Group #18069170 — subgroups

Subgroups — #18069170

Order 4864.

240 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14561575	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1955	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
6	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
7	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	C₈	1	1	yes	characteristic
9	C₂³×C₄×C₁₉	—	2	1	no	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	2	yes	—
12	C₄×D₄×C₁₉	—	4	1	no	—
13	C₄×D₄×C₁₉	—	4	1	no	—
14	C₂×C₄⋊C₄×C₁₉	C₈	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₁₉×C₂²⋊C₈	—	4	4	no	—
19	C₁₉×#97	—	4	1	no	—
20	C₂×C₁₉⋊C₁₆	—	4	2	no	—
21	C₂⁴×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	4	1	no	—
23	C₂×D₄×C₁₉	—	4	2	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	—	4	2	no	—
26	C₂²×C₄×C₁₉	—	4	2	no	—
27	C₂²×C₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	—	4	1	no	—
35	C₂×C₈×C₁₉	—	4	1	no	—
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₄⋊C₄×C₁₉	—	4	1	no	—
38	C₂²⋊C₄×C₁₉	—	4	2	no	—
39	C₄²×C₁₉	—	2	1	no	—
40	C₄²×C₁₉	—	2	1	no	—
41	C₁₉⋊C₁₆	—	8	2	no	—
42	#7060	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	—	2	2	no	—
44	C₂³×C₁₉	—	4	2	no	—
45	C₂³×C₁₉	—	4	1	no	—
46	C₂³×C₁₉	—	4	1	no	—
47	C₂³×C₁₉	—	4	2	no	—
48	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
49	D₄×C₁₉	—	4	2	no	—
50	D₄×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	8	2	no	—
60	C₂×C₄×C₁₉	—	8	1	no	—
61	C₂×C₄×C₁₉	—	8	1	no	—
62	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
63	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
64	C₈×C₁₉	—	4	2	no	—
65	C₈×C₁₉	—	4	2	no	—
66	#1955	D₁₉	1	1	yes	characteristic
67	#1322	—	19	2	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	4	4	no	—
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	—	8	2	no	—
73	C₂²×C₁₉	—	8	1	no	—
74	C₂²×C₁₉	—	8	1	no	—
75	C₂²×C₁₉	#323	1	1	yes	characteristic
76	C₂²×C₁₉	#350	1	2	yes	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	4	1	no	—
79	C₄×C₁₉	—	4	1	no	—
80	C₄×C₁₉	—	8	1	no	—
81	C₄×C₁₉	#353	1	1	yes	characteristic
82	C₄×C₁₉	#355	1	1	yes	characteristic
83	C₂×C₄×D₄	Dic₁₉	1	1	yes	characteristic
84	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₂×C₂²⋊C₈	—	2	2	no	—
86	C₂×#97	Dic₁₉	1	1	yes	characteristic
87	C₂²⋊C₁₆	—	38	2	no	—
88	C₂×C₁₉	—	2	2	no	—
89	C₂×C₁₉	—	8	2	no	—
90	C₂×C₁₉	#1315	1	1	yes	characteristic
91	C₂×C₁₉	#1318	1	1	yes	characteristic
92	C₂×C₁₉	#1320	1	1	yes	characteristic
93	C₂²×D₄	C₁₉⋊C₈	1	1	yes	characteristic
94	C₂³×C₄	—	2	1	no	—
95	C₂²×C₈	—	2	1	no	—
96	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
97	C₄×D₄	—	4	1	no	—
98	C₄×D₄	—	4	1	no	—
99	C₂×C₄⋊C₄	C₁₉⋊C₈	1	1	yes	characteristic
100	C₂×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
102	C₂×C₁₆	—	76	2	no	—
103	C₄⋊C₈	—	4	1	no	—
104	C₂²⋊C₈	—	4	4	no	—
105	#97	—	4	1	no	—
106	C₁₉	#7060	1	1	yes	characteristic, complemented, Sylow
107	C₂⁴	—	2	1	no	—
108	C₂×D₄	—	4	1	no	—
109	C₂×D₄	—	4	2	no	—
110	C₂²×C₄	—	2	1	no	—
111	C₂²×C₄	—	4	2	no	—
112	C₂²×C₄	—	4	2	no	—
113	C₂²×C₄	—	4	1	no	—
114	C₂²×C₄	—	4	1	no	—
115	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
116	C₂²×C₄	#64520	1	1	yes	characteristic
117	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	4	1	no	—
121	C₂×C₈	—	4	1	no	—
122	C₂×C₈	—	4	2	no	—
123	C₄⋊C₄	—	4	1	no	—
124	C₂²⋊C₄	—	4	2	no	—
125	C₄²	—	2	1	no	—
126	C₄²	—	2	1	no	—
127	C₁₆	—	152	2	no	—
128	C₂³	—	2	2	no	—
129	C₂³	—	4	2	no	—
130	C₂³	—	4	1	no	—
131	C₂³	—	4	2	no	—
132	C₂³	—	4	1	no	—
133	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
134	D₄	—	4	2	no	—
135	D₄	—	4	2	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	4	1	no	—
144	C₂×C₄	—	8	2	no	—
145	C₂×C₄	—	8	1	no	—
146	C₂×C₄	—	8	1	no	—
147	C₂×C₄	#10597290	1	1	yes	characteristic
148	C₂×C₄	#10597291	1	1	yes	characteristic
149	C₈	—	4	2	no	—
150	C₈	—	4	2	no	—
151	C₂²	—	2	1	no	—
152	C₂²	—	2	1	no	—
153	C₂²	—	4	4	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	8	2	no	—
156	C₂²	—	8	1	no	—
157	C₂²	—	8	1	no	—
158	C₂²	#11926268	1	1	yes	characteristic
159	C₂²	#11926328	1	2	yes	—
160	C₄	—	2	1	no	—
161	C₄	—	4	1	no	—
162	C₄	—	4	1	no	—
163	C₄	—	8	1	no	—
164	C₄	#11926337	1	1	yes	characteristic
165	C₄	#11926341	1	1	yes	characteristic
166	C₂	—	2	2	no	—
167	C₂	—	8	2	no	—
168	C₂	#14561561	1	1	yes	characteristic
169	C₂	#14561567	1	1	yes	characteristic
170	C₂	#14561571	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561575

