Group #14562034 — subgroups

Subgroups — #14562034

Order 2432.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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	#11926597	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄⋊(C₁₉⋊C₈)	C₂	1	4	yes	maximal, complemented
4	C₁₉×#532	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₁₉	—	2	1	no	—
6	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
7	C₁₉×#127	C₄	1	1	yes	characteristic
8	C₁₉×#124	—	2	1	no	—
9	C₁₉×#121	—	2	1	no	—
10	C₁₉×#121	C₄	1	2	yes	—
11	C₄×D₄×C₁₉	—	2	1	no	—
12	C₄×D₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	—	2	1	no	—
15	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
17	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
18	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
19	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
20	#41×C₁₉	—	4	2	no	—
21	#41×C₁₉	—	4	2	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	2	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₁₉	—	2	2	no	—
28	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	4	2	no	—
42	C₂³×C₁₉	—	2	2	no	—
43	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	Q₈×C₁₉	—	4	2	no	—
45	D₄×C₁₉	—	2	4	no	—
46	D₄×C₁₉	—	4	2	no	—
47	D₄×C₁₉	—	4	4	no	—
48	D₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	D₈	1	2	yes	—
58	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
59	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₁₉⋊C₈	—	4	2	no	—
63	C₁₉⋊C₈	—	4	2	no	—
64	#1480	—	19	1	no	maximal, Sylow
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	#102	1	2	yes	—
71	C₂²×C₁₉	C₂×C₂²⋊C₄	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	—	4	2	no	—
76	C₄×C₁₉	#102	1	2	yes	—
77	C₄×C₁₉	#131	1	2	yes	—
78	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
79	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
80	#532	D₁₉	1	1	yes	characteristic
81	#431	—	19	1	no	—
82	C₂×C₄⋊C₈	—	19	1	no	—
83	D₄⋊C₈	—	19	4	no	—
84	C₂×C₁₉	—	2	2	no	—
85	C₂×C₁₉	—	8	2	no	—
86	C₂×C₁₉	#408	1	1	yes	characteristic
87	C₂×C₁₉	C₂×#102	1	1	yes	characteristic
88	C₂×C₁₉	#421	1	1	yes	characteristic
89	C₂×#41	—	2	1	no	—
90	C₂²×C₈	—	38	1	no	—
91	C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
92	#127	Dic₁₉	1	1	yes	characteristic
93	#124	—	2	1	no	—
94	#121	—	2	1	no	—
95	#121	Dic₁₉	1	2	yes	—
96	C₄×D₄	—	2	1	no	—
97	C₄×D₄	C₂×D₁₉	1	2	yes	—
98	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
99	C₄⋊C₈	—	19	2	no	—
100	C₄⋊C₈	—	38	1	no	—
101	C₄⋊C₈	—	38	1	no	—
102	C₂²⋊C₈	—	38	1	no	—
103	C₄×C₈	—	19	2	no	—
104	C₁₉	#1480	1	1	yes	characteristic, complemented, Sylow
105	#41	—	4	2	no	—
106	#41	—	4	2	no	—
107	C₂×Q₈	—	2	1	no	—
108	C₂×D₄	—	2	2	no	—
109	C₂×D₄	—	2	1	no	—
110	C₂×D₄	—	2	1	no	—
111	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
114	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₂×C₈	—	38	2	no	—
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	—	76	2	no	—
119	C₄⋊C₄	—	2	1	no	—
120	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
121	C₂²⋊C₄	—	2	2	no	—
122	C₂²⋊C₄	—	2	2	no	—
123	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
124	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
125	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
126	C₄²	C₂²×D₁₉	1	1	yes	characteristic
127	C₂³	—	2	2	no	—
128	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
129	Q₈	—	4	2	no	—
130	D₄	—	2	4	no	—
131	D₄	—	4	2	no	—
132	D₄	—	4	4	no	—
133	D₄	—	4	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	#64525	1	2	yes	—
140	C₂×C₄	#64526	1	2	yes	—
141	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
142	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
143	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
144	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
145	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
146	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
147	C₈	—	76	2	no	—
148	C₈	—	76	2	no	—
149	C₂²	—	2	1	no	—
150	C₂²	—	2	1	no	—
151	C₂²	—	4	2	no	—
152	C₂²	—	4	2	no	—
153	C₂²	—	4	2	no	—
154	C₂²	#10597289	1	2	yes	—
155	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	—	2	1	no	—
159	C₄	—	4	2	no	—
160	C₄	#10597289	1	2	yes	—
161	C₄	C₂×#64525	1	1	yes	characteristic
162	C₄	C₂×#64526	1	1	yes	characteristic
163	C₄	#10597394	1	2	yes	—
164	C₂	—	2	2	no	—
165	C₂	—	8	2	no	—
166	C₂	#11926511	1	1	yes	characteristic
167	C₂	C₂×#10597289	1	1	yes	characteristic
168	C₂	#11926561	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926597

