Group #18069173 — subgroups

Subgroups — #18069173

Order 4864.

180 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14563751	C₂	1	1	yes	maximal, characteristic
2	#14561575	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
5	C₄²×Dic₁₉	C₄	1	1	yes	characteristic
6	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
7	#11926298	—	2	1	no	—
8	#11926298	—	2	1	no	—
9	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	—	2	1	no	—
15	C₂×C₄×Dic₁₉	—	2	1	no	—
16	C₂×C₄×Dic₁₉	C₈	1	1	yes	characteristic
17	C₂×C₄×Dic₁₉	C₈	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	—	2	1	no	—
19	C₂×C₁₆×C₁₉	—	4	1	no	—
20	C₁₉×C₄⋊C₈	—	4	1	no	—
21	C₂×C₁₉⋊C₁₆	—	4	1	no	—
22	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
23	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	1	no	—
27	C₂²×Dic₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	4	1	no	—
31	C₂×C₈×C₁₉	—	4	1	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	—	2	1	no	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₄×Dic₁₉	—	4	2	no	—
36	C₄×Dic₁₉	—	4	1	no	—
37	C₄×Dic₁₉	—	4	1	no	—
38	C₄×Dic₁₉	—	4	1	no	—
39	C₄×Dic₁₉	C₁₆	1	2	yes	complemented
40	C₂×C₁₉⋊C₈	—	4	2	no	—
41	C₂×C₁₉⋊C₈	—	4	1	no	—
42	C₁₆×C₁₉	—	8	1	no	—
43	C₁₉⋊C₁₆	—	8	1	no	—
44	#7062	—	19	1	no	maximal, Sylow
45	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
55	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	2	2	no	—
58	C₂×Dic₁₉	—	4	1	no	—
59	C₂×Dic₁₉	—	4	1	no	—
60	C₂×Dic₁₉	—	4	1	no	—
61	C₂×Dic₁₉	—	4	1	no	—
62	C₈×C₁₉	—	4	1	no	—
63	C₈×C₁₉	—	4	1	no	—
64	C₁₉⋊C₈	—	8	1	no	—
65	#1831	—	19	1	no	—
66	#1322	—	19	1	no	—
67	#1322	D₁₉	1	1	yes	characteristic
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	#324	1	1	yes	characteristic
71	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
72	C₂²×C₁₉	#349	1	1	yes	characteristic
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	4	1	no	—
77	C₄×C₁₉	#354	1	1	yes	characteristic
78	C₄×C₁₉	#355	1	1	yes	characteristic
79	Dic₁₉	—	4	2	no	—
80	Dic₁₉	—	4	2	no	—
81	C₂×C₄⋊C₈	—	19	1	no	—
82	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
83	C₄³	—	19	1	no	—
84	C₂²⋊C₁₆	—	2	1	no	—
85	C₂²⋊C₁₆	—	38	1	no	—
86	#336	—	38	1	no	—
87	#336	—	38	1	no	—
88	C₂×C₁₉	—	2	1	no	—
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	#1322	1	1	yes	characteristic
91	C₂×C₁₉	#1324	1	1	yes	characteristic
92	C₂×C₁₉	#1327	1	1	yes	characteristic
93	C₂²×C₈	—	38	1	no	—
94	C₂²×C₈	D₇₆	1	1	yes	characteristic
95	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
96	C₂×C₄²	—	19	1	no	—
97	C₂×C₄²	—	19	1	no	—
98	C₂×C₄²	—	38	1	no	—
99	C₂×C₄²	—	38	1	no	—
100	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
101	C₂×C₁₆	—	4	1	no	—
102	C₂×C₁₆	—	76	1	no	—
103	C₄⋊C₈	—	4	1	no	—
104	C₄⋊C₈	—	76	1	no	—
105	C₁₉	#7062	1	1	yes	characteristic, complemented, Sylow
106	C₂²×C₄	—	38	1	no	—
107	C₂²×C₄	—	38	1	no	—
108	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
109	C₂²×C₄	#64515	1	1	yes	characteristic
110	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	—	4	1	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	76	2	no	—
116	C₂×C₈	—	76	1	no	—
117	C₄²	—	2	1	no	—
118	C₄²	—	2	1	no	—
119	C₄²	—	19	2	no	—
120	C₄²	—	38	1	no	—
121	C₄²	—	76	1	no	—
122	C₄²	—	76	1	no	—
123	C₄²	—	76	1	no	—
124	C₄²	—	76	2	no	—
125	C₁₆	—	8	1	no	—
126	C₁₆	—	152	1	no	—
127	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	38	2	no	—
135	C₂×C₄	—	38	2	no	—
136	C₂×C₄	—	76	1	no	—
137	C₂×C₄	—	76	1	no	—
138	C₂×C₄	—	76	1	no	—
139	C₂×C₄	—	76	1	no	—
140	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
141	C₂×C₄	#10597255	1	1	yes	characteristic
142	C₂×C₄	#10597263	1	1	yes	characteristic
143	C₂×C₄	#10597281	1	1	yes	characteristic
144	C₈	—	4	1	no	—
145	C₈	—	4	1	no	—
146	C₈	—	152	1	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	#11926269	1	1	yes	characteristic
150	C₂²	(C₂×D₁₉)⋊C₁₆	1	1	yes	characteristic
151	C₂²	#11926325	1	1	yes	characteristic
152	C₄	—	2	1	no	—
153	C₄	—	2	1	no	—
154	C₄	—	2	1	no	—
155	C₄	—	4	1	no	—
156	C₄	—	76	2	no	—
157	C₄	—	76	2	no	—
158	C₄	#11926338	1	1	yes	characteristic
159	C₄	#11926340	1	1	yes	characteristic
160	C₂	—	2	1	no	—
161	C₂	—	2	1	no	—
162	C₂	#14561574	1	1	yes	characteristic
163	C₂	#14561578	1	1	yes	characteristic
164	C₂	#14561585	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563751

