Group #18075533 — subgroups

Subgroups — #18075533

Order 4864.

320 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 101 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	#14572570	C₂	1	1	yes	maximal, characteristic
2	#14562396	C₂	1	2	yes	maximal
3	#14562273	C₂	1	1	yes	maximal, characteristic
4	#14561545	C₂	1	2	yes	maximal
5	C₁₉×#1537	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	2	no	—
7	Q₈×C₁₉⋊C₈	—	2	2	no	—
8	#11926601	C₂²	1	2	yes	—
9	#11926571	C₄	1	2	yes	—
10	#11926568	C₂²	1	1	yes	characteristic
11	#11926500	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926286	—	2	2	no	—
16	C₁₉×#533	C₂²	1	1	yes	characteristic
17	C₁₉×#432	C₂²	1	2	yes	—
18	C₁₉×#330	—	2	2	no	—
19	C₁₉×C₄⋊Q₈	Q₈	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	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×#64520	C₂×C₄	1	2	yes	—
26	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₂²⋊C₈	—	2	2	no	—
30	C₁₉×#97	—	2	2	no	—
31	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
35	#10597260	—	2	2	no	—
36	#10597260	—	2	2	no	—
37	C₄×C₁₉⋊C₈	—	2	2	no	—
38	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
40	C₂×Q₈×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	2	yes	—
43	C₂×C₈×C₁₉	—	4	2	no	—
44	C₄⋊C₄×C₁₉	—	2	4	no	—
45	C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
47	C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	C₂×D₄	1	2	yes	—
50	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	#64520	—	4	2	no	—
53	C₂×C₁₉⋊C₈	—	2	2	no	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	—	4	1	no	—
56	C₂×C₁₉⋊C₈	—	4	2	no	—
57	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
59	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
60	#8631	—	19	1	no	maximal, Sylow
61	C₂³×C₁₉	#117	1	1	yes	characteristic
62	Q₈×C₁₉	—	4	4	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	4	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	#121	1	2	yes	—
70	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
71	C₈×C₁₉	—	8	2	no	—
72	C₁₉⋊C₈	—	2	1	no	—
73	C₁₉⋊C₈	—	2	2	no	—
74	C₁₉⋊C₈	—	4	2	no	—
75	C₁₉⋊C₈	—	8	2	no	—
76	C₁₉⋊C₈	#101	1	2	yes	—
77	#2960	—	19	1	no	—
78	#1568	—	19	2	no	—
79	#1537	—	19	1	no	—
80	#1537	D₁₉	1	1	yes	characteristic
81	#1307	—	19	2	no	—
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	—	2	2	no	—
84	C₂²×C₁₉	#380	1	1	yes	characteristic
85	C₄×C₁₉	—	2	1	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	4	4	no	—
89	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
90	C₄×C₁₉	#413	1	1	yes	characteristic
91	#533	C₂×D₁₉	1	1	yes	characteristic
92	#446	—	38	2	no	—
93	C₈×Q₈	—	38	2	no	—
94	#432	—	19	2	no	—
95	#432	C₂×D₁₉	1	2	yes	—
96	#424	—	19	2	no	—
97	#423	—	19	1	no	—
98	#405	—	19	2	no	—
99	C₂×C₄×C₈	—	19	1	no	—
100	#335	—	38	2	no	—
101	#334	—	38	2	no	—
102	#330	—	2	2	no	—
103	#330	—	38	2	no	—
104	C₂×C₁₉	—	4	1	no	—
105	C₂×C₁₉	#1801	1	1	yes	characteristic
106	C₂×C₁₉	#1814	1	2	yes	—
107	C₂×M₁₆	—	19	2	no	—
108	C₂²×C₈	—	19	1	no	—
109	C₂²×C₈	—	19	1	no	—
110	C₄⋊Q₈	Dic₃₈	1	2	yes	—
111	#125	C₂²⋊D₁₉	1	2	yes	—
112	C₂²⋊Q₈	—	2	2	no	—
113	C₄×Q₈	—	2	2	no	—
114	#117	C₄×D₁₉	1	2	yes	—
115	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
116	C₄⋊C₈	—	2	2	no	—
117	C₄⋊C₈	—	38	4	no	—
118	C₄⋊C₈	—	38	2	no	—
119	C₄⋊C₈	—	38	2	no	—
120	C₂²⋊C₈	—	2	2	no	—
121	C₂²⋊C₈	—	38	2	no	—
122	#97	—	2	2	no	—
123	#97	—	38	2	no	—
124	#97	—	38	2	no	—
125	C₄×C₈	—	19	2	no	—
126	C₄×C₈	—	19	2	no	—
127	C₄×C₈	—	38	2	no	—
128	C₁₉	#8631	1	1	yes	characteristic, complemented, Sylow
129	C₂×Q₈	—	2	2	no	—
130	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
131	C₂²×C₄	#64543	1	2	yes	—
132	M₁₆	—	76	2	no	—
133	C₂×C₈	—	4	2	no	—
134	C₂×C₈	—	19	1	no	—
135	C₂×C₈	—	19	1	no	—
136	C₂×C₈	—	19	2	no	—
137	C₂×C₈	—	38	2	no	—
138	C₂×C₈	—	38	2	no	—
139	C₂×C₈	—	76	1	no	—
140	C₂×C₈	—	76	2	no	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	2	2	no	—
143	C₄⋊C₄	Dic₁₉⋊C₄	1	4	yes	—
144	C₂²⋊C₄	—	2	2	no	—
145	C₄²	—	2	2	no	—
146	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
147	C₄²	D₄×D₁₉	1	2	yes	—
148	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
149	C₂³	#10597323	1	1	yes	characteristic
150	Q₈	—	4	4	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	#10597324	1	2	yes	—
156	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
157	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
158	C₂×C₄	#10597385	1	2	yes	—
159	C₈	—	8	2	no	—
160	C₈	—	19	2	no	—
161	C₈	—	38	1	no	—
162	C₈	—	38	2	no	—
163	C₈	—	76	2	no	—
164	C₈	—	152	2	no	—
165	C₂²	—	2	1	no	—
166	C₂²	—	2	2	no	—
167	C₂²	#11926402	1	1	yes	characteristic
168	C₄	—	2	1	no	—
169	C₄	—	2	2	no	—
170	C₄	—	2	2	no	—
171	C₄	—	4	4	no	—
172	C₄	#101×D₁₉	1	1	yes	characteristic
173	C₄	#11926527	1	1	yes	characteristic
174	C₂	—	4	1	no	—
175	C₂	#14563629	1	1	yes	characteristic
176	C₂	#14563687	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572570

