Group #18081934 — subgroups

Subgroups — #18081934

Order 4864.

478 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14574063	C₂	1	1	yes	maximal, characteristic
2	#14562194	C₂	1	4	yes	maximal, complemented
3	#14561927	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597350	—	2	2	no	—
6	#11927094	C₂²	1	2	yes	—
7	#11926928	—	2	2	no	—
8	#11926924	C₄	1	1	yes	characteristic, complemented
9	#11926921	C₄	1	1	yes	characteristic, complemented
10	#11926917	C₄	1	2	yes	complemented
11	#11926597	C₂²	1	2	yes	—
12	#11926277	—	2	8	no	—
13	#11926266	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#382	C₂²	1	2	yes	—
16	C₁₉×#340	—	2	2	no	—
17	C₂×#64541	—	2	2	no	—
18	C₂²×C₈×C₁₉	D₄	1	2	yes	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	#10597376	—	2	4	no	—
22	C₂×Dic₇₆	—	2	2	no	—
23	#10597350	—	4	8	no	—
24	C₂×D₁₅₂	—	2	2	no	—
25	C₂×#64516	—	2	4	no	—
26	#10597321	—	2	2	no	—
27	#10597320	C₂×C₄	1	2	yes	—
28	C₄×D₇₆	—	2	4	no	—
29	#10597315	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₉	D₄	1	2	yes	—
33	C₁₉×#95	—	2	4	no	—
34	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	C₄×C₁₉⋊C₈	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₂²⋊D₁₉	—	4	2	no	—
41	#64541	—	4	8	no	—
42	C₂×D₇₆	—	2	2	no	—
43	C₂×D₇₆	—	2	4	no	—
44	C₂×C₄×D₁₉	—	4	2	no	—
45	C₂×Dic₃₈	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	4	no	—
47	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₄⋊C₄×C₁₉	—	4	4	no	—
50	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₄²×C₁₉	#41	1	2	yes	—
53	(C₂×D₁₉)⋊C₄	—	4	4	no	—
54	C₄⋊Dic₁₉	—	2	4	no	—
55	C₂×C₁₉⋊C₈	—	2	4	no	—
56	Dic₇₆	—	4	4	no	—
57	D₁₅₂	—	4	4	no	—
58	#64516	—	4	8	no	—
59	#9760	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	#127	1	1	yes	characteristic
61	C₂²×D₁₉	—	4	2	no	—
62	C₂×C₄×C₁₉	—	4	2	no	—
63	C₂×C₄×C₁₉	—	8	4	no	—
64	C₂×C₄×C₁₉	—	8	2	no	—
65	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
67	C₂×C₄×C₁₉	#121	1	2	yes	—
68	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
69	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
70	C₂²⋊D₁₉	—	8	4	no	—
71	C₂×Dic₁₉	—	4	2	no	—
72	D₇₆	—	4	4	no	—
73	D₇₆	—	8	4	no	—
74	C₄×D₁₉	—	8	4	no	—
75	Dic₃₈	—	4	4	no	—
76	C₈×C₁₉	—	2	2	no	—
77	C₈×C₁₉	—	2	2	no	—
78	C₁₉⋊C₈	—	4	4	no	—
79	#3147	—	19	1	no	—
80	#1835	D₁₉	1	1	yes	characteristic, complemented
81	#1517	—	19	4	no	—
82	#1452	—	19	1	no	—
83	C₂²×C₁₉	—	2	2	no	—
84	C₂²×C₁₉	#390	1	1	yes	characteristic
85	C₂²×C₁₉	#496	1	2	yes	—
86	C₂×D₁₉	—	8	2	no	—
87	C₂×D₁₉	—	8	4	no	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	2	2	no	—
90	C₄×C₁₉	—	16	2	no	—
91	C₄×C₁₉	#418	1	2	yes	—
92	C₄×C₁₉	#490	1	2	yes	—
93	Dic₁₉	—	8	2	no	—
