Group #18069437 — subgroups

Subgroups — #18069437

Order 4864.

222 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₂×#11926320	C₂	1	1	yes	maximal, characteristic
3	C₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₁₉⋊C₁₆)	C₄	1	2	yes	—
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	#11926320	—	2	1	no	—
8	#11926320	—	2	1	no	—
9	#11926320	C₄	1	2	yes	—
10	C₁₉×#431	C₄	1	1	yes	characteristic
11	C₄×M₁₆×C₁₉	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#322	—	2	1	no	—
14	C₈²×C₁₉	—	2	1	no	—
15	C₂×M₁₆×C₁₉	—	2	1	no	—
16	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₁₉×C₄⋊C₈	—	2	1	no	—
20	C₁₉×C₂²⋊C₈	C₈	1	2	yes	—
21	C₁₉×#97	C₈	1	2	yes	—
22	C₄×C₈×C₁₉	—	2	1	no	—
23	C₄×C₈×C₁₉	—	2	1	no	—
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₁₉⋊C₁₆	—	2	4	no	—
29	C₂×C₁₉⋊C₁₆	—	2	2	no	—
30	C₂×C₁₉⋊C₁₆	—	2	2	no	—
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
34	M₁₆×C₁₉	—	2	4	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	—	2	2	no	—
39	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₄²×C₁₉	C₄²	1	1	yes	characteristic
44	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
46	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
47	C₁₉⋊C₁₆	—	2	4	no	—
48	C₁₉⋊C₁₆	—	4	2	no	—
49	#7165	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	C₄⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
61	C₈×C₁₉	—	2	4	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	2	1	no	—
64	C₈×C₁₉	—	4	2	no	—
65	C₈×C₁₉	#104	1	2	yes	—
66	C₈×C₁₉	#108	1	2	yes	—
67	#2163	—	19	1	no	—
68	C₂×#346	—	19	1	no	—
69	C₈×M₁₆	D₁₉	1	1	yes	characteristic
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	#336	1	1	yes	characteristic
73	C₂²×C₁₉	#364	1	2	yes	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	2	1	no	—
79	C₄×C₁₉	#339	1	1	yes	characteristic
80	C₄×C₁₉	#341	1	1	yes	characteristic
81	C₂²×C₁₆	—	38	1	no	—
82	#431	Dic₁₉	1	1	yes	characteristic
83	C₄×M₁₆	Dic₁₉	1	1	yes	characteristic
84	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₄⋊C₁₆	—	19	2	no	—
86	C₂²⋊C₁₆	—	38	1	no	—
87	#346	—	19	2	no	—
88	#346	—	38	1	no	—
89	#346	—	38	1	no	—
90	#322	—	2	1	no	—
91	C₈²	—	2	1	no	—
92	C₂×C₁₉	—	2	2	no	—
93	C₂×C₁₉	#1278	1	1	yes	characteristic
94	C₂×C₁₉	#1376	1	1	yes	characteristic
95	C₂×C₁₉	#1378	1	1	yes	characteristic
96	C₂×M₁₆	—	2	1	no	—
97	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
98	C₂²×C₈	D₇₆	1	1	yes	characteristic
99	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
100	C₂×C₁₆	—	38	4	no	—
101	C₂×C₁₆	—	38	2	no	—
102	C₂×C₁₆	—	38	2	no	—
103	C₄⋊C₈	—	2	1	no	—
104	C₂²⋊C₈	C₁₉⋊C₈	1	2	yes	—
105	#97	C₁₉⋊C₈	1	2	yes	—
106	C₄×C₈	—	2	1	no	—
107	C₄×C₈	—	2	1	no	—
108	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
109	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
110	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
111	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₁₉	#7165	1	1	yes	characteristic, complemented, Sylow
113	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
114	C₂²×C₄	#64520	1	1	yes	characteristic
115	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
116	M₁₆	—	2	4	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
122	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
123	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
124	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
125	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
126	C₄²	#64520	1	1	yes	characteristic
127	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
128	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
129	C₁₆	—	38	4	no	—
130	C₁₆	—	76	2	no	—
131	C₂³	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
137	C₂×C₄	#10597260	1	1	yes	characteristic
138	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
139	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
140	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
141	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
142	C₈	—	2	4	no	—
143	C₈	—	2	1	no	—
144	C₈	—	2	1	no	—
145	C₈	—	4	2	no	—
146	C₈	#10597279	1	2	yes	—
147	C₈	#10597282	1	2	yes	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	#11926299	1	1	yes	characteristic
151	C₂²	#11926365	1	2	yes	—
152	C₄	—	2	1	no	—
153	C₄	—	2	1	no	—
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	#11926305	1	1	yes	characteristic
158	C₄	#11926308	1	1	yes	characteristic
159	C₂	—	2	2	no	—
160	C₂	#14561473	1	1	yes	characteristic
161	C₂	#14561717	1	1	yes	characteristic
162	C₂	#14561721	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565438

