Group #18069145 — subgroups

Subgroups — #18069145

Order 4864.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14563397	C₂	1	2	yes	maximal
2	C₁₉×#1817	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
4	C₂×#10597260	—	2	2	no	—
5	#11926299	C₄	1	4	yes	—
6	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
8	C₁₉×#336	—	2	2	no	—
9	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	—	2	2	no	—
13	C₂×C₄²×C₁₉	—	4	2	no	—
14	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₉	D₄	1	2	yes	—
16	C₂²×C₁₉⋊C₈	—	2	4	no	—
17	C₁₉×C₂²⋊C₈	—	4	2	no	—
18	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
19	#10597260	—	4	4	no	—
20	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	4	no	—
24	C₂²×C₄×C₁₉	—	4	1	no	—
25	C₂²×C₄×C₁₉	—	4	1	no	—
26	C₂²×C₄×C₁₉	—	4	2	no	—
27	C₂²×C₄×C₁₉	—	4	1	no	—
28	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₉	—	4	4	no	—
33	C₂×C₈×C₁₉	—	4	2	no	—
34	C₄²×C₁₉	—	2	4	no	—
35	C₄²×C₁₉	—	4	2	no	—
36	C₂×C₁₉⋊C₈	—	2	8	no	—
37	C₂×C₁₉⋊C₈	—	4	4	no	—
38	C₂×C₁₉⋊C₈	—	4	4	no	—
39	#7046	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	—	2	1	no	—
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	—	2	1	no	—
43	C₂³×C₁₉	—	2	2	no	—
44	C₂³×C₁₉	#95	1	1	yes	characteristic
45	C₂³×C₁₉	#108	1	2	yes	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	4	4	no	—
55	C₂×C₄×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	—	4	4	no	—
57	C₂×C₄×C₁₉	#99	1	2	yes	—
58	C₂×C₄×C₁₉	#104	1	4	yes	—
59	C₈×C₁₉	—	8	2	no	—
60	C₁₉⋊C₈	—	4	8	no	—
61	#1817	D₁₉	1	1	yes	characteristic
62	#1749	—	19	2	no	—
63	C₂²×C₁₉	—	2	2	no	—
64	C₂²×C₁₉	—	2	4	no	—
65	C₂²×C₁₉	—	4	2	no	—
66	C₂²×C₁₉	—	4	1	no	—
67	C₂²×C₁₉	—	4	1	no	—
68	C₂²×C₁₉	#338	1	1	yes	characteristic
69	C₂²×C₁₉	#339	1	2	yes	—
70	C₂²×C₁₉	#341	1	1	yes	characteristic
71	C₂²×C₁₉	#342	1	1	yes	characteristic
72	C₂²×C₁₉	#344	1	2	yes	—
73	C₄×C₁₉	—	2	4	no	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	4	2	no	—
76	C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
78	C₂×C₂²⋊C₈	—	38	2	no	—
79	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
80	C₂×#97	—	38	2	no	—
81	#336	—	2	2	no	—
82	#336	—	19	4	no	—
83	C₂×C₁₉	—	4	2	no	—
84	C₂×C₁₉	#1291	1	2	yes	—
85	C₂×C₁₉	#1293	1	1	yes	characteristic
86	C₂×C₁₉	#1297	1	1	yes	characteristic
87	C₂×C₁₉	#1302	1	2	yes	—
88	C₂×C₁₉	#1306	1	1	yes	characteristic
89	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
90	C₂³×C₄	D₇₆	1	1	yes	characteristic
91	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
92	C₂²×C₈	—	2	2	no	—
93	C₂²×C₈	—	38	4	no	—
94	C₂×C₄²	—	4	2	no	—
95	C₂×C₄²	C₄×D₁₉	1	2	yes	—
96	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
97	C₂²⋊C₈	—	4	2	no	—
98	C₂²⋊C₈	—	38	8	no	—
99	#97	—	76	4	no	—
100	C₁₉	#7046	1	1	yes	characteristic, complemented, Sylow
101	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
102	C₂²×C₄	—	2	2	no	—
103	C₂²×C₄	—	2	4	no	—
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	—	4	1	no	—
106	C₂²×C₄	—	4	1	no	—
107	C₂²×C₄	—	4	1	no	—
108	C₂²×C₄	—	4	2	no	—
109	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
110	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
111	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
112	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
113	C₂×C₈	—	4	4	no	—
114	C₂×C₈	—	4	2	no	—
115	C₂×C₈	—	38	8	no	—
116	C₂×C₈	—	76	4	no	—
117	C₂×C₈	—	76	4	no	—
118	C₄²	—	2	4	no	—
119	C₄²	—	4	2	no	—
120	C₂³	—	2	1	no	—
121	C₂³	—	2	2	no	—
122	C₂³	—	2	1	no	—
123	C₂³	—	2	2	no	—
124	C₂³	#10597276	1	2	yes	—
125	C₂³	C₁₉⋊#95	1	1	yes	characteristic
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	4	4	no	—
137	C₂×C₄	#10597282	1	4	yes	—
138	C₂×C₄	#10597291	1	2	yes	—
139	C₈	—	8	2	no	—
140	C₈	—	76	8	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	2	4	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	4	2	no	—
145	C₂²	—	4	1	no	—
146	C₂²	C₁₉⋊#338	1	1	yes	characteristic
147	C₂²	#11926305	1	2	yes	—
148	C₂²	#11926309	1	1	yes	characteristic
149	C₂²	#11926311	1	1	yes	characteristic
150	C₂²	#11926314	1	2	yes	—
151	C₄	—	2	2	no	—
152	C₄	—	2	4	no	—
153	C₄	—	4	1	no	—
154	C₄	—	4	2	no	—
155	C₂	—	4	2	no	—
156	C₂	#14561508	1	2	yes	—
157	C₂	#14561512	1	1	yes	characteristic
158	C₂	#14561520	1	1	yes	characteristic
159	C₂	#14561535	1	2	yes	—
160	C₂	#14561543	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563397

