Group #18069517 — subgroups

Subgroups — #18069517

Order 4864.

184 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14565438	C₂	1	1	yes	maximal, characteristic
2	#14561927	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2163	C₂	1	1	yes	maximal, characteristic
4	#11926597	C₄	1	1	yes	characteristic
5	#11926597	C₄	1	1	yes	characteristic
6	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	C₂²⋊(C₁₉⋊C₁₆)	C₄	1	2	yes	—
8	#11926320	—	2	1	no	—
9	#11926266	—	2	1	no	—
10	#11926266	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₁₆	—	2	1	no	—
13	C₁₉×C₂²⋊C₁₆	C₄	1	2	yes	—
14	C₁₉×#346	—	2	1	no	—
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₉	—	2	2	no	—
19	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
23	C₂²⋊(C₁₉⋊C₈)	C₈	1	2	yes	—
24	C₂²⋊(C₁₉⋊C₈)	C₈	1	2	yes	—
25	C₂×C₁₉⋊C₁₆	—	2	2	no	—
26	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
27	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
28	C₄×C₁₉⋊C₈	—	2	1	no	—
29	C₄×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	4	1	no	—
35	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
42	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₁₆×C₁₉	—	4	2	no	—
46	C₁₉⋊C₁₆	—	4	2	no	—
47	#7197	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	C₄×C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
59	C₈×C₁₉	—	2	1	no	—
60	C₈×C₁₉	—	2	1	no	—
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₁₉⋊C₈	—	4	2	no	—
64	C₁₉⋊C₈	—	4	2	no	—
65	#2163	—	19	1	no	—
66	#2163	D₁₉	1	1	yes	characteristic
67	#1452	—	19	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	#336	1	1	yes	characteristic
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	#344	1	1	yes	characteristic
78	C₄×C₁₉	#344	1	1	yes	characteristic
79	#431	—	19	1	no	—
80	#431	—	19	1	no	—
81	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
82	C₄⋊C₁₆	—	2	1	no	—
83	C₄⋊C₁₆	—	38	1	no	—
84	C₂²⋊C₁₆	—	19	2	no	—
85	C₂²⋊C₁₆	Dic₁₉	1	2	yes	—
86	#346	—	2	1	no	—
87	#346	—	38	1	no	—
88	#322	—	38	1	no	—
89	#322	—	38	1	no	—
90	C₂×C₁₉	—	4	1	no	—
91	C₂×C₁₉	#1281	1	1	yes	characteristic
92	C₂×C₁₉	#1378	1	1	yes	characteristic
93	C₂×C₁₉	#1378	1	1	yes	characteristic
94	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
95	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
96	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
97	C₂×C₁₆	—	2	2	no	—
98	C₂×C₁₆	—	38	2	no	—
99	C₄⋊C₈	—	38	1	no	—
100	C₄⋊C₈	—	38	1	no	—
101	C₂²⋊C₈	—	19	2	no	—
102	C₂²⋊C₈	—	19	2	no	—
103	C₄×C₈	—	38	1	no	—
104	C₄×C₈	—	38	1	no	—
105	C₄×C₈	Dic₃₈	1	1	yes	characteristic
106	C₄×C₈	D₇₆	1	1	yes	characteristic
107	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
108	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
109	C₁₉	#7197	1	1	yes	characteristic, complemented, Sylow
110	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
111	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
112	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
113	C₂×C₈	—	4	1	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	38	2	no	—
116	C₂×C₈	—	38	2	no	—
117	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
118	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
119	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
120	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
121	C₄²	#64515	1	1	yes	characteristic
122	C₄²	#64515	1	1	yes	characteristic
123	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
124	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
125	C₁₆	—	4	2	no	—
126	C₁₆	—	76	2	no	—
127	C₂³	C₈×Dic₁₉	1	1	yes	characteristic
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
133	C₂×C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
134	C₂×C₄	#10597272	1	1	yes	characteristic
135	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
136	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
137	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
138	C₈	—	2	1	no	—
139	C₈	—	2	1	no	—
140	C₈	—	2	1	no	—
141	C₈	—	2	1	no	—
142	C₈	—	76	2	no	—
143	C₈	—	76	2	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	#11926298	1	1	yes	characteristic
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	—	2	1	no	—
152	C₄	—	2	1	no	—
153	C₄	#11926314	1	1	yes	characteristic
154	C₄	#11926316	1	1	yes	characteristic
155	C₂	—	4	1	no	—
156	C₂	#14561479	1	1	yes	characteristic
157	C₂	#14561720	1	1	yes	characteristic
158	C₂	#14561722	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565438

C₂

yes

maximal, characteristic

#14561927

C₂

yes

maximal, characteristic

C₁₉×#2163

C₂

yes

maximal, characteristic

#11926597

C₄

yes

characteristic

#11926597

C₄

yes

characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

C₄

yes

—

#11926320

—

#11926266

—

#11926266

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

C₄

yes

—

C₁₉×#346

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

C₈

yes

—

C₂²⋊(C₁₉⋊C₈)

C₈

yes

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7197

—

maximal, Sylow

C₂³×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2163

—

#2163

D₁₉

yes

characteristic

#1452

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#336

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

Dic₁₉

yes

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

C₄×D₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₂²⋊C₈

—

102

C₂²⋊C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

Dic₃₈

yes

characteristic

106

C₄×C₈

D₇₆

yes

characteristic

107

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

108

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

109

C₁₉

#7197

yes

characteristic, complemented, Sylow

110

C₂²×C₄

C₈×D₁₉

yes

characteristic

111

C₂²×C₄

C₈×D₁₉

yes

characteristic

112

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

118

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

119

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

120

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

121

C₄²

#64515

yes

characteristic

122

C₄²

#64515

yes

characteristic

123

C₄²

Dic₁₉⋊C₄

yes

characteristic

124

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

125

C₁₆

—

126

C₁₆

—

127

C₂³

C₈×Dic₁₉

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

Dic₁₉⋊C₈

yes

characteristic

133

C₂×C₄

Dic₁₉⋊C₈

yes

characteristic

134

C₂×C₄

#10597272

yes

characteristic

135

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

136

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

137

C₂×C₄

C₁₉⋊#95

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11926298

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

#11926314

yes

characteristic

154

C₄

#11926316

yes

characteristic

155

C₂

—

156

C₂

#14561479

yes

characteristic

157

C₂

#14561720

yes

characteristic

158

C₂

#14561722

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₁₉⋊#95
commutator, prime radical	C₂³×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#2163	C₂
socle	C₂²×C₁₉	#336
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#2163	D₁₉
hypocenter	C₁₉	#7197
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₁₉⋊#95

commutator, prime radical

C₂³×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#2163

C₂

socle

C₂²×C₁₉

#336

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

N	H ≅ G/N	type
109. C₁₉	#7197	semidirect

H ≅ G/N

type

109. C₁₉

#7197

semidirect

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

subgroup	index
#14565438	2
#14561927	2
C₁₉×#2163	2
#7197	19

subgroup

index

#14565438

#14561927

C₁₉×#2163

#7197

Subgroups — #18069517

Conjugacy classes of subgroups

Complements

Maximal subgroups