Group #18069582 — subgroups

Subgroups — #18069582

Order 4864.

196 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14563773	C₂	1	1	yes	maximal, characteristic
2	#14562391	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2162	C₂	1	1	yes	maximal, characteristic
4	#11926568	—	2	1	no	—
5	#11926568	—	2	1	no	—
6	#11926309	—	2	1	no	—
7	#11926309	C₄	1	2	yes	—
8	#11926295	—	2	1	no	—
9	#11926295	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×C₄⋊C₁₆	—	2	1	no	—
12	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
13	C₄×C₁₆×C₁₉	C₄	1	2	yes	—
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
17	C₂×#64520	—	2	2	no	—
18	C₂×#64520	—	4	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	Q₈	1	1	yes	characteristic
24	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
26	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
27	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
31	C₂×C₈×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₄²×C₁₉	D₈	1	1	yes	characteristic
40	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
41	#64520	—	4	2	no	—
42	#64520	—	4	2	no	—
43	#64520	—	8	2	no	—
44	C₂×C₁₉⋊C₈	—	4	2	no	—
45	C₂×C₁₉⋊C₈	—	4	2	no	—
46	C₁₆×C₁₉	—	4	2	no	—
47	#7219	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	#103	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#107	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	—	8	2	no	—
64	C₁₉⋊C₈	—	8	2	no	—
65	#2162	D₁₉	1	1	yes	characteristic
66	#1837	—	19	1	no	—
67	#1566	—	19	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	#340	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	H(3,ℤ/4)	1	1	yes	characteristic
76	C₄×C₁₉	#344	1	1	yes	characteristic
77	C₄×C₁₉	#365	1	2	yes	—
78	C₄×C₁₉	#368	1	2	yes	—
79	#423	—	38	1	no	—
80	#423	—	38	1	no	—
81	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
82	C₄⋊C₁₆	—	2	1	no	—
83	C₂²⋊C₁₆	—	2	1	no	—
84	C₄×C₁₆	Dic₁₉	1	2	yes	—
85	#341	—	19	2	no	—
86	#341	—	38	1	no	—
87	#334	—	19	2	no	—
88	#334	—	38	1	no	—
89	C₂×C₁₉	—	4	1	no	—
90	C₂×C₁₉	#1286	1	1	yes	characteristic
91	C₂×C₁₉	#1381	1	1	yes	characteristic
92	C₂×C₁₉	#1383	1	1	yes	characteristic
93	C₂×M₁₆	—	38	2	no	—
94	C₂×M₁₆	—	76	1	no	—
95	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
96	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂×C₄²	D₇₆	1	1	yes	characteristic
98	C₂×C₁₆	—	2	2	no	—
99	C₄⋊C₈	—	38	2	no	—
100	C₄⋊C₈	—	76	1	no	—
101	C₄⋊C₈	—	76	1	no	—
102	C₄⋊C₈	—	76	1	no	—
103	C₄×C₈	Dic₃₈	1	1	yes	characteristic
104	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
105	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
106	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
107	C₁₉	#7219	1	1	yes	characteristic, complemented, Sylow
108	C₂²×C₄	#64516	1	1	yes	characteristic
109	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
110	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
111	M₁₆	—	76	2	no	—
112	M₁₆	—	76	2	no	—
113	M₁₆	—	152	2	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	4	1	no	—
116	C₂×C₈	—	76	2	no	—
117	C₂×C₈	—	76	2	no	—
118	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
119	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
120	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
121	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
122	C₄²	#64516	1	1	yes	characteristic
123	C₄²	D₁₅₂	1	1	yes	characteristic
124	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
125	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
126	C₁₆	—	4	2	no	—
127	C₂³	#10597273	1	1	yes	characteristic
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	#10597273	1	1	yes	characteristic
133	C₂×C₄	#10597274	1	1	yes	characteristic
134	C₂×C₄	#10597275	1	1	yes	characteristic
135	C₂×C₄	#10597278	1	1	yes	characteristic
136	C₂×C₄	#10597278	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	—	152	2	no	—
143	C₈	—	152	2	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	#11926307	1	1	yes	characteristic
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	#11926300	1	1	yes	characteristic
152	C₄	#11926315	1	1	yes	characteristic
153	C₄	#11926367	1	2	yes	—
154	C₄	#11926374	1	2	yes	—
155	C₂	—	4	1	no	—
156	C₂	#14561494	1	1	yes	characteristic
157	C₂	#14561729	1	1	yes	characteristic
158	C₂	#14561734	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563773

C₂

yes

maximal, characteristic

#14562391

C₂

yes

maximal, characteristic

C₁₉×#2162

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

—

#11926295

—

#11926295

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

—

C₄×C₁₆×C₁₉

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×#64520

—

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

Q₈

yes

characteristic

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

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

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2162

D₁₉

yes

characteristic

#1837

—

#1566

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#368

yes

—

#423

—

#423

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

Dic₁₉

yes

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₄⋊C₈

—

103

C₄×C₈

Dic₃₈

yes

characteristic

104

C₄×C₈

C₄×D₁₉

yes

characteristic

105

C₄×C₈

C₂×Dic₁₉

yes

characteristic

106

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

107

C₁₉

#7219

yes

characteristic, complemented, Sylow

108

C₂²×C₄

#64516

yes

characteristic

109

C₂²×C₄

Dic₇₆

yes

characteristic

110

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

152

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

C₄×Dic₁₉

yes

characteristic

119

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

120

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

121

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

122

C₄²

#64516

yes

characteristic

123

C₄²

D₁₅₂

yes

characteristic

124

C₄²

C₄⋊Dic₁₉

yes

characteristic

125

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

126

C₁₆

—

127

C₂³

#10597273

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

#10597273

yes

characteristic

133

C₂×C₄

#10597274

yes

characteristic

134

C₂×C₄

#10597275

yes

characteristic

135

C₂×C₄

#10597278

yes

characteristic

136

C₂×C₄

#10597278

yes

characteristic

137

C₂×C₄

C₁₉⋊#95

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

152

—

143

C₈

—

152

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11926307

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

#11926300

yes

characteristic

152

C₄

#11926315

yes

characteristic

153

C₄

#11926367

yes

—

154

C₄

#11926374

yes

—

155

C₂

—

156

C₂

#14561494

yes

characteristic

157

C₂

#14561729

yes

characteristic

158

C₂

#14561734

yes

characteristic

	subgroup	G/H
center	C₂²	#11926307
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#2162	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#103
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#2162	D₁₉
hypocenter	C₁₉	#7219
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂²

#11926307

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#2162

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
107. C₁₉	#7219	semidirect

H ≅ G/N

type

107. C₁₉

#7219

semidirect

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

subgroup	index
#14563773	2
#14562391	2
C₁₉×#2162	2
#7219	19

subgroup

index

#14563773

#14562391

C₁₉×#2162

#7219

Subgroups — #18069582

Conjugacy classes of subgroups

Complements

Maximal subgroups