Group #14562284 — subgroups

Subgroups — #14562284

Order 2432.

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

normal subgroups only

This group has 256 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	#11926290	C₂	1	2	yes	maximal, complemented
4	#11926288	C₂	1	2	yes	maximal, complemented
5	C₁₉×#532	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	—	2	1	no	—
7	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₉×#127	C₂²	1	1	yes	characteristic
9	C₁₉×#124	—	2	1	no	—
10	C₁₉×#121	—	2	1	no	—
11	C₁₉×#121	C₄	1	2	yes	—
12	C₄×D₄×C₁₉	—	2	1	no	—
13	C₄×D₄×C₁₉	C₄	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	1	no	—
16	C₂²⋊(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	C₄×C₁₉⋊C₈	—	2	1	no	—
21	#41×C₁₉	—	4	2	no	—
22	#41×C₁₉	—	4	2	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	2	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₁₉	—	2	2	no	—
29	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	—	4	2	no	—
43	C₂³×C₁₉	—	2	2	no	—
44	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	Q₈×C₁₉	—	4	1	no	—
46	Q₈×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	4	2	no	—
48	D₄×C₁₉	—	4	4	no	—
49	D₄×C₁₉	—	4	1	no	—
50	D₄×C₁₉	—	4	1	no	—
51	D₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	D₈	1	2	yes	—
60	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
61	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₁₉⋊C₈	—	4	2	no	—
65	C₁₉⋊C₈	—	4	2	no	—
66	#1540	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	4	2	no	—
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	#102	1	2	yes	—
73	C₂²×C₁₉	C₂×C₂²⋊C₄	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	—	4	2	no	—
78	C₄×C₁₉	#102	1	2	yes	—
79	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
80	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
81	C₄×C₁₉	#135	1	2	yes	—
82	#532	D₁₉	1	1	yes	characteristic
83	#431	—	19	1	no	—
84	C₂×C₄⋊C₈	—	19	1	no	—
85	#332	—	19	2	no	—
86	#331	—	19	2	no	—
87	C₂×C₁₉	—	2	2	no	—
88	C₂×C₁₉	—	8	2	no	—
89	C₂×C₁₉	#413	1	1	yes	characteristic
90	C₂×C₁₉	C₂×#102	1	1	yes	characteristic
91	C₂×C₁₉	#416	1	1	yes	characteristic
92	C₂×#41	—	2	1	no	—
93	C₂²×C₈	—	38	1	no	—
94	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
95	#127	C₂×D₁₉	1	1	yes	characteristic
96	#124	—	2	1	no	—
97	#121	—	2	1	no	—
98	#121	Dic₁₉	1	2	yes	—
99	C₄×D₄	—	2	1	no	—
100	C₄×D₄	Dic₁₉	1	2	yes	—
101	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
102	C₄⋊C₈	—	19	2	no	—
103	C₄⋊C₈	—	19	2	no	—
104	C₄⋊C₈	—	38	1	no	—
105	C₂²⋊C₈	—	38	1	no	—
106	C₄×C₈	—	38	1	no	—
107	C₁₉	#1540	1	1	yes	characteristic, complemented, Sylow
108	#41	—	4	2	no	—
109	#41	—	4	2	no	—
110	C₂×Q₈	—	2	1	no	—
111	C₂×D₄	—	2	2	no	—
112	C₂×D₄	—	2	1	no	—
113	C₂×D₄	—	2	1	no	—
114	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
117	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
118	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
119	C₂×C₈	—	38	2	no	—
120	C₂×C₈	—	38	2	no	—
121	C₂×C₈	—	76	2	no	—
122	C₄⋊C₄	—	2	1	no	—
123	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
124	C₂²⋊C₄	—	2	2	no	—
125	C₂²⋊C₄	—	2	2	no	—
126	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
127	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
128	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
129	C₄²	C₂²×D₁₉	1	1	yes	characteristic
130	C₂³	—	2	2	no	—
131	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
132	Q₈	—	4	1	no	—
133	Q₈	—	4	1	no	—
134	D₄	—	4	2	no	—
135	D₄	—	4	4	no	—
136	D₄	—	4	1	no	—
137	D₄	—	4	1	no	—
138	D₄	—	4	2	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	—	4	4	no	—
143	C₂×C₄	#64525	1	2	yes	—
144	C₂×C₄	#64526	1	2	yes	—
145	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
146	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
147	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
148	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
149	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
150	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
151	C₈	—	76	2	no	—
152	C₈	—	76	2	no	—
153	C₂²	—	2	1	no	—
154	C₂²	—	2	1	no	—
155	C₂²	—	4	2	no	—
156	C₂²	—	4	2	no	—
157	C₂²	—	4	2	no	—
158	C₂²	#10597289	1	2	yes	—
159	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
160	C₄	—	2	1	no	—
161	C₄	—	2	1	no	—
162	C₄	—	2	1	no	—
163	C₄	—	4	2	no	—
164	C₄	#10597289	1	2	yes	—
165	C₄	C₂×#64525	1	1	yes	characteristic
166	C₄	C₂×#64526	1	1	yes	characteristic
167	C₄	#10597396	1	2	yes	—
168	C₂	—	2	2	no	—
169	C₂	—	8	2	no	—
170	C₂	#11926528	1	1	yes	characteristic
171	C₂	C₂×#10597289	1	1	yes	characteristic
172	C₂	#11926540	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

