Group #18077491 — subgroups

Subgroups — #18077491

Order 4864.

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

normal subgroups only

This group has 376 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	#14574157	C₂	1	1	yes	maximal, characteristic
2	#14572741	C₂	1	1	yes	maximal, characteristic
3	#14562109	C₂	1	2	yes	maximal
4	#14561535	C₂	1	2	yes	maximal
5	C₁₉×#1544	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926954	C₄	1	4	yes	—
8	#11926950	—	2	2	no	—
9	#11926675	—	2	4	no	—
10	#11926605	—	2	2	no	—
11	#11926601	C₂²	1	2	yes	—
12	#11926580	—	2	2	no	—
13	C₂×#10597260	C₂²	1	1	yes	characteristic
14	#11926276	—	2	4	no	—
15	C₁₉×#533	C₂²	1	1	yes	characteristic
16	C₁₉×#431	C₂²	1	2	yes	—
17	C₁₉×#332	—	2	2	no	—
18	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
19	C₁₉×#125	C₂×C₄	1	2	yes	—
20	C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₁₉×#117	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	#10597372	—	2	1	no	—
25	#10597370	—	2	2	no	—
26	C₂²×C₁₉⋊C₈	—	2	1	no	—
27	#10597316	—	2	1	no	—
28	#10597315	C₂×C₄	1	2	yes	—
29	C₄×Dic₃₈	—	2	2	no	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×C₂²⋊C₈	—	2	2	no	—
32	C₄×C₈×C₁₉	—	2	2	no	—
33	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
34	#10597265	—	2	4	no	—
35	#10597264	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
37	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
38	#10597260	—	2	2	no	—
39	#10597260	—	2	2	no	—
40	#10597260	—	2	1	no	—
41	#10597260	C₂×C₄	1	2	yes	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	#41	1	2	yes	—
46	C₂×Dic₃₈	—	2	2	no	—
47	C₂×C₈×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₄²×C₁₉	—	2	2	no	—
53	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×D₄	1	2	yes	—
55	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²⋊Dic₁₉	—	4	1	no	—
57	C₄⋊Dic₁₉	—	2	2	no	—
58	C₄⋊Dic₁₉	—	2	2	no	—
59	Dic₁₉⋊C₄	—	4	2	no	—
60	C₄×Dic₁₉	—	4	1	no	—
61	C₂×C₁₉⋊C₈	—	2	4	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	2	4	no	—
64	#9006	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	#123	1	1	yes	characteristic
66	Q₈×C₁₉	—	8	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	2	4	no	—
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
72	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#121	1	2	yes	—
74	C₂×Dic₁₉	—	4	2	no	—
75	Dic₃₈	—	4	4	no	—
76	C₈×C₁₉	—	8	2	no	—
77	C₁₉⋊C₈	—	2	4	no	—
78	C₁₉⋊C₈	—	4	4	no	—
79	#3162	—	19	1	no	—
80	#2987	—	19	1	no	—
81	#1544	D₁₉	1	1	yes	characteristic
82	#1497	—	19	2	no	—
83	#1302	—	19	2	no	—
84	C₂²×C₁₉	—	2	2	no	—
85	C₂²×C₁₉	—	2	1	no	—
86	C₂²×C₁₉	#386	1	1	yes	characteristic
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	2	1	no	—
90	C₄×C₁₉	—	4	4	no	—
91	C₄×C₁₉	#456	1	2	yes	—
92	Dic₁₉	—	8	2	no	—
93	#533	—	19	1	no	—
94	#533	C₂×D₁₉	1	1	yes	characteristic
95	#501	—	19	4	no	—
96	#501	—	38	2	no	—
97	#446	—	38	4	no	—
98	#433	—	38	2	no	—
99	#432	—	19	2	no	—
100	#431	C₂×D₁₉	1	2	yes	—
101	#427	—	38	2	no	—
102	C₂×#97	—	19	1	no	—
103	#332	—	2	2	no	—
104	Q₈⋊C₈	—	38	4	no	—
105	C₂×C₁₉	—	4	1	no	—
106	C₂×C₁₉	#1881	1	2	yes	—
107	C₂×C₁₉	#1886	1	1	yes	characteristic
108	C₂²×C₈	—	38	1	no	—
109	C₄⋊Q₈	—	19	2	no	—
110	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
111	#125	—	38	1	no	—
112	#125	C₄×D₁₉	1	2	yes	—
113	C₂²⋊Q₈	—	2	2	no	—
114	C₂²⋊Q₈	—	38	2	no	—
115	C₄×Q₈	—	2	2	no	—
116	C₄×Q₈	—	38	2	no	—
117	#117	—	38	1	no	—
118	#117	D₇₆	1	2	yes	—
119	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
120	#107	—	38	4	no	—
121	#106	—	38	4	no	—
122	C₄⋊C₈	—	2	2	no	—
123	C₄⋊C₈	—	19	4	no	—
124	C₄⋊C₈	—	38	4	no	—
125	C₂²⋊C₈	—	2	2	no	—
126	C₂²⋊C₈	—	38	2	no	—
127	#97	—	19	2	no	—
128	#97	—	38	2	no	—
129	#97	—	38	2	no	—
130	#97	—	38	1	no	—
131	C₄×C₈	—	2	2	no	—
132	C₄×C₈	—	38	2	no	—
133	C₁₉	#9006	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	38	2	no	—
136	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
137	C₂²×C₄	#64543	1	2	yes	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	—	38	4	no	—
140	C₂×C₈	—	38	2	no	—
141	C₂×C₈	—	38	4	no	—
142	C₄⋊C₄	—	2	2	no	—
143	C₄⋊C₄	—	2	4	no	—
144	C₄⋊C₄	—	38	2	no	—
145	C₄⋊C₄	—	38	2	no	—
146	C₄⋊C₄	—	76	2	no	—
147	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
148	C₂²⋊C₄	—	2	2	no	—
149	C₂²⋊C₄	—	76	1	no	—
150	C₄²	—	2	2	no	—
151	C₄²	—	76	1	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	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	76	2	no	—
162	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
163	C₂×C₄	#10597328	1	1	yes	characteristic
164	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
165	C₂×C₄	#10597385	1	2	yes	—
166	C₈	—	8	2	no	—
167	C₈	—	38	4	no	—
168	C₈	—	76	4	no	—
169	C₂²	—	2	2	no	—
170	C₂²	—	2	1	no	—
171	C₂²	#11926421	1	1	yes	characteristic
172	C₄	—	2	2	no	—
173	C₄	—	2	2	no	—
174	C₄	—	2	1	no	—
175	C₄	—	4	4	no	—
176	C₄	—	152	2	no	—
177	C₄	#11926729	1	2	yes	—
178	C₂	—	4	1	no	—
179	C₂	#14563995	1	2	yes	—
180	C₂	#14564026	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574157

