. #14563776

C₂

semidirect

4. #14561494

C₂

semidirect

5. C₁₉×#1281

C₂

semidirect

79. #1281

D₁₉

semidirect

123. C₁₉

#10634

semidirect

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

subgroup	index
#14564459	2
#14563776	2
#14562302	2
#14561494	2
C₁₉×#1281	2
#10634	19

subgroup

index

C₁₉×#1281

Subgroups — #18087346

Conjugacy classes of subgroups

Complements

Maximal subgroups