Group #18080059 — subgroups

Subgroups — #18080059

Order 4864.

384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14574017	C₂	1	1	yes	maximal, characteristic
2	#14572741	C₂	1	1	yes	maximal, characteristic
3	#14562351	C₂	1	2	yes	maximal
4	#14561508	C₂	1	2	yes	maximal
5	C₁₉×#1537	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	#11926914	—	2	2	no	—
8	#11926896	C₄	1	4	yes	—
9	#11926675	—	2	4	no	—
10	#11926605	—	2	2	no	—
11	#11926601	C₂²	1	2	yes	—
12	#11926552	—	2	2	no	—
13	C₄×#64520	C₂²	1	1	yes	characteristic
14	#11926289	—	2	4	no	—
15	C₁₉×#533	C₂²	1	1	yes	characteristic
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#330	—	2	2	no	—
18	C₂²×Dic₃₈	—	2	1	no	—
19	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
20	C₁₉×#125	D₄	1	2	yes	—
21	C₁₉×C₂²⋊Q₈	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₁₉×#117	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×#64520	—	2	1	no	—
27	#10597315	—	2	2	no	—
28	#10597315	—	2	1	no	—
29	#10597315	C₂×C₄	1	2	yes	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×C₂²⋊C₈	—	2	2	no	—
32	C₁₉×#97	—	2	2	no	—
33	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
34	#10597267	—	2	8	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
37	#10597260	—	2	2	no	—
38	#10597260	—	2	2	no	—
39	#10597260	—	2	1	no	—
40	C₄×C₁₉⋊C₈	—	2	2	no	—
41	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₂×Q₈×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	#41	1	2	yes	—
45	C₂²×Dic₁₉	—	4	1	no	—
46	C₂×Dic₃₈	—	2	2	no	—
47	C₂×Dic₃₈	—	4	4	no	—
48	C₂×Dic₃₈	—	4	1	no	—
49	C₂×C₈×C₁₉	—	4	2	no	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
53	C₂²⋊C₄×C₁₉	—	2	2	no	—
54	C₄²×C₁₉	—	2	2	no	—
55	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₉	C₂×D₄	1	2	yes	—
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄⋊Dic₁₉	—	2	4	no	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	#64520	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	2	2	no	—
62	C₂×C₁₉⋊C₈	—	2	4	no	—
63	#9422	—	19	1	no	maximal, Sylow
64	C₂³×C₁₉	#123	1	1	yes	characteristic
65	Q₈×C₁₉	—	8	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
71	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#121	1	2	yes	—
73	C₂×Dic₁₉	—	4	2	no	—
74	C₂×Dic₁₉	—	8	2	no	—
75	Dic₃₈	—	4	4	no	—
76	Dic₃₈	—	8	2	no	—
77	C₈×C₁₉	—	8	2	no	—
78	C₁₉⋊C₈	—	4	2	no	—
79	C₁₉⋊C₈	—	4	4	no	—
80	#3139	—	19	1	no	—
81	#2987	—	19	1	no	—
82	#1556	—	19	2	no	—
83	#1537	D₁₉	1	1	yes	characteristic
84	#1291	—	19	2	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	—	2	2	no	—
87	C₂²×C₁₉	#386	1	1	yes	characteristic
88	C₄×C₁₉	—	2	1	no	—
89	C₄×C₁₉	—	2	2	no	—
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	—	4	4	no	—
92	C₄×C₁₉	#454	1	2	yes	—
93	Dic₁₉	—	8	2	no	—
94	#533	C₂×D₁₉	1	1	yes	characteristic
95	C₂×C₄⋊Q₈	—	19	1	no	—
96	#491	—	38	2	no	—
97	#487	—	19	4	no	—
98	#446	—	38	4	no	—
99	#433	—	38	2	no	—
100	#432	—	19	2	no	—
101	#432	C₂×D₁₉	1	2	yes	—
102	#419	—	38	2	no	—
103	C₄×M₁₆	—	19	1	no	—
104	#332	—	38	4	no	—
105	#330	—	2	2	no	—
106	C₂×C₁₉	—	4	1	no	—
107	C₂×C₁₉	#1888	1	1	yes	characteristic
108	C₂×C₁₉	#1902	1	2	yes	—
109	C₂²×Q₈	—	38	1	no	—
110	C₂×M₁₆	—	38	1	no	—
111	C₄⋊Q₈	—	19	2	no	—
112	C₄⋊Q₈	—	38	2	no	—
113	C₄⋊Q₈	—	38	1	no	—
114	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
115	#125	C₂²⋊D₁₉	1	2	yes	—
116	C₂²⋊Q₈	—	2	2	no	—
117	C₄×Q₈	—	2	2	no	—
118	#117	D₇₆	1	2	yes	—
119	C₂×C₄⋊C₄	—	38	2	no	—
120	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
121	C₄⋊C₈	—	2	2	no	—
122	C₄⋊C₈	—	19	4	no	—
123	C₄⋊C₈	—	38	4	no	—
124	#103	—	38	8	no	—
125	C₂²⋊C₈	—	2	2	no	—
126	C₂²⋊C₈	—	38	2	no	—
127	#97	—	2	2	no	—
128	#97	—	38	2	no	—
129	#97	—	38	2	no	—
130	#97	—	38	1	no	—
131	C₄×C₈	—	19	2	no	—
132	C₄×C₈	—	38	2	no	—
133	C₁₉	#9422	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	38	2	no	—
136	C₂×Q₈	—	76	4	no	—
137	C₂×Q₈	—	76	1	no	—
138	C₂²×C₄	—	76	1	no	—
139	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
140	C₂²×C₄	#64543	1	2	yes	—
141	M₁₆	—	76	2	no	—
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	38	4	no	—
144	C₂×C₈	—	38	2	no	—
145	C₄⋊C₄	—	2	4	no	—
146	C₄⋊C₄	—	2	2	no	—
147	C₄⋊C₄	—	38	4	no	—
148	C₄⋊C₄	—	76	2	no	—
149	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
150	C₂²⋊C₄	—	2	2	no	—
151	C₄²	—	2	2	no	—
152	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
153	C₄²	D₄×D₁₉	1	2	yes	—
154	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
155	C₂³	#10597332	1	1	yes	characteristic
156	Q₈	—	8	2	no	—
157	Q₈	—	76	4	no	—
158	Q₈	—	152	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	4	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	76	2	no	—
163	C₂×C₄	—	152	2	no	—
164	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
165	C₂×C₄	#10597328	1	1	yes	characteristic
166	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
167	C₂×C₄	#10597385	1	2	yes	—
168	C₈	—	8	2	no	—
169	C₈	—	76	2	no	—
170	C₈	—	76	4	no	—
171	C₂²	—	2	2	no	—
172	C₂²	—	2	1	no	—
173	C₂²	#11926421	1	1	yes	characteristic
174	C₄	—	2	2	no	—
175	C₄	—	2	2	no	—
176	C₄	—	2	1	no	—
177	C₄	—	4	4	no	—
178	C₄	—	152	2	no	—
179	C₄	#11926719	1	2	yes	—
180	C₂	—	4	1	no	—
181	C₂	#14564036	1	1	yes	characteristic
182	C₂	#14564106	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574017

