Group #18069182 — subgroups

Subgroups — #18069182

Order 4864.

176 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14563788	C₂	1	1	yes	maximal, characteristic
2	#14561575	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
5	C₂×Dic₁₉⋊C₈	—	2	1	no	—
6	C₂×Dic₁₉⋊C₈	—	2	1	no	—
7	#11926390	C₄	1	1	yes	characteristic
8	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	—	2	1	no	—
15	C₂²×C₁₉⋊C₈	—	2	1	no	—
16	C₂×C₁₆×C₁₉	—	4	1	no	—
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₁₉⋊#95	—	2	1	no	—
19	C₁₉⋊#95	C₈	1	1	yes	characteristic
20	C₁₉⋊#95	C₈	1	1	yes	characteristic
21	Dic₁₉⋊C₈	—	4	2	no	—
22	Dic₁₉⋊C₈	—	4	2	no	—
23	C₂×C₁₉⋊C₁₆	—	4	1	no	—
24	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
25	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	2	1	no	—
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	—	2	1	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₄²×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₄×Dic₁₉	—	2	2	no	—
37	C₄×Dic₁₉	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	4	1	no	—
39	C₂×C₁₉⋊C₈	—	4	1	no	—
40	C₂×C₁₉⋊C₈	—	4	1	no	—
41	C₁₆×C₁₉	—	8	1	no	—
42	C₁₉⋊C₁₆	—	8	1	no	—
43	#7066	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
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	#99	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	—	2	2	no	—
56	C₂×Dic₁₉	—	4	1	no	—
57	C₂×Dic₁₉	—	4	1	no	—
58	C₂×Dic₁₉	—	4	1	no	—
59	C₂×Dic₁₉	—	4	1	no	—
60	C₈×C₁₉	—	4	1	no	—
61	C₈×C₁₉	—	4	1	no	—
62	C₁₉⋊C₈	—	8	1	no	—
63	#1843	—	19	1	no	—
64	#1322	—	19	1	no	—
65	#1322	D₁₉	1	1	yes	characteristic
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	#324	1	1	yes	characteristic
69	C₂²×C₁₉	#350	1	1	yes	characteristic
70	C₂²×C₁₉	#350	1	1	yes	characteristic
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	4	1	no	—
73	C₄×C₁₉	—	4	1	no	—
74	C₄×C₁₉	#353	1	1	yes	characteristic
75	C₄×C₁₉	#356	1	1	yes	characteristic
76	Dic₁₉	—	4	2	no	—
77	Dic₁₉	—	4	2	no	—
78	C₂×C₄⋊C₈	—	19	1	no	—
79	C₂×C₄⋊C₈	—	38	1	no	—
80	C₂×C₄⋊C₈	—	38	1	no	—
81	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
82	#376	—	19	1	no	—
83	C₂²⋊C₁₆	—	2	1	no	—
84	C₂²⋊C₁₆	—	38	1	no	—
85	C₂×C₁₉	—	2	1	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	#1323	1	1	yes	characteristic
88	C₂×C₁₉	#1325	1	1	yes	characteristic
89	C₂×C₁₉	#1328	1	1	yes	characteristic
90	C₂²×C₈	—	38	1	no	—
91	C₂²×C₈	D₇₆	1	1	yes	characteristic
92	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
93	C₂×C₄²	—	38	1	no	—
94	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
95	C₂×C₁₆	—	4	1	no	—
96	C₂×C₁₆	—	76	1	no	—
97	C₄⋊C₈	—	4	1	no	—
98	C₄⋊C₈	—	76	1	no	—
99	C₄⋊C₈	—	76	2	no	—
100	C₄⋊C₈	—	76	2	no	—
101	#95	—	19	1	no	—
102	#95	—	19	1	no	—
103	#95	—	38	1	no	—
104	C₁₉	#7066	1	1	yes	characteristic, complemented, Sylow
105	C₂²×C₄	—	38	1	no	—
106	C₂²×C₄	—	38	1	no	—
107	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
108	C₂²×C₄	#64515	1	1	yes	characteristic
109	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	4	1	no	—
113	C₂×C₈	—	4	1	no	—
114	C₂×C₈	—	76	1	no	—
115	C₂×C₈	—	76	1	no	—
116	C₂×C₈	—	76	1	no	—
117	C₄²	—	2	1	no	—
118	C₄²	—	2	1	no	—
119	C₄²	—	38	2	no	—
120	C₄²	—	38	2	no	—
121	C₁₆	—	8	1	no	—
122	C₁₆	—	152	1	no	—
123	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	38	2	no	—
132	C₂×C₄	—	38	2	no	—
133	C₂×C₄	—	76	1	no	—
134	C₂×C₄	—	76	1	no	—
135	C₂×C₄	—	76	1	no	—
136	C₂×C₄	—	76	1	no	—
137	C₂×C₄	#10597263	1	1	yes	characteristic
138	C₂×C₄	#10597281	1	1	yes	characteristic
139	C₈	—	4	1	no	—
140	C₈	—	4	1	no	—
141	C₈	—	152	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	—	2	1	no	—
144	C₂²	#11926269	1	1	yes	characteristic
145	C₂²	#11926327	1	1	yes	characteristic
146	C₂²	#11926329	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	4	1	no	—
149	C₄	—	4	1	no	—
150	C₄	—	76	2	no	—
151	C₄	—	76	2	no	—
152	C₄	#11926336	1	1	yes	characteristic
153	C₄	#11926342	1	1	yes	characteristic
154	C₂	—	2	1	no	—
155	C₂	—	2	1	no	—
156	C₂	#14561576	1	1	yes	characteristic
157	C₂	#14561580	1	1	yes	characteristic
158	C₂	#14561587	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563788

C₂

yes

maximal, characteristic

#14561575

C₂

yes

maximal, characteristic

C₁₉×#1322

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

characteristic

C₂×Dic₁₉⋊C₈

—

C₂×Dic₁₉⋊C₈

—

#11926390

C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

C₈

yes

characteristic

C₁₉⋊#95

C₈

yes

characteristic

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7066

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1843

—

#1322

—

#1322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

#376

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

D₇₆

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

#95

—

102

#95

—

103

#95

—

104

C₁₉

#7066

yes

characteristic, complemented, Sylow

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₈×D₁₉

yes

characteristic

108

C₂²×C₄

#64515

yes

characteristic

109

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₁₆

—

122

C₁₆

—

152

—

123

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#10597263

yes

characteristic

138

C₂×C₄

#10597281

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

152

—

142

C₂²

—

143

C₂²

—

144

C₂²

#11926269

yes

characteristic

145

C₂²

#11926327

yes

characteristic

146

C₂²

#11926329

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

#11926336

yes

characteristic

153

C₄

#11926342

yes

characteristic

154

C₂

—

155

C₂

—

156

C₂

#14561576

yes

characteristic

157

C₂

#14561580

yes

characteristic

158

C₂

#14561587

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1322	C₂
socle	C₂²×C₁₉	#324
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1322	D₁₉
hypocenter	C₁₉	#7066
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1322

C₂

socle

C₂²×C₁₉

#324

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

N	H ≅ G/N	type
104. C₁₉	#7066	semidirect

H ≅ G/N

type

104. C₁₉

#7066

semidirect

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

subgroup	index
#14563788	2
#14561575	2
C₁₉×#1322	2
#7066	19

subgroup

index

#14563788

#14561575

C₁₉×#1322

#7066

Subgroups — #18069182

Conjugacy classes of subgroups

Complements

Maximal subgroups