C₂

yes

maximal

C₁₉×#1817

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

—

#11926299

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₄

yes

—

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7046

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂³×C₁₉

#108

yes

—

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

#99

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1817

D₁₉

yes

characteristic

#1749

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#338

yes

characteristic

C₂²×C₁₉

#339

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

Dic₁₉

yes

—

C₂×#97

—

#336

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

#1291

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#1306

yes

characteristic

C₂³×C₄

Dic₃₈

yes

characteristic

C₂³×C₄

D₇₆

yes

characteristic

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

100

C₁₉

#7046

yes

characteristic, complemented, Sylow

101

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

110

C₂²×C₄

Dic₁₉⋊C₄

yes

—

111

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

112

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₄²

—

119

C₄²

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

#10597276

yes

—

125

C₂³

C₁₉⋊#95

yes

characteristic

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

#10597282

yes

—

138

C₂×C₄

#10597291

yes

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₁₉⋊#338

yes

characteristic

147

C₂²

#11926305

yes

—

148

C₂²

#11926309

yes

characteristic

149

C₂²

#11926311

yes

characteristic

150

C₂²

#11926314

yes

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₂

—

156

C₂

#14561508

yes

—

157

C₂

#14561512

yes

characteristic

158

C₂

#14561520

yes

characteristic

159

C₂

#14561535

yes

—

160

C₂

#14561543

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂²×C₄²	C₂×D₁₉
Fitting	C₁₉×#1817	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂²×C₄²×C₁₉	C₂²
hypercenter	#1817	D₁₉
hypocenter	C₁₉	#7046
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1817

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂²×C₄²

C₂×D₁₉

Fitting

C₁₉×#1817

C₂

socle

C₂³×C₁₉

#95

prime radical

C₂⁴×C₁₉

C₄⋊C₄

cosocle

C₂²×C₄²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1817

N	H ≅ G/N	type
100. C₁₉	#7046	semidirect

H ≅ G/N

type

100. C₁₉

#7046

semidirect

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

subgroup	index
#14563397	2
C₁₉×#1817	2
#7046	19

subgroup

index

#14563397

C₁₉×#1817

#7046

Subgroups — #18069145

Conjugacy classes of subgroups

Complements

Maximal subgroups