#11926290

C₂

yes

maximal, complemented

#11926288

C₂

yes

maximal, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

C₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

C₄

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

—

#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

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

#1540

—

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

C₂×D₈

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

#135

yes

—

#532

D₁₉

yes

characteristic

#431

—

C₂×C₄⋊C₈

—

#332

—

#331

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×#41

—

C₂²×C₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#127

C₂×D₁₉

yes

—

—

Dic₁₉

yes

—

C₄×D₄

—

100

C₄×D₄

Dic₁₉

yes

—

101

C₂×C₄²

C₂×D₁₉

yes

characteristic

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₂²⋊C₈

—

106

C₄×C₈

—

107

C₁₉

#1540

yes

characteristic, complemented, Sylow

108

#41

—

109

#41

—

110

C₂×Q₈

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

C₂×Dic₁₉

yes

—

115

C₂²×C₄

—

116

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

117

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

118

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₄⋊C₄

—

123

C₄⋊C₄

C₂×Dic₁₉

yes

—

124

C₂²⋊C₄

—

125

C₂²⋊C₄

—

126

C₄²

C₂×Dic₁₉

yes

characteristic

127

C₄²

C₂²⋊D₁₉

yes

characteristic

128

C₄²

C₂²⋊D₁₉

yes

characteristic

129

C₄²

C₂²×D₁₉

yes

characteristic

130

C₂³

—

131

C₂³

C₂²⋊Dic₁₉

yes

characteristic

132

Q₈

—

133

Q₈

—

134

D₄

—

135

D₄

—

136

D₄

—

137

D₄

—

138

D₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

#64525

yes

—

144

C₂×C₄

#64526

yes

—

145

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

146

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

147

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

148

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

149

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

150

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

151

C₈

—

152

C₈

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

#10597289

yes

—

159

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

#10597289

yes

—

165

C₄

C₂×#64525

yes

characteristic

166

C₄

C₂×#64526

yes

characteristic

167

C₄

#10597396

yes

—

168

C₂

—

169

C₂

—

170

C₂

#11926528

yes

characteristic

171

C₂

C₂×#10597289

yes

characteristic

172

C₂

#11926540

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₁₉
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	#1540
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₁₉

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 ▷ C₂²×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. #11926290	C₂	semidirect
4. #11926288	C₂	semidirect
107. C₁₉	#1540	semidirect

H ≅ G/N

type

1. #11926597

C₂

semidirect

2. C₂×C₄⋊(C₁₉⋊C₈)

C₂

semidirect

3. #11926290

C₂

semidirect

4. #11926288

C₂

semidirect

107. C₁₉

#1540

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
#11926290	2
#11926288	2
C₁₉×#532	2
#1540	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₁₉×#532

Subgroups — #14562284

Conjugacy classes of subgroups

Complements

Maximal subgroups