94	C₂×#135	—	38	2	no	—
95	#532	—	19	2	no	—
96	#495	—	38	2	no	—
97	#494	—	19	1	no	—
98	#493	—	19	1	no	—
99	#492	—	19	2	no	—
100	#431	—	19	2	no	—
101	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
102	#382	C₂×D₁₉	1	2	yes	—
103	#340	—	2	2	no	—
104	#327	—	38	8	no	—
105	#322	—	38	2	no	—
106	C₂×C₁₉	—	2	2	no	—
107	C₂×C₁₉	#1961	1	1	yes	characteristic
108	C₂×C₁₉	#1976	1	2	yes	—
109	D₁₉	—	16	2	no	—
110	C₂×#41	—	38	2	no	—
111	#135	—	76	8	no	—
112	C₂×Q₁₆	—	38	2	no	—
113	C₂×SD₁₆	—	38	4	no	—
114	C₂×D₈	—	38	2	no	—
115	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
116	C₄⋊Q₈	—	19	2	no	—
117	#127	—	19	2	no	—
118	#124	—	38	2	no	—
119	#121	—	38	4	no	—
120	C₄×D₄	—	38	4	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
123	C₄⋊C₈	—	38	2	no	—
124	C₂²⋊C₈	—	19	4	no	—
125	C₄×C₈	—	38	2	no	—
126	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
127	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
128	C₄×C₈	D₇₆	1	2	yes	—
129	#95	—	2	4	no	—
130	C₁₉	#9760	1	1	yes	characteristic, complemented, Sylow
131	#41	—	76	8	no	—
132	C₂×Q₈	—	38	2	no	—
133	C₂×D₄	—	38	4	no	—
134	C₂×D₄	—	38	2	no	—
135	C₂×D₄	—	76	2	no	—
136	C₂²×C₄	—	4	2	no	—
137	C₂²×C₄	—	76	2	no	—
138	C₂²×C₄	D₄×D₁₉	1	2	yes	—
139	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
140	Q₁₆	—	76	4	no	—
141	SD₁₆	—	76	8	no	—
142	D₈	—	76	4	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	—	38	4	no	—
145	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
146	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
147	C₄⋊C₄	—	4	4	no	—
148	C₄⋊C₄	—	38	4	no	—
149	C₂²⋊C₄	—	76	4	no	—
150	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
151	C₄²	C₂×D₇₆	1	1	yes	characteristic
152	C₄²	#64545	1	2	yes	—
153	C₂³	—	76	2	no	—
154	C₂³	#10597386	1	1	yes	characteristic
155	Q₈	—	76	4	no	—
156	D₄	—	76	4	no	—
157	D₄	—	152	4	no	—
158	D₄	—	152	4	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	—	8	4	no	—
161	C₂×C₄	—	8	2	no	—
162	C₂×C₄	—	76	2	no	—
163	C₂×C₄	—	152	4	no	—
164	C₂×C₄	#10597339	1	2	yes	—
165	C₂×C₄	#10597341	1	2	yes	—
166	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
167	C₂×C₄	#10597393	1	1	yes	characteristic
168	C₂×C₄	#10597395	1	4	yes	—
169	C₈	—	2	2	no	—
170	C₈	—	2	2	no	—
171	C₈	—	76	4	no	—
172	C₂²	—	2	2	no	—
173	C₂²	—	152	2	no	—
174	C₂²	—	152	4	no	—
175	C₂²	#11926445	1	1	yes	characteristic
176	C₂²	#11926934	1	2	yes	—
177	C₄	—	2	2	no	—
178	C₄	—	2	2	no	—
179	C₄	—	16	2	no	—
180	C₄	—	152	2	no	—
181	C₄	#11926548	1	2	yes	—
182	C₄	#11926910	1	2	yes	—
183	C₂	—	2	2	no	—
184	C₂	—	304	2	no	—
185	C₂	#14564458	1	1	yes	characteristic
186	C₂	#14564531	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574063