C₂

yes

maximal, characteristic

#14572741

C₂

yes

maximal, characteristic

#14562351

C₂

yes

maximal

#14561508

C₂

yes

maximal

C₁₉×#1537

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

#11926914

—

#11926896

C₄

yes

—

#11926675

—

#11926605

—

#11926601

C₂²

yes

—

#11926552

—

C₄×#64520

C₂²

yes

characteristic

#11926289

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#432

C₂²

yes

—

C₁₉×#330

—

C₂²×Dic₃₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

—

—

—

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

#10597267

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

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

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

#1291

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#386

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#454

yes

—

Dic₁₉

—

#533

C₂×D₁₉

yes

characteristic

C₂×C₄⋊Q₈

—

—

—

—

—

100

#432

—

101

#432

C₂×D₁₉

yes

—

102

#419

—

103

C₄×M₁₆

—

104

#332

—

105

#330

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#1888

yes

characteristic

108

C₂×C₁₉

#1902

yes

—

109

C₂²×Q₈

—

110

C₂×M₁₆

—

111

C₄⋊Q₈

—

112

C₄⋊Q₈

—

113

C₄⋊Q₈

—

114

C₄⋊Q₈

C₄×D₁₉

yes

—

115

#125

C₂²⋊D₁₉

yes

—

116

C₂²⋊Q₈

—

117

C₄×Q₈

—

118

#117

D₇₆

yes

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄²

C₂²×D₁₉

yes

characteristic

121

C₄⋊C₈

—

122

C₄⋊C₈

—

123

C₄⋊C₈

—

124

#103

—

125

C₂²⋊C₈

—

126

C₂²⋊C₈

—

127

#97

—

128

#97

—

129

#97

—

130

#97

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₁₉

#9422

yes

characteristic, complemented, Sylow

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂²×C₄

—

139

C₂²×C₄

C₂×D₇₆

yes

characteristic

140

C₂²×C₄

#64543

yes

—

141

M₁₆

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

(C₂×D₁₉)⋊C₄

yes

—

150

C₂²⋊C₄

—

151

C₄²

—

152

C₄²

C₂×C₄×D₁₉

yes

characteristic

153

C₄²

D₄×D₁₉

yes

—

154

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

155

C₂³

#10597332

yes

characteristic

156

Q₈

—

157

Q₈

—

158

Q₈

—

152

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

152

—

164

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

165

C₂×C₄

#10597328

yes

characteristic

166

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

167

C₂×C₄

#10597385

yes

—

168

C₈

—

169

C₈

—

170

C₈

—

171

C₂²

—

172

C₂²

—

173

C₂²

#11926421

yes

characteristic

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

152

—

179

C₄

#11926719

yes

—

180

C₂

—

181

C₂

#14564036

yes

characteristic

182

C₂

#14564106

yes

—

	subgroup	G/H
center	C₂²	#11926421
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1537	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	#123
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1537	D₁₉
hypocenter	C₁₉	#9422
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1537

subgroup

G/H

center

C₂²

#11926421

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1537

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1537

N	H ≅ G/N	type
133. C₁₉	#9422	semidirect

H ≅ G/N

type

133. C₁₉

#9422

semidirect

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

subgroup	index
#14574017	2
#14572741	2
#14562351	2
#14561508	2
C₁₉×#1537	2
#9422	19

subgroup

index

C₁₉×#1537

Subgroups — #18080059

Conjugacy classes of subgroups

Complements

Maximal subgroups