Group #14564509 — subgroups

Subgroups — #14564509

Order 2432.

376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₂²×D₁₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597266	C₂	1	2	yes	maximal, complemented
3	C₂×#10597272	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926445	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
10	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×D₁₅₂	—	2	2	no	—
13	C₂×D₁₅₂	—	2	2	no	—
14	C₂×D₁₅₂	C₄	1	4	yes	complemented
15	C₁₉×#106	—	2	2	no	—
16	#10597272	—	2	2	no	—
17	#10597266	—	2	4	no	—
18	C₂³×D₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₉	D₄	1	2	yes	—
22	C₂×D₇₆	—	2	2	no	—
23	C₂×D₇₆	—	2	2	no	—
24	C₂×D₇₆	—	2	2	no	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×D₇₆	—	2	2	no	—
27	C₂×D₇₆	C₂×C₄	1	4	yes	—
28	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₁₉	D₄	1	2	yes	—
30	C₂×C₈×C₁₉	D₄	1	2	yes	—
31	C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₄⋊C₄×C₁₉	—	2	2	no	—
33	(C₂×D₁₉)⋊C₄	—	4	8	no	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₄×Dic₁₉	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
39	D₁₅₂	—	2	8	no	—
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×D₁₉	—	2	4	no	—
42	C₂²×D₁₉	—	4	2	no	—
43	C₂²×D₁₉	—	4	2	no	—
44	C₂²×D₁₉	—	4	4	no	—
45	C₂²×D₁₉	—	4	4	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	4	no	—
48	C₂×C₄×C₁₉	C₂²×C₄	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	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	—	2	4	no	—
56	D₇₆	—	2	4	no	—
57	D₇₆	—	2	4	no	—
58	D₇₆	—	4	2	no	—
59	D₇₆	—	4	2	no	—
60	C₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
61	C₁₉⋊C₈	—	2	2	no	—
62	#1972	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
64	C₂²×C₁₉	#121	1	1	yes	characteristic
65	C₂²×C₁₉	#127	1	1	yes	characteristic
66	C₂²×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
67	C₂×D₁₉	—	4	4	no	—
68	C₂×D₁₉	—	4	8	no	—
69	C₂×D₁₉	—	8	4	no	—
70	C₂×D₁₉	—	8	2	no	—
71	C₂×D₁₉	—	8	2	no	—
72	C₄×C₁₉	—	8	2	no	—
73	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
75	C₄×C₁₉	#121	1	1	yes	characteristic
76	C₄×C₁₉	#124	1	1	yes	characteristic
77	Dic₁₉	—	4	2	no	—
78	C₂²×D₈	—	19	1	no	—
79	C₂×#106	D₁₉	1	1	yes	characteristic, complemented
80	C₂×#102	—	19	2	no	—
81	C₂×#97	—	19	1	no	—
82	#390	—	19	2	no	—
83	C₂×C₁₉	#390	1	1	yes	characteristic
84	C₂×C₁₉	#442	1	2	yes	—
85	C₂×C₁₉	#469	1	2	yes	—
86	C₂×C₁₉	#496	1	2	yes	—
87	D₁₉	—	8	4	no	—
88	C₂²×D₄	—	19	2	no	—
89	C₂×D₈	—	19	4	no	—
90	C₂×D₈	—	38	2	no	—
91	C₂×D₈	—	38	2	no	—
92	C₂²×C₈	—	19	1	no	—
93	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
95	C₂×C₂²⋊C₄	—	38	4	no	—
96	C₂×C₄²	—	19	1	no	—
97	#106	—	2	2	no	—
98	#102	—	38	4	no	—
99	#97	—	38	2	no	—
100	C₁₉	#1972	1	1	yes	characteristic, complemented, Sylow
101	C₂⁴	—	38	2	no	—
102	C₂×D₄	—	19	4	no	—
103	C₂×D₄	—	38	2	no	—
104	C₂×D₄	—	38	2	no	—
105	C₂×D₄	—	38	2	no	—
106	C₂×D₄	—	38	2	no	—
107	C₂×D₄	—	38	2	no	—
108	C₂²×C₄	—	2	2	no	—
109	C₂²×C₄	—	19	2	no	—
110	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
111	D₈	—	38	8	no	—
112	C₂×C₈	—	19	2	no	—
113	C₂×C₈	—	38	1	no	—
114	C₂×C₈	—	38	1	no	—
115	C₂×C₈	C₄×D₁₉	1	2	yes	—
116	C₂×C₈	D₇₆	1	2	yes	—
117	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
118	C₄⋊C₄	—	2	2	no	—
119	C₄⋊C₄	—	2	2	no	—
120	C₂²⋊C₄	—	76	8	no	—
121	C₄²	—	38	1	no	—
122	C₄²	—	38	1	no	—
123	C₂³	—	38	4	no	—
124	C₂³	—	76	2	no	—
125	C₂³	—	76	2	no	—
126	C₂³	—	76	4	no	—
127	C₂³	—	76	4	no	—
128	C₂³	D₄×D₁₉	1	1	yes	characteristic
129	D₄	—	38	4	no	—
130	D₄	—	38	4	no	—
131	D₄	—	76	2	no	—
132	D₄	—	76	2	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	38	2	no	—
136	C₂×C₄	—	38	4	no	—
137	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
138	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
139	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
140	C₂×C₄	#64545	1	1	yes	characteristic
141	C₂×C₄	#64545	1	1	yes	characteristic
142	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
143	C₈	—	38	2	no	—
144	C₈	(C₂×D₁₉)⋊C₄	1	4	yes	complemented
145	C₂²	—	76	8	no	—
146	C₂²	—	76	4	no	—
147	C₂²	—	152	4	no	—
148	C₂²	—	152	2	no	—
149	C₂²	—	152	2	no	—
150	C₂²	#10597339	1	1	yes	characteristic
151	C₂²	#10597341	1	1	yes	characteristic
152	C₂²	#10597360	1	4	yes	—
153	C₂²	#10597386	1	1	yes	characteristic
154	C₄	—	8	2	no	—
155	C₄	—	76	2	no	—
156	C₄	#10597339	1	1	yes	characteristic
157	C₄	#10597341	1	1	yes	characteristic
158	C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
159	C₄	#10597393	1	1	yes	characteristic
160	C₂	—	152	4	no	—
161	C₂	#11926445	1	1	yes	characteristic
162	C₂	#11926655	1	2	yes	—
163	C₂	#11926798	1	2	yes	—
164	C₂	#11926930	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₅₂