C₂

yes

maximal, characteristic

#14562194

C₂

yes

maximal, complemented

#14561927

C₂

yes

maximal, characteristic, complemented

C₁₉×#1835

C₂

yes

maximal, characteristic, complemented

C₂×#10597350

—

#11927094

C₂²

yes

—

#11926928

—

#11926924

C₄

yes

characteristic, complemented

#11926921

C₄

yes

characteristic, complemented

#11926917

C₄

yes

complemented

#11926597

C₂²

yes

—

#11926277

—

#11926266

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#382

C₂²

yes

—

C₁₉×#340

—

C₂×#64541

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

C₂×Dic₇₆

—

#10597350

—

C₂×D₁₅₂

—

C₂×#64516

—

#10597321

—

#10597320

C₂×C₄

yes

—

C₄×D₇₆

—

#10597315

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

D₁₅₂

—

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3147

—

#1835

D₁₉

yes

characteristic, complemented

#1517

—

#1452

—

C₂²×C₁₉

—

C₂²×C₁₉

#390

yes

characteristic

C₂²×C₁₉

#496

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#418

yes

—

C₄×C₁₉

#490

yes

—

Dic₁₉

—

—

—

—

—

—

—

100

#431

—

101

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

102

#382

C₂×D₁₉

yes

—

103

#340

—

104

#327

—

105

#322

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#1961

yes

characteristic

108

C₂×C₁₉

#1976

yes

—

109

D₁₉

—

110

C₂×#41

—

111

#135

—

112

C₂×Q₁₆

—

113

C₂×SD₁₆

—

114

C₂×D₈

—

115

C₂²×C₈

C₂²⋊D₁₉

yes

—

116

C₄⋊Q₈

—

117

#127

—

118

#124

—

119

#121

—

120

C₄×D₄

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄²

C₂²×D₁₉

yes

characteristic

123

C₄⋊C₈

—

124

C₂²⋊C₈

—

125

C₄×C₈

—

126

C₄×C₈

C₄×D₁₉

yes

characteristic

127

C₄×C₈

C₄×D₁₉

yes

characteristic

128

C₄×C₈

D₇₆

yes

—

129

#95

—

130

C₁₉

#9760

yes

characteristic, complemented, Sylow

131

#41

—

132

C₂×Q₈

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

D₄×D₁₉

yes

—

139

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

140

Q₁₆

—

141

SD₁₆

—

142

D₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

146

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₂²⋊C₄

—

150

C₄²

C₂×C₄×D₁₉

yes

characteristic

151

C₄²

C₂×D₇₆

yes

characteristic

152

C₄²

#64545

yes

—

153

C₂³

—

154

C₂³

#10597386

yes

characteristic

155

Q₈

—

156

D₄

—

157

D₄

—

152

—

158

D₄

—

152

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

152

—

164

C₂×C₄

#10597339

yes

—

165

C₂×C₄

#10597341

yes

—

166

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

167

C₂×C₄

#10597393

yes

characteristic

168

C₂×C₄

#10597395

yes

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₂²

—

173

C₂²

—

152

—

174

C₂²

—

152

—

175

C₂²

#11926445

yes

characteristic

176

C₂²

#11926934

yes

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

152

—

181

C₄

#11926548

yes

—

182

C₄

#11926910

yes

—

183

C₂

—

184

C₂

—

304

—

185

C₂

#14564458

yes

characteristic

186

C₂

#14564531

yes

—

	subgroup	G/H
center	C₂²	#11926445
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1835	C₂
socle	C₂²×C₁₉	#390
prime radical	#14574063	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1835	D₁₉
hypocenter	C₁₉	#9760
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

subgroup

G/H

center

C₂²

#11926445

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1835

C₂

C₂²×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1835

N	H ≅ G/N	type
2. #14562194	C₂	semidirect
3. #14561927	C₂	semidirect
4. C₁₉×#1835	C₂	semidirect
8. #11926924	C₄	semidirect
9. #11926921	C₄	semidirect
10. #11926917	C₄	semidirect
80. #1835	D₁₉	semidirect
130. C₁₉	#9760	semidirect

H ≅ G/N

type

2. #14562194

C₂

semidirect

3. #14561927

C₂

semidirect

4. C₁₉×#1835

C₂

semidirect

8. #11926924

C₄

semidirect

9. #11926921

C₄

semidirect

10. #11926917

C₄

semidirect

80. #1835

D₁₉

semidirect

130. C₁₉

#9760

semidirect

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

subgroup	index
#14574063	2
#14562194	2
#14561927	2
C₁₉×#1835	2
#9760	19

subgroup

index

C₁₉×#1835

Subgroups — #18081934

Conjugacy classes of subgroups

Complements

Maximal subgroups