C₂

yes

maximal, characteristic

#14561575

C₂

yes

maximal, characteristic

C₁₉×#1322

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

characteristic

C₄²×Dic₁₉

C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

#11926298

—

#11926298

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₂²⋊C₁₆

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₈

yes

characteristic

C₂×C₄×Dic₁₉

C₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₁₆

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7062

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

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

C₂×C₄×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1831

—

#1322

—

#1322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#324

yes

characteristic

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₂²×C₁₉

#349

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₄³

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

#336

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

D₇₆

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

100

C₂×C₄²

C₄×D₁₉

yes

characteristic

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₁₉

#7062

yes

characteristic, complemented, Sylow

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₈×D₁₉

yes

characteristic

109

C₂²×C₄

#64515

yes

characteristic

110

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₄²

—

125

C₁₆

—

126

C₁₆

—

152

—

127

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

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

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

C₁₆×D₁₉

yes

characteristic

141

C₂×C₄

#10597255

yes

characteristic

142

C₂×C₄

#10597263

yes

characteristic

143

C₂×C₄

#10597281

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

152

—

147

C₂²

—

148

C₂²

—

149

C₂²

#11926269

yes

characteristic

150

C₂²

(C₂×D₁₉)⋊C₁₆

yes

characteristic

151

C₂²

#11926325

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

#11926338

yes

characteristic

159

C₄

#11926340

yes

characteristic

160

C₂

—

161

C₂

—

162

C₂

#14561574

yes

characteristic

163

C₂

#14561578

yes

characteristic

164

C₂

#14561585

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂×C₄×C₁₉	C₂×C₁₆
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1322	C₂
socle	C₂²×C₁₉	#324
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1322	D₁₉
hypocenter	C₁₉	#7062
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂×C₄×C₁₉

C₂×C₁₆

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1322

C₂

socle

C₂²×C₁₉

#324

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1322

N	H ≅ G/N	type
39. C₄×Dic₁₉	C₁₆	semidirect
105. C₁₉	#7062	semidirect

H ≅ G/N

type

39. C₄×Dic₁₉

C₁₆

semidirect

105. C₁₉

#7062

semidirect

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

subgroup	index
#14563751	2
#14561575	2
C₁₉×#1322	2
#7062	19

subgroup

index

#14563751

#14561575

C₁₉×#1322

#7062

Subgroups — #18069173

Conjugacy classes of subgroups

Complements

Maximal subgroups