Group #18069432 — subgroups

Subgroups — #18069432

Order 4864.

212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₄×#10597269	C₂	1	1	yes	maximal, characteristic
2	#14561924	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2163	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	#11926597	C₄	1	1	yes	characteristic
6	C₄×#64520	C₄	1	1	yes	characteristic
7	#11926320	—	2	1	no	—
8	C₄×C₁₉⋊C₁₆	C₄	1	2	yes	—
9	#11926266	—	2	1	no	—
10	#11926265	—	2	1	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₁₆	C₄	1	2	yes	—
13	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
14	C₁₉×#346	—	2	1	no	—
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×#64520	—	2	1	no	—
19	C₂×C₁₆×C₁₉	—	2	2	no	—
20	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂²⋊(C₁₉⋊C₈)	C₈	1	2	yes	—
25	#10597269	—	2	4	no	—
26	C₂×C₁₉⋊C₁₆	—	2	2	no	—
27	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
28	#10597260	C₈	1	2	yes	—
29	C₄×C₁₉⋊C₈	—	2	1	no	—
30	C₄×C₁₉⋊C₈	—	2	1	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	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₄²	1	1	yes	characteristic
41	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
43	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
44	#64520	—	4	2	no	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	—	2	2	no	—
47	C₁₆×C₁₉	—	4	2	no	—
48	C₁₉⋊C₁₆	—	2	4	no	—
49	#7164	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	C₄⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	2	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	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	#104	1	2	yes	—
64	C₈×C₁₉	#108	1	2	yes	—
65	C₁₉⋊C₈	—	4	2	no	—
66	C₁₉⋊C₈	—	4	2	no	—
67	#2163	D₁₉	1	1	yes	characteristic
68	C₄×M₃₂	—	19	1	no	—
69	#1451	—	19	1	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	2	1	no	—
73	C₂²×C₁₉	#336	1	1	yes	characteristic
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	#339	1	1	yes	characteristic
79	C₄×C₁₉	#341	1	1	yes	characteristic
80	C₄×C₁₉	#347	1	2	yes	—
81	C₂×M₃₂	—	38	1	no	—
82	#431	—	19	1	no	—
83	C₄×M₁₆	—	19	1	no	—
84	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₄⋊C₁₆	Dic₁₉	1	2	yes	—
86	C₂²⋊C₁₆	—	2	1	no	—
87	#346	—	2	1	no	—
88	#346	—	38	1	no	—
89	C₄×C₁₆	—	19	2	no	—
90	#322	—	38	1	no	—
91	#322	—	38	1	no	—
92	C₂×C₁₉	—	4	1	no	—
93	C₂×C₁₉	#1278	1	1	yes	characteristic
94	C₂×C₁₉	#1375	1	1	yes	characteristic
95	C₂×C₁₉	#1378	1	1	yes	characteristic
96	C₂×M₁₆	—	38	1	no	—
97	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
98	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
99	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
100	M₃₂	—	38	4	no	—
101	C₂×C₁₆	—	2	2	no	—
102	C₂×C₁₆	—	38	2	no	—
103	C₄⋊C₈	—	38	1	no	—
104	C₂²⋊C₈	—	19	2	no	—
105	#97	—	19	2	no	—
106	C₄×C₈	—	38	1	no	—
107	C₄×C₈	—	38	1	no	—
108	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
109	C₄×C₈	D₇₆	1	1	yes	characteristic
110	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
111	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₁₉	#7164	1	1	yes	characteristic, complemented, Sylow
113	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
114	C₂²×C₄	#64515	1	1	yes	characteristic
115	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
116	M₁₆	—	76	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	38	2	no	—
120	C₂×C₈	—	38	2	no	—
121	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
122	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
123	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
124	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
125	C₄²	C₈×D₁₉	1	1	yes	characteristic
126	C₄²	#64515	1	1	yes	characteristic
127	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
128	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
129	C₁₆	—	4	2	no	—
130	C₁₆	—	38	4	no	—
131	C₂³	Dic₁₉⋊C₈	1	1	yes	characteristic
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
137	C₂×C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
138	C₂×C₄	#10597272	1	1	yes	characteristic
139	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
140	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
141	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	—	2	1	no	—
144	C₈	—	76	2	no	—
145	C₈	—	76	2	no	—
146	C₈	#10597279	1	2	yes	—
147	C₈	#10597294	1	2	yes	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	—	2	1	no	—
151	C₂²	#11926298	1	1	yes	characteristic
152	C₄	—	2	1	no	—
153	C₄	—	2	1	no	—
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	#11926303	1	1	yes	characteristic
157	C₄	#11926308	1	1	yes	characteristic
158	C₄	#11926321	1	2	yes	—
159	C₂	—	4	1	no	—
160	C₂	#14561471	1	1	yes	characteristic
161	C₂	#14561714	1	1	yes	characteristic
162	C₂	#14561722	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597269

