Group #18075534 — subgroups

Subgroups — #18075534

Order 4864.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14572565	C₂	1	1	yes	maximal, characteristic
2	#14562396	C₂	1	2	yes	maximal
3	#14562272	C₂	1	2	yes	maximal
4	#14561546	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926671	—	2	2	no	—
8	#11926668	—	2	2	no	—
9	#11926601	C₂²	1	2	yes	—
10	#11926572	C₄	1	2	yes	—
11	#11926502	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	#11926285	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	#10597372	C₂×C₄	1	2	yes	—
21	#10597370	—	2	2	no	—
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#10597316	D₄	1	2	yes	—
25	#10597315	Q₈	1	2	yes	—
26	C₄×Dic₃₈	—	2	2	no	—
27	C₁₉×C₄⋊C₈	—	2	2	no	—
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	#10597272	—	2	2	no	—
33	Dic₁₉⋊C₈	—	2	4	no	—
34	C₈×Dic₁₉	—	2	2	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
36	#10597260	—	2	2	no	—
37	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
38	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	#41	1	2	yes	—
41	C₂×Dic₃₈	—	2	2	no	—
42	M₁₆×C₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	4	2	no	—
45	C₄²×C₁₉	C₂×D₄	1	2	yes	—
46	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
48	C₂²⋊Dic₁₉	—	2	2	no	—
49	C₄⋊Dic₁₉	—	2	2	no	—
50	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
51	Dic₁₉⋊C₄	—	2	4	no	—
52	C₄×Dic₁₉	—	2	2	no	—
53	C₂×C₁₉⋊C₈	—	2	2	no	—
54	C₂×C₁₉⋊C₈	—	4	1	no	—
55	C₂×C₁₉⋊C₈	—	4	2	no	—
56	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
57	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
59	#8631	—	19	1	no	maximal, Sylow
60	C₂³×C₁₉	#117	1	1	yes	characteristic
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#121	1	2	yes	—
67	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
68	C₂×Dic₁₉	—	2	4	no	—
69	Dic₃₈	—	4	4	no	—
70	C₈×C₁₉	—	4	2	no	—
71	C₈×C₁₉	—	8	2	no	—
72	C₁₉⋊C₈	—	2	1	no	—
73	C₁₉⋊C₈	—	2	2	no	—
74	C₁₉⋊C₈	—	8	2	no	—
75	C₁₉⋊C₈	#101	1	2	yes	—
76	#2960	—	19	1	no	—
77	#1568	—	19	2	no	—
78	#1537	—	19	2	no	—
79	#1307	—	19	1	no	—
80	#1307	D₁₉	1	1	yes	characteristic
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	—	2	2	no	—
83	C₂²×C₁₉	#380	1	1	yes	characteristic
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
88	C₄×C₁₉	#413	1	1	yes	characteristic
89	Dic₁₉	—	4	4	no	—
90	#533	—	19	1	no	—
91	#446	—	38	2	no	—
92	C₈×Q₈	—	38	2	no	—
93	#432	—	19	2	no	—
94	#432	C₂×D₁₉	1	2	yes	—
95	#424	—	19	2	no	—
96	#423	C₂×D₁₉	1	1	yes	characteristic
97	#405	—	19	2	no	—
98	C₂×C₄×C₈	—	19	1	no	—
99	#335	—	38	2	no	—
100	#334	—	38	2	no	—
101	#330	—	38	4	no	—
102	C₂×C₁₉	—	4	1	no	—
103	C₂×C₁₉	#1801	1	1	yes	characteristic
104	C₂×C₁₉	#1814	1	2	yes	—
105	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
106	C₂²×C₈	—	19	1	no	—
107	C₂²×C₈	—	19	1	no	—
108	C₄⋊Q₈	—	19	2	no	—
109	#125	—	19	2	no	—
110	C₂²⋊Q₈	—	38	2	no	—
111	C₄×Q₈	—	38	2	no	—
112	#117	—	19	2	no	—
113	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
114	C₄⋊C₈	—	2	2	no	—
115	C₄⋊C₈	—	2	2	no	—
116	C₄⋊C₈	—	38	4	no	—
117	C₄⋊C₈	—	38	2	no	—
118	C₂²⋊C₈	—	2	2	no	—
119	C₂²⋊C₈	—	38	2	no	—
120	#97	—	2	2	no	—
121	#97	—	38	2	no	—
122	#97	—	38	2	no	—
123	C₄×C₈	—	19	2	no	—
124	C₄×C₈	—	19	2	no	—
125	C₄×C₈	—	38	2	no	—
126	C₁₉	#8631	1	1	yes	characteristic, complemented, Sylow
127	C₂×Q₈	—	38	2	no	—
128	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
129	C₂²×C₄	#64541	1	2	yes	—
130	M₁₆	—	4	2	no	—
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	4	2	no	—
133	C₂×C₈	—	19	1	no	—
134	C₂×C₈	—	19	1	no	—
135	C₂×C₈	—	19	2	no	—
136	C₂×C₈	—	38	2	no	—
137	C₂×C₈	—	76	1	no	—
138	C₂×C₈	—	76	2	no	—
139	C₄⋊C₄	—	19	4	no	—
140	C₄⋊C₄	—	38	4	no	—
141	C₄⋊C₄	—	38	2	no	—
142	C₂²⋊C₄	—	38	2	no	—
143	C₄²	—	38	2	no	—
144	C₄²	D₄×D₁₉	1	2	yes	—
145	C₄²	D₄×D₁₉	1	1	yes	characteristic
146	C₄²	Q₈×D₁₉	1	1	yes	characteristic
147	C₂³	#10597318	1	1	yes	characteristic
148	Q₈	—	76	4	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	38	4	no	—
153	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
154	C₂×C₄	#10597330	1	2	yes	—
155	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
156	C₂×C₄	#10597342	1	2	yes	—
157	C₈	—	4	2	no	—
158	C₈	—	8	2	no	—
159	C₈	—	19	2	no	—
160	C₈	—	38	1	no	—
161	C₈	—	38	2	no	—
162	C₈	—	152	2	no	—
163	C₂²	—	2	1	no	—
164	C₂²	—	2	2	no	—
165	C₂²	#11926403	1	1	yes	characteristic
166	C₄	—	2	1	no	—
167	C₄	—	2	2	no	—
168	C₄	—	2	2	no	—
169	C₄	—	76	4	no	—
170	C₄	#101×D₁₉	1	1	yes	characteristic
171	C₄	#11926525	1	1	yes	characteristic
172	C₂	—	4	1	no	—
173	C₂	#14563630	1	1	yes	characteristic
174	C₂	#14563688	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572565

