Group #14563699 — subgroups

Subgroups — #14563699

Order 2432.

264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂×#10597276	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597275	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926545	C₂	1	2	yes	maximal
4	#11926312	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#131	—	2	2	no	—
8	C₁₉×#131	C₄	1	4	yes	complemented
9	C₂×M₁₆×C₁₉	—	2	1	no	—
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×#64520	C₂²	1	2	yes	—
15	#10597292	—	2	2	no	—
16	#10597289	—	2	2	no	—
17	#10597276	—	2	2	no	—
18	#10597275	—	2	1	no	—
19	#10597275	—	2	1	no	—
20	#41×C₁₉	—	2	1	no	—
21	#41×C₁₉	—	2	1	no	—
22	#41×C₁₉	C₂×C₄	1	2	yes	—
23	#41×C₁₉	Q₈	1	2	yes	—
24	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	2	no	—
30	M₁₆×C₁₉	—	2	1	no	—
31	M₁₆×C₁₉	—	2	4	no	—
32	M₁₆×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	4	no	—
35	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	D₄	1	2	yes	—
39	C₄⋊Dic₁₉	—	2	2	no	—
40	C₄⋊Dic₁₉	—	2	2	no	—
41	#64520	—	2	2	no	—
42	#64520	—	2	2	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂³×C₁₉	—	2	1	no	—
45	C₂³×C₁₉	#41	1	1	yes	characteristic
46	Q₈×C₁₉	—	2	1	no	—
47	Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
48	D₄×C₁₉	—	2	2	no	—
49	D₄×C₁₉	—	2	2	no	—
50	D₄×C₁₉	—	2	1	no	—
51	D₄×C₁₉	C₄⋊C₄	1	2	yes	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂×Dic₁₉	—	4	2	no	—
62	C₂×Dic₁₉	—	8	2	no	—
63	C₈×C₁₉	—	2	2	no	—
64	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₁₉⋊C₈	—	4	2	no	—
67	#1816	—	19	1	no	maximal, Sylow
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	2	2	no	—
71	C₂²×C₁₉	—	4	1	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	#117	1	1	yes	characteristic
74	C₂²×C₁₉	#121	1	1	yes	characteristic
75	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₄×C₁₉	#121	1	1	yes	characteristic
80	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
81	Dic₁₉	—	8	2	no	—
82	C₂×#131	D₁₉	1	1	yes	characteristic
83	C₂×#108	—	19	1	no	—
84	C₂×#107	—	19	1	no	—
85	#417	—	19	2	no	—
86	#343	—	19	2	no	—
87	C₂×C₁₉	—	2	1	no	—
88	C₂×C₁₉	—	2	1	no	—
89	C₂×C₁₉	—	4	2	no	—
90	C₂×C₁₉	#380	1	1	yes	characteristic
91	C₂×C₁₉	#472	1	1	yes	characteristic
92	C₂×C₁₉	#473	1	1	yes	characteristic
93	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
94	#131	—	2	2	no	—
95	#131	Dic₁₉	1	4	yes	complemented
96	C₂×M₁₆	—	2	1	no	—
97	C₂×M₁₆	—	19	2	no	—
98	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
99	C₂²×C₈	—	2	1	no	—
100	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
101	C₂×C₄⋊C₄	—	19	2	no	—
102	#108	—	38	2	no	—
103	#107	—	38	1	no	—
104	#107	—	38	1	no	—
105	#103	—	38	2	no	—
106	#102	—	38	2	no	—
107	C₁₉	#1816	1	1	yes	characteristic, complemented, Sylow
108	#41	—	2	1	no	—
109	#41	—	2	1	no	—
110	#41	Dic₃₈	1	2	yes	—
111	#41	C₂×Dic₁₉	1	2	yes	—
112	C₂×Q₈	D₇₆	1	1	yes	characteristic
113	C₂×D₄	—	2	1	no	—
114	C₂×D₄	D₇₆	1	1	yes	characteristic
115	C₂²×C₄	—	2	1	no	—
116	C₂²×C₄	—	38	2	no	—
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	M₁₆	—	2	1	no	—
119	M₁₆	—	2	4	no	—
120	M₁₆	—	38	2	no	—
121	M₁₆	—	38	2	no	—
122	M₁₆	C₂×Dic₁₉	1	2	yes	—
123	C₂×C₈	—	2	1	no	—
124	C₂×C₈	—	2	4	no	—
125	C₂×C₈	—	38	2	no	—
126	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
127	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
128	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
129	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
130	C₄⋊C₄	—	38	2	no	—
131	C₄⋊C₄	—	38	2	no	—
132	C₂³	—	2	1	no	—
133	C₂³	#64541	1	1	yes	characteristic
134	Q₈	—	2	1	no	—
135	Q₈	C₄⋊Dic₁₉	1	2	yes	—
136	D₄	—	2	2	no	—
137	D₄	—	2	2	no	—
138	D₄	—	2	1	no	—
139	D₄	C₄⋊Dic₁₉	1	2	yes	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	76	2	no	—
144	C₂×C₄	—	152	2	no	—
145	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
146	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
147	C₂×C₄	#64541	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	—	2	2	no	—
152	C₈	—	76	2	no	—
153	C₈	C₂²⋊Dic₁₉	1	2	yes	—
154	C₈	C₂²⋊Dic₁₉	1	2	yes	—
155	C₂²	—	2	1	no	—
156	C₂²	—	2	1	no	—
157	C₂²	—	2	2	no	—
158	C₂²	—	4	1	no	—
159	C₂²	—	4	1	no	—
160	C₂²	#10597370	1	1	yes	characteristic
161	C₂²	#10597372	1	1	yes	characteristic
162	C₂²	#10597376	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	152	2	no	—
165	C₄	#10597370	1	1	yes	characteristic
166	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
167	C₄	#10597376	1	1	yes	characteristic
168	C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
169	C₂	—	2	1	no	—
170	C₂	—	2	1	no	—
171	C₂	—	4	2	no	—
172	C₂	#11926404	1	1	yes	characteristic
173	C₂	#11926814	1	1	yes	characteristic
174	C₂	#11926819	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597276

