Group #14564526 — subgroups

Subgroups — #14564526

Order 2432.

292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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×#10597350	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597282	C₂	1	2	yes	maximal, complemented
3	#11926512	C₂	1	2	yes	maximal, complemented
4	C₂×#10597272	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₆	C₄	1	1	yes	characteristic, complemented
12	#10597350	—	2	2	no	—
13	#10597350	—	2	2	no	—
14	C₂×D₁₅₂	C₄	1	1	yes	characteristic, complemented
15	C₂×#64516	C₄	1	2	yes	complemented
16	C₁₉×#108	—	2	2	no	—
17	#10597282	—	2	4	no	—
18	(C₂×D₁₉)⋊C₈	—	2	4	no	—
19	#10597272	—	2	2	no	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₂²⋊D₁₉	—	2	2	no	—
22	C₂²×Dic₁₉	—	2	1	no	—
23	#64541	—	2	2	no	—
24	#64541	—	2	2	no	—
25	#64541	—	2	2	no	—
26	#64541	—	2	2	no	—
27	C₂×D₇₆	C₂×C₄	1	2	yes	—
28	C₂×C₄×D₁₉	—	2	2	no	—
29	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
30	M₁₆×C₁₉	—	2	2	no	—
31	M₁₆×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	D₄	1	2	yes	—
36	C₂×C₈×C₁₉	D₄	1	2	yes	—
37	C₄×Dic₁₉	—	2	1	no	—
38	C₄×Dic₁₉	D₄	1	2	yes	—
39	C₂×C₁₉⋊C₈	—	2	1	no	—
40	C₂×C₁₉⋊C₈	—	2	1	no	—
41	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
42	Dic₇₆	—	2	2	no	—
43	D₁₅₂	—	2	2	no	—
44	#64516	—	2	4	no	—
45	C₂³×C₁₉	#41	1	1	yes	characteristic
46	C₂²×D₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²⋊D₁₉	—	4	2	no	—
54	C₂²⋊D₁₉	—	4	2	no	—
55	C₂×Dic₁₉	—	2	2	no	—
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	4	2	no	—
58	D₇₆	—	2	2	no	—
59	D₇₆	—	2	2	no	—
60	C₄×D₁₉	—	4	2	no	—
61	C₄×D₁₉	—	4	2	no	—
62	Dic₃₈	—	2	2	no	—
63	Dic₃₈	—	2	2	no	—
64	C₈×C₁₉	—	4	2	no	—
65	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₁₉⋊C₈	—	2	2	no	—
68	#1975	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	—	2	2	no	—
70	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
71	C₂²×C₁₉	#121	1	1	yes	characteristic
72	C₂²×C₁₉	#124	1	1	yes	characteristic
73	C₂×D₁₉	—	4	2	no	—
74	C₂×D₁₉	—	4	4	no	—
75	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
77	C₄×C₁₉	#121	1	1	yes	characteristic
78	C₄×C₁₉	#127	1	1	yes	characteristic
79	Dic₁₉	—	4	2	no	—
80	Dic₁₉	—	4	2	no	—
81	C₂×#135	—	19	1	no	—
82	C₂×#108	D₁₉	1	1	yes	characteristic, complemented
83	C₂×#104	—	19	2	no	—
84	#408	—	19	2	no	—
85	C₂×#97	—	19	1	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	2	1	no	—
88	C₂×C₁₉	#390	1	1	yes	characteristic
89	C₂×C₁₉	#444	1	2	yes	—
90	D₁₉	—	8	2	no	—
91	C₂×#41	—	19	2	no	—
92	#135	—	38	2	no	—
93	#135	—	38	2	no	—
94	C₂×Q₁₆	—	19	1	no	—
95	C₂×SD₁₆	—	19	2	no	—
96	C₂×D₈	—	19	1	no	—
97	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
98	C₂²×C₈	—	19	1	no	—
99	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
100	C₂×C₄²	—	19	1	no	—
101	#108	—	2	2	no	—
102	#104	—	38	4	no	—
103	C₂²⋊C₈	—	38	4	no	—
104	#97	—	38	2	no	—
105	C₁₉	#1975	1	1	yes	characteristic, complemented, Sylow
106	#41	—	38	2	no	—
107	#41	—	38	2	no	—
108	#41	—	38	2	no	—
109	#41	—	38	2	no	—
110	C₂×Q₈	—	19	2	no	—
111	C₂×D₄	—	19	2	no	—
112	C₂×D₄	—	38	2	no	—
113	C₂²×C₄	—	38	1	no	—
114	C₂²×C₄	—	38	2	no	—
115	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
116	Q₁₆	—	38	2	no	—
117	SD₁₆	—	38	4	no	—
118	D₈	—	38	2	no	—
119	M₁₆	—	2	2	no	—
120	M₁₆	—	2	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	19	2	no	—
123	C₂×C₈	—	38	1	no	—
124	C₂×C₈	—	38	1	no	—
125	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
126	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
127	C₂×C₈	D₇₆	1	2	yes	—
128	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
129	C₄²	—	19	2	no	—
130	C₄²	—	38	1	no	—
131	C₂³	—	38	2	no	—
132	C₂³	#64545	1	1	yes	characteristic
133	Q₈	—	38	2	no	—
134	Q₈	—	38	2	no	—
135	D₄	—	38	2	no	—
136	D₄	—	38	2	no	—
137	D₄	—	76	2	no	—
138	D₄	—	76	2	no	—
139	C₂×C₄	—	38	2	no	—
140	C₂×C₄	—	38	2	no	—
141	C₂×C₄	—	76	2	no	—
142	C₂×C₄	—	76	2	no	—
143	C₂×C₄	—	76	2	no	—
144	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
145	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
146	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
147	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
148	C₂×C₄	#64545	1	1	yes	characteristic
149	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
150	C₈	—	4	2	no	—
151	C₈	—	38	2	no	—
152	C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
153	C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
154	C₂²	—	2	2	no	—
155	C₂²	—	76	4	no	—
156	C₂²	—	76	2	no	—
157	C₂²	#10597339	1	1	yes	characteristic
158	C₂²	#10597341	1	1	yes	characteristic
159	C₂²	#10597393	1	1	yes	characteristic
160	C₄	—	76	2	no	—
161	C₄	—	76	2	no	—
162	C₄	#10597339	1	1	yes	characteristic
163	C₄	#10597341	1	1	yes	characteristic
164	C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
165	C₄	#10597386	1	1	yes	characteristic
166	C₂	—	2	1	no	—
167	C₂	—	2	1	no	—
168	C₂	—	152	2	no	—
169	C₂	#11926445	1	1	yes	characteristic
170	C₂	#11926665	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597350