C₂

yes

maximal, characteristic

#14562396

C₂

yes

maximal

#14562272

C₂

yes

maximal

#14561546

C₂

yes

maximal, characteristic

C₁₉×#1307

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

—

C₂²

yes

—

#11926572

C₄

yes

—

#11926502

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉×#432

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

C₂×C₄

yes

—

#10597370

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

#10597316

D₄

yes

—

#10597315

Q₈

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂³×C₁₉

yes

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

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#101

yes

—

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#380

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#533

—

#446

—

C₈×Q₈

—

#432

—

#432

C₂×D₁₉

yes

—

#424

—

#423

C₂×D₁₉

yes

characteristic

#405

—

C₂×C₄×C₈

—

#335

—

100

#334

—

101

#330

—

102

C₂×C₁₉

—

103

C₂×C₁₉

#1801

yes

characteristic

104

C₂×C₁₉

#1814

yes

—

105

C₂×M₁₆

C₄×D₁₉

yes

—

106

C₂²×C₈

—

107

C₂²×C₈

—

108

C₄⋊Q₈

—

109

#125

—

110

C₂²⋊Q₈

—

111

C₄×Q₈

—

112

#117

—

113

C₂×C₄²

C₂²×D₁₉

yes

characteristic

114

C₄⋊C₈

—

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₄⋊C₈

—

118

C₂²⋊C₈

—

119

C₂²⋊C₈

—

120

#97

—

121

#97

—

122

#97

—

123

C₄×C₈

—

124

C₄×C₈

—

125

C₄×C₈

—

126

C₁₉

#8631

yes

characteristic, complemented, Sylow

127

C₂×Q₈

—

128

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

129

C₂²×C₄

#64541

yes

—

130

M₁₆

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₂²⋊C₄

—

143

C₄²

—

144

C₄²

D₄×D₁₉

yes

—

145

C₄²

D₄×D₁₉

yes

characteristic

146

C₄²

Q₈×D₁₉

yes

characteristic

147

C₂³

#10597318

yes

characteristic

148

Q₈

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

154

C₂×C₄

#10597330

yes

—

155

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

156

C₂×C₄

#10597342

yes

—

157

C₈

—

158

C₈

—

159

C₈

—

160

C₈

—

161

C₈

—

162

C₈

—

152

—

163

C₂²

—

164

C₂²

—

165

C₂²

#11926403

yes

characteristic

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

#101×D₁₉

yes

characteristic

171

C₄

#11926525

yes

characteristic

172

C₂

—

173

C₂

#14563630

yes

characteristic

174

C₂

#14563688

yes

—

	subgroup	G/H
center	C₂²	#11926403
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1307	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1307	D₁₉
hypocenter	C₁₉	#8631
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1307

subgroup

G/H

center

C₂²

#11926403

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1307

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1307

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

H ≅ G/N

type

126. C₁₉

#8631

semidirect

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

subgroup	index
#14572565	2
#14562396	2
#14562272	2
#14561546	2
C₁₉×#1307	2
#8631	19

subgroup

index

C₁₉×#1307

Subgroups — #18075534

Conjugacy classes of subgroups

Complements

Maximal subgroups