C₂

yes

maximal, characteristic

#14572741

C₂

yes

maximal, characteristic

#14562109

C₂

yes

maximal

#14561535

C₂

yes

maximal

C₁₉×#1544

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926954

C₄

yes

—

—

—

—

C₂²

yes

—

#11926580

—

C₂×#10597260

C₂²

yes

characteristic

#11926276

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

—

C₁₉×#332

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

C₂×C₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

#10597370

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

#10597265

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

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

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

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

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3162

—

#2987

—

#1544

D₁₉

yes

characteristic

#1497

—

#1302

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#386

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#456

yes

—

Dic₁₉

—

#533

—

#533

C₂×D₁₉

yes

—

—

—

—

—

100

#431

C₂×D₁₉

yes

—

101

#427

—

102

C₂×#97

—

103

#332

—

104

Q₈⋊C₈

—

105

C₂×C₁₉

—

106

C₂×C₁₉

#1881

yes

—

107

C₂×C₁₉

#1886

yes

characteristic

108

C₂²×C₈

—

109

C₄⋊Q₈

—

110

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

111

#125

—

112

#125

C₄×D₁₉

yes

—

113

C₂²⋊Q₈

—

114

C₂²⋊Q₈

—

115

C₄×Q₈

—

116

C₄×Q₈

—

117

#117

—

118

#117

D₇₆

yes

—

119

C₂×C₄²

C₂²×D₁₉

yes

characteristic

120

#107

—

121

#106

—

122

C₄⋊C₈

—

123

C₄⋊C₈

—

124

C₄⋊C₈

—

125

C₂²⋊C₈

—

126

C₂²⋊C₈

—

127

#97

—

128

#97

—

129

#97

—

130

#97

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₁₉

#9006

yes

characteristic, complemented, Sylow

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂²×C₄

C₂×D₇₆

yes

characteristic

137

C₂²×C₄

#64543

yes

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

(C₂×D₁₉)⋊C₄

yes

—

148

C₂²⋊C₄

—

149

C₂²⋊C₄

—

150

C₄²

—

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

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

163

C₂×C₄

#10597328

yes

characteristic

164

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

165

C₂×C₄

#10597385

yes

—

166

C₈

—

167

C₈

—

168

C₈

—

169

C₂²

—

170

C₂²

—

171

C₂²

#11926421

yes

characteristic

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

152

—

177

C₄

#11926729

yes

—

178

C₂

—

179

C₂

#14563995

yes

—

180

C₂

#14564026

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1544	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	#123
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1544	D₁₉
hypocenter	C₁₉	#9006
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1544

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1544

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1544

N	H ≅ G/N	type
133. C₁₉	#9006	semidirect

H ≅ G/N

type

133. C₁₉

#9006

semidirect

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

subgroup	index
#14574157	2
#14572741	2
#14562109	2
#14561535	2
C₁₉×#1544	2
#9006	19

subgroup

index

C₁₉×#1544

Subgroups — #18077491

Conjugacy classes of subgroups

Complements

Maximal subgroups