C₂

yes

maximal, characteristic, complemented

C₂×#10597275

C₂

yes

maximal, characteristic, complemented

#11926545

C₂

yes

maximal

#11926312

C₂

yes

maximal, complemented

C₂×C₁₉×#131

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₁₉×#131

—

C₁₉×#131

C₄

yes

complemented

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

—

—

—

—

—

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

C₂×C₄

yes

—

#41×C₁₉

Q₈

yes

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

#41

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

C₄⋊C₄

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₁₉⋊C₈

—

#1816

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

Dic₁₉

—

C₂×#131

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×#41

C₂×D₁₉

yes

characteristic

#131

—

#131

Dic₁₉

yes

complemented

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

100

C₂²×C₈

C₂×D₁₉

yes

characteristic

101

C₂×C₄⋊C₄

—

102

#108

—

103

#107

—

104

#107

—

105

#103

—

106

#102

—

107

C₁₉

#1816

yes

characteristic, complemented, Sylow

108

#41

—

109

#41

—

110

#41

Dic₃₈

yes

—

111

#41

C₂×Dic₁₉

yes

—

112

C₂×Q₈

D₇₆

yes

characteristic

113

C₂×D₄

—

114

C₂×D₄

D₇₆

yes

characteristic

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

M₁₆

—

122

M₁₆

C₂×Dic₁₉

yes

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

C₂×Dic₁₉

yes

—

127

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

128

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

129

C₂×C₈

C₂²⋊D₁₉

yes

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₂³

—

133

C₂³

#64541

yes

characteristic

134

Q₈

—

135

Q₈

C₄⋊Dic₁₉

yes

—

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

C₄⋊Dic₁₉

yes

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

152

—

145

C₂×C₄

C₂×Dic₃₈

yes

characteristic

146

C₂×C₄

C₂×D₇₆

yes

characteristic

147

C₂×C₄

#64541

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

C₈

C₂²⋊Dic₁₉

yes

—

154

C₈

C₂²⋊Dic₁₉

yes

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

#10597370

yes

characteristic

161

C₂²

#10597372

yes

characteristic

162

C₂²

#10597376

yes

characteristic

163

C₄

—

164

C₄

—

152

—

165

C₄

#10597370

yes

characteristic

166

C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

167

C₄

#10597376

yes

characteristic

168

C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

169

C₂

—

170

C₂

—

171

C₂

—

172

C₂

#11926404

yes

characteristic

173

C₂

#11926814

yes

characteristic

174

C₂

#11926819

yes

characteristic

	subgroup	G/H
center	C₂²	#10597376
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#131	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂×#41×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#131	D₁₉
hypocenter	C₁₉	#1816
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131

subgroup

G/H

center

C₂²

#10597376

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#131

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂×#41×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131

N	H ≅ G/N	type
1. C₂×#10597276	C₂	semidirect
2. C₂×#10597275	C₂	semidirect
4. #11926312	C₂	semidirect
8. C₁₉×#131	C₄	semidirect
95. #131	Dic₁₉	semidirect
107. C₁₉	#1816	semidirect

H ≅ G/N

type

1. C₂×#10597276

C₂

semidirect

2. C₂×#10597275

C₂

semidirect

4. #11926312

C₂

semidirect

8. C₁₉×#131

C₄

semidirect

95. #131

Dic₁₉

semidirect

107. C₁₉

#1816

semidirect

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

subgroup	index
C₂×#10597276	2
C₂×#10597275	2
#11926545	2
#11926312	2
C₂×C₁₉×#131	2
#1816	19

subgroup

index

C₂×C₁₉×#131

Subgroups — #14563699

Conjugacy classes of subgroups

Complements

Maximal subgroups