C₂

yes

maximal, characteristic

C₂×#10597266

C₂

yes

maximal, complemented

C₂×#10597272

C₂

yes

maximal, characteristic, complemented

#11926445

C₂

yes

maximal, complemented

C₂×C₁₉×#106

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

C₄

yes

complemented

C₁₉×#106

—

#10597272

—

#10597266

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

D₁₅₂

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

C₂²⋊C₄

yes

complemented

C₁₉⋊C₈

—

#1972

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂²×D₈

—

C₂×#106

D₁₉

yes

characteristic, complemented

C₂×#102

—

C₂×#97

—

#390

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#442

yes

—

C₂×C₁₉

#469

yes

—

C₂×C₁₉

#496

yes

—

D₁₉

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#106

—

#102

—

#97

—

100

C₁₉

#1972

yes

characteristic, complemented, Sylow

101

C₂⁴

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²×D₁₉

yes

characteristic

111

D₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₄×D₁₉

yes

—

116

C₂×C₈

D₇₆

yes

—

117

C₂×C₈

C₂²⋊D₁₉

yes

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

D₄×D₁₉

yes

characteristic

129

D₄

—

130

D₄

—

131

D₄

—

132

D₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

138

C₂×C₄

C₂×D₇₆

yes

characteristic

139

C₂×C₄

D₄×D₁₉

yes

characteristic

140

C₂×C₄

#64545

yes

characteristic

141

C₂×C₄

#64545

yes

characteristic

142

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

143

C₈

—

144

C₈

(C₂×D₁₉)⋊C₄

yes

complemented

145

C₂²

—

146

C₂²

—

147

C₂²

—

152

—

148

C₂²

—

152

—

149

C₂²

—

152

—

150

C₂²

#10597339

yes

characteristic

151

C₂²

#10597341

yes

characteristic

152

C₂²

#10597360

yes

—

153

C₂²

#10597386

yes

characteristic

154

C₄

—

155

C₄

—

156

C₄

#10597339

yes

characteristic

157

C₄

#10597341

yes

characteristic

158

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

159

C₄

#10597393

yes

characteristic

160

C₂

—

152

—

161

C₂

#11926445

yes

characteristic

162

C₂

#11926655

yes

—

163

C₂

#11926798

yes

—

164

C₂

#11926930

yes

—

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₁₅₂	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	#1972
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₁₅₂

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
2. C₂×#10597266	C₂	semidirect
3. C₂×#10597272	C₂	semidirect
4. #11926445	C₂	semidirect
5. C₂×C₁₉×#106	C₂	semidirect
14. C₂×D₁₅₂	C₄	semidirect
60. C₈×C₁₉	C₂²⋊C₄	semidirect
79. C₂×#106	D₁₉	semidirect
100. C₁₉	#1972	semidirect
144. C₈	(C₂×D₁₉)⋊C₄	semidirect

H ≅ G/N

type

2. C₂×#10597266

C₂

semidirect

3. C₂×#10597272

C₂

semidirect

4. #11926445

C₂

semidirect

5. C₂×C₁₉×#106

C₂

semidirect

14. C₂×D₁₅₂

C₄

semidirect

60. C₈×C₁₉

C₂²⋊C₄

semidirect

79. C₂×#106

D₁₉

semidirect

100. C₁₉

#1972

semidirect

144. C₈

(C₂×D₁₉)⋊C₄

semidirect

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

subgroup	index
C₂²×D₁₅₂	2
C₂×#10597266	2
C₂×#10597272	2
#11926445	2
C₂×C₁₉×#106	2
#1972	19

subgroup

index

C₂²×D₁₅₂

C₂×C₁₉×#106

Subgroups — #14564509

Conjugacy classes of subgroups

Complements

Maximal subgroups