C₂

yes

maximal, characteristic

C₂×#10597282

C₂

yes

maximal, complemented

#11926512

C₂

yes

maximal, complemented

C₂×#10597272

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#108

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Dic₇₆

C₄

yes

characteristic, complemented

#10597350

—

#10597350

—

C₂×D₁₅₂

C₄

yes

characteristic, complemented

C₂×#64516

C₄

yes

complemented

C₁₉×#108

—

#10597282

—

(C₂×D₁₉)⋊C₈

—

#10597272

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

—

—

—

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

Dic₇₆

—

D₁₅₂

—

#64516

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

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×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₁₉⋊C₈

—

#1975

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×#135

—

C₂×#108

D₁₉

yes

characteristic, complemented

C₂×#104

—

#408

—

C₂×#97

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#444

yes

—

D₁₉

—

C₂×#41

—

#135

—

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

100

C₂×C₄²

—

101

#108

—

102

#104

—

103

C₂²⋊C₈

—

104

#97

—

105

C₁₉

#1975

yes

characteristic, complemented, Sylow

106

#41

—

107

#41

—

108

#41

—

109

#41

—

110

C₂×Q₈

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

C₂²×D₁₉

yes

characteristic

116

Q₁₆

—

117

SD₁₆

—

118

D₈

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₄×D₁₉

yes

characteristic

126

C₂×C₈

C₄×D₁₉

yes

characteristic

127

C₂×C₈

D₇₆

yes

—

128

C₂×C₈

C₂²⋊D₁₉

yes

—

129

C₄²

—

130

C₄²

—

131

C₂³

—

132

C₂³

#64545

yes

characteristic

133

Q₈

—

134

Q₈

—

135

D₄

—

136

D₄

—

137

D₄

—

138

D₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

145

C₂×C₄

C₂×D₇₆

yes

characteristic

146

C₂×C₄

D₄×D₁₉

yes

characteristic

147

C₂×C₄

D₄×D₁₉

yes

characteristic

148

C₂×C₄

#64545

yes

characteristic

149

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

150

C₈

—

151

C₈

—

152

C₈

(C₂×D₁₉)⋊C₄

yes

—

153

C₈

(C₂×D₁₉)⋊C₄

yes

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

#10597339

yes

characteristic

158

C₂²

#10597341

yes

characteristic

159

C₂²

#10597393

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

#10597339

yes

characteristic

163

C₄

#10597341

yes

characteristic

164

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

165

C₄

#10597386

yes

characteristic

166

C₂

—

167

C₂

—

168

C₂

—

152

—

169

C₂

#11926445

yes

characteristic

170

C₂

#11926665

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#108	C₂
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×#10597350	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#1975
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#108

C₂

socle

C₂²×C₁₉

C₄×D₄

prime radical

C₂×#10597350

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
2. C₂×#10597282	C₂	semidirect
3. #11926512	C₂	semidirect
4. C₂×#10597272	C₂	semidirect
5. C₂×C₁₉×#108	C₂	semidirect
11. C₂×Dic₇₆	C₄	semidirect
14. C₂×D₁₅₂	C₄	semidirect
15. C₂×#64516	C₄	semidirect
82. C₂×#108	D₁₉	semidirect
105. C₁₉	#1975	semidirect

H ≅ G/N

type

2. C₂×#10597282

C₂

semidirect

3. #11926512

C₂

semidirect

4. C₂×#10597272

C₂

semidirect

5. C₂×C₁₉×#108

C₂

semidirect

11. C₂×Dic₇₆

C₄

semidirect

14. C₂×D₁₅₂

C₄

semidirect

15. C₂×#64516

C₄

semidirect

82. C₂×#108

D₁₉

semidirect

105. C₁₉

#1975

semidirect

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

subgroup	index
C₂×#10597350	2
C₂×#10597282	2
#11926512	2
C₂×#10597272	2
C₂×C₁₉×#108	2
#1975	19

subgroup

index

C₂×C₁₉×#108

Subgroups — #14564526

Conjugacy classes of subgroups

Complements

Maximal subgroups