C₂

yes

maximal, characteristic

#14562396

C₂

yes

maximal

#14562273

C₂

yes

maximal, characteristic

#14561545

C₂

yes

maximal

C₁₉×#1537

C₂

yes

maximal, characteristic

#11926675

—

Q₈×C₁₉⋊C₈

—

#11926601

C₂²

yes

—

#11926571

C₄

yes

—

#11926568

C₂²

yes

characteristic

#11926500

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#432

C₂²

yes

—

C₁₉×#330

—

C₁₉×C₄⋊Q₈

Q₈

yes

—

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₄⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#101

yes

—

—

—

—

D₁₉

yes

characteristic

#1307

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#380

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×D₁₉

yes

characteristic

#446

—

C₈×Q₈

—

#432

—

#432

C₂×D₁₉

yes

—

#424

—

#423

—

#405

—

C₂×C₄×C₈

—

100

#335

—

101

#334

—

102

#330

—

103

#330

—

104

C₂×C₁₉

—

105

C₂×C₁₉

#1801

yes

characteristic

106

C₂×C₁₉

#1814

yes

—

107

C₂×M₁₆

—

108

C₂²×C₈

—

109

C₂²×C₈

—

110

C₄⋊Q₈

Dic₃₈

yes

—

111

#125

C₂²⋊D₁₉

yes

—

112

C₂²⋊Q₈

—

113

C₄×Q₈

—

114

#117

C₄×D₁₉

yes

—

115

C₂×C₄²

C₂²×D₁₉

yes

characteristic

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

C₄⋊C₈

—

119

C₄⋊C₈

—

120

C₂²⋊C₈

—

121

C₂²⋊C₈

—

122

#97

—

123

#97

—

124

#97

—

125

C₄×C₈

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₁₉

#8631

yes

characteristic, complemented, Sylow

129

C₂×Q₈

—

130

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

131

C₂²×C₄

#64543

yes

—

132

M₁₆

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

Dic₁₉⋊C₄

yes

—

144

C₂²⋊C₄

—

145

C₄²

—

146

C₄²

C₂×Dic₃₈

yes

characteristic

147

C₄²

D₄×D₁₉

yes

—

148

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

149

C₂³

#10597323

yes

characteristic

150

Q₈

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

#10597324

yes

—

156

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

157

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

158

C₂×C₄

#10597385

yes

—

159

C₈

—

160

C₈

—

161

C₈

—

162

C₈

—

163

C₈

—

164

C₈

—

152

—

165

C₂²

—

166

C₂²

—

167

C₂²

#11926402

yes

characteristic

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

#101×D₁₉

yes

characteristic

173

C₄

#11926527

yes

characteristic

174

C₂

—

175

C₂

#14563629

yes

characteristic

176

C₂

#14563687

yes

—

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1537	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1537	D₁₉
hypocenter	C₁₉	#8631
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1537

subgroup

G/H

center

C₂²

#11926402

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1537

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1537

N	H ≅ G/N	type
128. C₁₉	#8631	semidirect

H ≅ G/N

type

128. C₁₉

#8631

semidirect

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

subgroup	index
#14572570	2
#14562396	2
#14562273	2
#14561545	2
C₁₉×#1537	2
#8631	19

subgroup

index

C₁₉×#1537

Subgroups — #18075533

Conjugacy classes of subgroups

Complements

Maximal subgroups