C₂

yes

maximal, characteristic

C₂×#11926320

C₂

yes

maximal, characteristic

C₈×M₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₁₆)

C₄

yes

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926320

—

#11926320

—

#11926320

C₄

yes

—

C₁₉×#431

C₄

yes

characteristic

C₄×M₁₆×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₈²×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₈

yes

—

C₁₉×#97

C₈

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

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

C₄²

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

#7165

—

maximal, Sylow

C₂³×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#104

yes

—

C₈×C₁₉

#108

yes

—

#2163

—

C₂×#346

—

C₈×M₁₆

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#336

yes

characteristic

C₂²×C₁₉

#364

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×C₁₆

—

#431

Dic₁₉

yes

characteristic

C₄×M₁₆

Dic₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

—

—

—

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

D₇₆

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₄⋊C₈

—

104

C₂²⋊C₈

C₁₉⋊C₈

yes

—

105

#97

C₁₉⋊C₈

yes

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

C₄×D₁₉

yes

characteristic

109

C₄×C₈

C₄×D₁₉

yes

characteristic

110

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

111

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

112

C₁₉

#7165

yes

characteristic, complemented, Sylow

113

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

114

C₂²×C₄

#64520

yes

characteristic

115

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

116

M₁₆

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

122

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

123

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

124

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

125

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

126

C₄²

#64520

yes

characteristic

127

C₄²

C₄×Dic₁₉

yes

characteristic

128

C₄²

C₂²⋊Dic₁₉

yes

characteristic

129

C₁₆

—

130

C₁₆

—

131

C₂³

C₄⋊(C₁₉⋊C₈)

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₄×C₁₉⋊C₈

yes

characteristic

137

C₂×C₄

#10597260

yes

characteristic

138

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

139

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

140

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

141

C₂×C₄

C₁₉⋊#95

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

#10597279

yes

—

147

C₈

#10597282

yes

—

148

C₂²

—

149

C₂²

—

150

C₂²

#11926299

yes

characteristic

151

C₂²

#11926365

yes

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

#11926305

yes

characteristic

158

C₄

#11926308

yes

characteristic

159

C₂

—

160

C₂

#14561473

yes

characteristic

161

C₂

#14561717

yes

characteristic

162

C₂

#14561721

yes

characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₈×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₄⋊C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₈×M₁₆	D₁₉
hypocenter	C₁₉	#7165
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

subgroup

G/H

center

C₂×C₈

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₈×M₁₆×C₁₉

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂³×C₁₉

C₄⋊C₈

cosocle

C₂×C₄×C₈×C₁₉

C₂²

hypercenter

C₈×M₁₆

D₁₉

hypocenter

C₁₉

#7165

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

N	H ≅ G/N	type
112. C₁₉	#7165	semidirect

H ≅ G/N

type

112. C₁₉

#7165

semidirect

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

subgroup	index
#14565438	2
C₂×#11926320	2
C₈×M₁₆×C₁₉	2
#7165	19

subgroup

index

#14565438

C₂×#11926320

C₈×M₁₆×C₁₉

#7165

Subgroups — #18069437

Conjugacy classes of subgroups

Complements

Maximal subgroups