Group #18076294 — subgroups

Subgroups — #18076294

Order 4864.

402 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 187 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	#14563787	C₂	1	1	yes	maximal, characteristic
2	#14563381	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926296	C₂	1	4	yes	maximal
4	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926299	C₄	1	2	yes	—
9	#11926299	C₄	1	2	yes	—
10	#11926296	—	2	8	no	—
11	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	D₄	1	2	yes	—
18	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×C₁₉⋊C₈	—	2	2	no	—
21	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
22	C₁₉×C₄⋊C₈	—	2	4	no	—
23	C₁₉×C₄⋊C₈	—	4	4	no	—
24	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
26	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
27	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
28	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₈×C₁₉	—	4	2	no	—
34	C₂×C₈×C₁₉	—	4	4	no	—
35	C₄²×C₁₉	—	2	2	no	—
36	C₄²×C₁₉	—	2	2	no	—
37	C₄²×C₁₉	—	4	2	no	—
38	C₄²×C₁₉	D₈	1	4	yes	—
39	C₄²×C₁₉	Q₁₆	1	4	yes	—
40	C₄²×C₁₉	C₂×D₄	1	2	yes	—
41	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
42	C₂×C₁₉⋊C₈	—	2	4	no	—
43	C₂×C₁₉⋊C₈	—	2	4	no	—
44	C₂×C₁₉⋊C₈	—	4	2	no	—
45	C₂×C₁₉⋊C₈	—	4	4	no	—
46	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	—
47	#8810	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	#107	1	4	yes	—
55	C₂×C₄×C₁₉	#107	1	4	yes	—
56	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
57	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
60	C₂×C₄×C₁₉	#131	1	2	yes	—
61	C₂×C₄×C₁₉	#131	1	2	yes	—
62	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
63	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
64	C₈×C₁₉	—	8	2	no	—
65	C₁₉⋊C₈	—	2	8	no	—
66	C₁₉⋊C₈	—	8	2	no	—
67	#1842	—	19	1	no	—
68	#1842	D₁₉	1	1	yes	characteristic
69	#1744	—	19	1	no	—
70	C₂×#335	—	19	4	no	—
71	C₂²×C₁₉	#384	1	1	yes	characteristic
72	C₂²×C₁₉	#424	1	1	yes	characteristic
73	C₂²×C₁₉	#424	1	1	yes	characteristic
74	C₂²×C₁₉	C₂×#107	1	2	yes	—
75	C₂²×C₁₉	#430	1	2	yes	—
76	C₄×C₁₉	—	2	4	no	—
77	C₄×C₁₉	—	2	4	no	—
78	C₄×C₁₉	—	2	2	no	—
79	C₄×C₁₉	#424	1	4	yes	—
80	C₄×C₁₉	#493	1	1	yes	characteristic
81	C₄×C₁₉	#494	1	1	yes	characteristic
82	C₄×C₁₉	#500	1	2	yes	—
83	C₂×C₄⋊C₈	—	2	2	no	—
84	C₂×C₄⋊C₈	—	19	2	no	—
85	C₂×C₄⋊C₈	—	38	2	no	—
86	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
87	C₂×C₄×C₈	—	19	2	no	—
88	C₄³	C₂×D₁₉	1	1	yes	characteristic
89	#336	—	19	2	no	—
90	#336	—	19	2	no	—
91	#335	—	38	8	no	—
92	C₂×C₁₉	#1571	1	2	yes	—
93	C₂×C₁₉	#1571	1	2	yes	—
94	C₂×C₁₉	#1843	1	1	yes	characteristic
95	C₂×C₁₉	#1845	1	1	yes	characteristic
96	C₂×C₁₉	#1849	1	1	yes	characteristic
97	C₂²×C₈	—	2	2	no	—
98	C₂²×C₈	—	19	4	no	—
99	C₂²×C₈	—	38	2	no	—
100	C₂×C₄²	Dic₃₈	1	2	yes	—
101	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
102	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
103	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
104	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
105	C₄⋊C₈	—	2	4	no	—
106	C₄⋊C₈	—	4	4	no	—
107	C₄⋊C₈	—	38	4	no	—
108	C₄⋊C₈	—	76	4	no	—
109	C₄×C₈	—	19	4	no	—
110	C₄×C₈	—	19	4	no	—
111	C₁₉	#8810	1	1	yes	characteristic, complemented, Sylow
112	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
113	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
114	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
115	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
116	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
117	C₂×C₈	—	4	4	no	—
118	C₂×C₈	—	4	2	no	—
119	C₂×C₈	—	19	8	no	—
120	C₂×C₈	—	38	4	no	—
121	C₂×C₈	—	38	4	no	—
122	C₂×C₈	—	76	4	no	—
123	C₂×C₈	—	76	2	no	—
124	C₄²	—	2	2	no	—
125	C₄²	—	2	2	no	—
126	C₄²	—	4	2	no	—
127	C₄²	#64525	1	4	yes	—
128	C₄²	#64528	1	4	yes	—
129	C₄²	D₄×D₁₉	1	2	yes	—
130	C₄²	Q₈×D₁₉	1	2	yes	—
131	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	#10597264	1	4	yes	—
138	C₂×C₄	#10597264	1	4	yes	—
139	C₂×C₄	#10597334	1	2	yes	—
140	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
141	C₂×C₄	#10597347	1	2	yes	—
142	C₂×C₄	#10597353	1	2	yes	—
143	C₂×C₄	C₂×#64525	1	2	yes	—
144	C₂×C₄	#10597386	1	1	yes	characteristic
145	C₂×C₄	C₂×#64528	1	2	yes	—
146	C₂×C₄	#10597390	1	1	yes	characteristic
147	C₈	—	8	2	no	—
148	C₈	—	38	8	no	—
149	C₈	—	152	2	no	—
150	C₂²	#11926413	1	1	yes	characteristic
151	C₂²	#11926570	1	1	yes	characteristic
152	C₂²	#11926572	1	1	yes	characteristic
153	C₂²	C₂×#10597264	1	2	yes	—
154	C₂²	#11926592	1	2	yes	—
155	C₄	—	2	4	no	—
156	C₄	—	2	4	no	—
157	C₄	—	2	2	no	—
158	C₄	#11926569	1	4	yes	—
159	C₄	#11926920	1	1	yes	characteristic
160	C₄	#11926923	1	1	yes	characteristic
161	C₄	#11926947	1	2	yes	—
162	C₂	#14562409	1	2	yes	—
163	C₂	#14562411	1	2	yes	—
164	C₂	#14563788	1	1	yes	characteristic
165	C₂	#14563794	1	1	yes	characteristic
166	C₂	#14563809	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563787