C₂

yes

maximal, characteristic

#14561924

C₂

yes

maximal, characteristic

C₁₉×#2163

C₂

yes

maximal, characteristic

C₂×#10597269

—

#11926597

C₄

yes

characteristic

C₄×#64520

C₄

yes

characteristic

#11926320

—

C₄×C₁₉⋊C₁₆

C₄

yes

—

#11926266

—

#11926265

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

C₄

yes

—

C₁₉×C₂²⋊C₁₆

—

C₁₉×#346

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×#64520

—

C₂×C₁₆×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

C₂²⋊(C₁₉⋊C₈)

C₈

yes

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

C₈

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₄⋊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

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

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7164

—

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

#104

yes

—

C₈×C₁₉

#108

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2163

D₁₉

yes

characteristic

C₄×M₃₂

—

#1451

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#336

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×M₃₂

—

#431

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₁₆

Dic₁₉

yes

—

C₂²⋊C₁₆

—

#346

—

#346

—

C₄×C₁₆

—

#322

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄²

C₄×D₁₉

yes

characteristic

100

M₃₂

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₄⋊C₈

—

104

C₂²⋊C₈

—

105

#97

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

C₄×D₁₉

yes

characteristic

109

C₄×C₈

D₇₆

yes

characteristic

110

C₄×C₈

C₂×Dic₁₉

yes

characteristic

111

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

112

C₁₉

#7164

yes

characteristic, complemented, Sylow

113

C₂²×C₄

C₈×D₁₉

yes

characteristic

114

C₂²×C₄

#64515

yes

characteristic

115

C₂²×C₄

Dic₁₉⋊C₄

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

C₄⋊Dic₁₉

yes

characteristic

123

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

124

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

125

C₄²

C₈×D₁₉

yes

characteristic

126

C₄²

#64515

yes

characteristic

127

C₄²

C₄×Dic₁₉

yes

characteristic

128

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

129

C₁₆

—

130

C₁₆

—

131

C₂³

Dic₁₉⋊C₈

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₈×Dic₁₉

yes

characteristic

137

C₂×C₄

Dic₁₉⋊C₈

yes

characteristic

138

C₂×C₄

#10597272

yes

characteristic

139

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

140

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

141

C₂×C₄

C₁₉⋊#95

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

#10597279

yes

—

147

C₈

#10597294

yes

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

#11926298

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

#11926303

yes

characteristic

157

C₄

#11926308

yes

characteristic

158

C₄

#11926321

yes

—

159

C₂

—

160

C₂

#14561471

yes

characteristic

161

C₂

#14561714

yes

characteristic

162

C₂

#14561722

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#2163	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₄⋊C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#2163	D₁₉
hypocenter	C₁₉	#7164
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₁₉⋊#95

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#2163

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂³×C₁₉

C₄⋊C₈

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

N	H ≅ G/N	type
112. C₁₉	#7164	semidirect

H ≅ G/N

type

112. C₁₉

#7164

semidirect

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

subgroup	index
C₄×#10597269	2
#14561924	2
C₁₉×#2163	2
#7164	19

subgroup

index

C₄×#10597269

#14561924

C₁₉×#2163

#7164

Subgroups — #18069432

Conjugacy classes of subgroups

Complements

Maximal subgroups