C₂

yes

maximal, complemented

C₁₉×#1955

C₂

yes

maximal, characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

C₂×C₄×D₄×C₁₉

C₄

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₄

yes

characteristic

C₂²×D₄×C₁₉

C₈

yes

characteristic

C₂³×C₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₉⋊C₁₆

—

#7060

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

C₈×C₁₉

—

C₈×C₁₉

—

#1955

D₁₉

yes

characteristic

#1322

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₂²×C₁₉

#350

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₄×D₄

Dic₁₉

yes

characteristic

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

C₂×#97

Dic₁₉

yes

characteristic

C₂²⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×D₄

C₁₉⋊C₈

yes

characteristic

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

C₁₉⋊C₈

yes

characteristic

100

C₂×C₂²⋊C₄

—

101

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

102

C₂×C₁₆

—

103

C₄⋊C₈

—

104

C₂²⋊C₈

—

105

#97

—

106

C₁₉

#7060

yes

characteristic, complemented, Sylow

107

C₂⁴

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

116

C₂²×C₄

#64520

yes

characteristic

117

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₄⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₄²

—

127

C₁₆

—

152

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

134

D₄

—

135

D₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

#10597290

yes

characteristic

148

C₂×C₄

#10597291

yes

characteristic

149

C₈

—

150

C₈

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

#11926268

yes

characteristic

159

C₂²

#11926328

yes

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

#11926337

yes

characteristic

165

C₄

#11926341

yes

characteristic

166

C₂

—

167

C₂

—

168

C₂

#14561561

yes

characteristic

169

C₂

#14561567

yes

characteristic

170

C₂

#14561571

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597291
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1955	C₂
socle	C₂²×C₁₉	#323
prime radical	C₂²×D₄×C₁₉	C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1955	D₁₉
hypocenter	C₁₉	#7060
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1955

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1955

C₂

socle

C₂²×C₁₉

#323

prime radical

C₂²×D₄×C₁₉

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 ◁ #1955

N	H ≅ G/N	type
1. #14561575	C₂	semidirect
106. C₁₉	#7060	semidirect

H ≅ G/N

type

1. #14561575

C₂

semidirect

106. C₁₉

#7060

semidirect

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

subgroup	index
#14561575	2
C₁₉×#1955	2
#7060	19

subgroup

index

#14561575

C₁₉×#1955

#7060

Subgroups — #18069170

Conjugacy classes of subgroups

Complements

Maximal subgroups