C₂

yes

maximal, characteristic

#14563381

C₂

yes

maximal, characteristic

C₂×#11926296

C₂

yes

maximal

C₁₉×#1842

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926299

C₄

yes

—

#11926299

C₄

yes

—

#11926296

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

#8810

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#107

yes

—

C₂×C₄×C₁₉

#107

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1842

—

#1842

D₁₉

yes

characteristic

#1744

—

C₂×#335

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#430

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#424

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

C₂×C₄×C₈

—

C₄³

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

#1571

yes

—

C₂×C₁₉

#1571

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

100

C₂×C₄²

Dic₃₈

yes

—

101

C₂×C₄²

C₄×D₁₉

yes

characteristic

102

C₂×C₄²

C₄×D₁₉

yes

characteristic

103

C₂×C₄²

C₂²⋊D₁₉

yes

—

104

C₂×C₄²

C₂²×D₁₉

yes

characteristic

105

C₄⋊C₈

—

106

C₄⋊C₈

—

107

C₄⋊C₈

—

108

C₄⋊C₈

—

109

C₄×C₈

—

110

C₄×C₈

—

111

C₁₉

#8810

yes

characteristic, complemented, Sylow

112

C₂²×C₄

Dic₁₉⋊C₄

yes

—

113

C₂²×C₄

Dic₁₉⋊C₄

yes

—

114

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

115

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

116

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₄²

—

125

C₄²

—

126

C₄²

—

127

C₄²

#64525

yes

—

128

C₄²

#64528

yes

—

129

C₄²

D₄×D₁₉

yes

—

130

C₄²

Q₈×D₁₉

yes

—

131

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#10597264

yes

—

138

C₂×C₄

#10597264

yes

—

139

C₂×C₄

#10597334

yes

—

140

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

141

C₂×C₄

#10597347

yes

—

142

C₂×C₄

#10597353

yes

—

143

C₂×C₄

C₂×#64525

yes

—

144

C₂×C₄

#10597386

yes

characteristic

145

C₂×C₄

C₂×#64528

yes

—

146

C₂×C₄

#10597390

yes

characteristic

147

C₈

—

148

C₈

—

149

C₈

—

152

—

150

C₂²

#11926413

yes

characteristic

151

C₂²

#11926570

yes

characteristic

152

C₂²

#11926572

yes

characteristic

153

C₂²

C₂×#10597264

yes

—

154

C₂²

#11926592

yes

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

#11926569

yes

—

159

C₄

#11926920

yes

characteristic

160

C₄

#11926923

yes

characteristic

161

C₄

#11926947

yes

—

162

C₂

#14562409

yes

—

163

C₂

#14562411

yes

—

164

C₂

#14563788

yes

characteristic

165

C₂

#14563794

yes

characteristic

166

C₂

#14563809

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#8810
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1842

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
111. C₁₉	#8810	semidirect

H ≅ G/N

type

111. C₁₉

#8810

semidirect

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

subgroup	index
#14563787	2
#14563381	2
C₂×#11926296	2
C₁₉×#1842	2
#8810	19

subgroup

index

C₁₉×#1842

Subgroups — #18076294

Conjugacy classes of subgroups

Complements

Maximal subgroups