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic, complemented

D₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₁₉×#127

C₄

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

C₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1480

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#102

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#102

yes

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

#532

D₁₉

yes

characteristic

#431

—

C₂×C₄⋊C₈

—

D₄⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×#41

—

C₂²×C₈

—

C₄⋊Q₈

Dic₁₉

yes

characteristic

#127

Dic₁₉

yes

—

—

Dic₁₉

yes

—

C₄×D₄

—

C₄×D₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₂²⋊C₈

—

103

C₄×C₈

—

104

C₁₉

#1480

yes

characteristic, complemented, Sylow

105

#41

—

106

#41

—

107

C₂×Q₈

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

C₂×Dic₁₉

yes

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

114

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

115

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₄⋊C₄

—

120

C₄⋊C₄

C₂×Dic₁₉

yes

—

121

C₂²⋊C₄

—

122

C₂²⋊C₄

—

123

C₄²

C₂×Dic₁₉

yes

characteristic

124

C₄²

C₂²⋊D₁₉

yes

characteristic

125

C₄²

C₂²⋊D₁₉

yes

characteristic

126

C₄²

C₂²×D₁₉

yes

characteristic

127

C₂³

—

128

C₂³

C₂²⋊Dic₁₉

yes

characteristic

129

Q₈

—

130

D₄

—

131

D₄

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

#64525

yes

—

140

C₂×C₄

#64526

yes

—

141

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

142

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

143

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

144

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

145

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

146

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

147

C₈

—

148

C₈

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

#10597289

yes

—

155

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

#10597289

yes

—

161

C₄

C₂×#64525

yes

characteristic

162

C₄

C₂×#64526

yes

characteristic

163

C₄

#10597394

yes

—

164

C₂

—

165

C₂

—

166

C₂

#11926511

yes

characteristic

167

C₂

C₂×#10597289

yes

characteristic

168

C₂

#11926561

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#532	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	#532	D₁₉
hypocenter	C₁₉	#1480
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#532

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. #11926597	C₂	semidirect
2. C₂×C₄⋊(C₁₉⋊C₈)	C₂	semidirect
3. D₄⋊(C₁₉⋊C₈)	C₂	semidirect
104. C₁₉	#1480	semidirect

H ≅ G/N

type

1. #11926597

C₂

semidirect

2. C₂×C₄⋊(C₁₉⋊C₈)

C₂

semidirect

3. D₄⋊(C₁₉⋊C₈)

C₂

semidirect

104. C₁₉

#1480

semidirect

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

subgroup	index
#11926597	2
C₂×C₄⋊(C₁₉⋊C₈)	2
D₄⋊(C₁₉⋊C₈)	2
C₁₉×#532	2
#1480	19

subgroup

index

#11926597

C₂×C₄⋊(C₁₉⋊C₈)

D₄⋊(C₁₉⋊C₈)

C₁₉×#532

#1480

Subgroups — #14562034

Conjugacy classes of subgroups

Complements

Maximal subgroups