Group #14564754 — subgroups

Subgroups — #14564754

Order 2432.

342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10597388	C₂	1	2	yes	maximal
2	C₂×#10597293	C₂	1	2	yes	maximal, complemented
3	#11926510	C₂	1	1	yes	maximal, characteristic
4	#11926309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₂×#64541	C₂²	1	1	yes	characteristic
8	C₂×Q₁₆×C₁₉	—	2	4	no	—
9	C₂×Q₁₆×C₁₉	—	2	2	no	—
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64528	—	2	2	no	—
12	#10597388	—	2	4	no	—
13	#10597388	—	2	4	no	—
14	C₂×#64527	—	2	2	no	—
15	C₂×#64520	C₂²	1	1	yes	characteristic
16	C₂×#64520	C₂²	1	2	yes	—
17	#10597293	—	2	4	no	—
18	(C₂×D₁₉)⋊C₈	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	—	2	2	no	—
24	C₂×Q₈×C₁₉	D₄	1	4	yes	—
25	C₂²×C₄×C₁₉	—	2	2	no	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₂²⋊D₁₉	—	2	1	no	—
28	#64541	—	2	2	no	—
29	#64541	—	2	2	no	—
30	C₂×D₇₆	D₄	1	1	yes	characteristic
31	C₂×C₄×D₁₉	—	2	1	no	—
32	C₂×Dic₃₈	D₄	1	1	yes	characteristic
33	Q₁₆×C₁₉	—	2	8	no	—
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	D₄	1	2	yes	—
36	#64528	—	2	8	no	—
37	#64527	—	2	8	no	—
38	#64520	—	2	2	no	—
39	#64520	—	2	2	no	—
40	#64520	D₄	1	4	yes	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	—	2	1	no	—
43	C₂³×C₁₉	#41	1	1	yes	characteristic
44	C₂²×D₁₉	—	2	1	no	—
45	Q₈×C₁₉	—	2	4	no	—
46	Q₈×C₁₉	—	2	4	no	—
47	Q₈×C₁₉	—	4	2	no	—
48	Q₈×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	2	4	no	—
50	C₂×C₄×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²⋊D₁₉	—	4	2	no	—
57	C₂×Dic₁₉	—	2	1	no	—
58	D₇₆	—	2	2	no	—
59	C₄×D₁₉	—	4	1	no	—
60	C₄×D₁₉	—	4	1	no	—
61	Dic₃₈	—	2	2	no	—
62	C₈×C₁₉	—	2	2	no	—
63	C₁₉⋊C₈	—	2	4	no	—
64	C₁₉⋊C₈	—	4	1	no	—
65	#2020	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	2	2	no	—
67	C₂²×C₁₉	#121	1	1	yes	characteristic
68	C₂²×C₁₉	#121	1	2	yes	—
69	C₂×D₁₉	—	4	1	no	—
70	C₂×D₁₉	—	4	2	no	—
71	C₄×C₁₉	—	4	4	no	—
72	C₄×C₁₉	#120	1	2	yes	—
73	C₄×C₁₉	#120	1	1	yes	characteristic
74	C₄×C₁₉	#127	1	1	yes	characteristic
75	Dic₁₉	—	4	1	no	—
76	C₂×#137	—	19	2	no	—
77	C₂²×Q₁₆	D₁₉	1	1	yes	characteristic, complemented
78	C₂×#101	—	19	2	no	—
79	#408	—	19	1	no	—
80	#341	—	19	1	no	—
81	C₂×C₁₉	—	2	2	no	—
82	C₂×C₁₉	#392	1	1	yes	characteristic
83	C₂×C₁₉	#473	1	2	yes	—
84	D₁₉	—	8	1	no	—
85	C₂×#41	—	19	1	no	—
86	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
87	#137	—	38	4	no	—
88	#137	—	38	4	no	—
89	C₂×Q₁₆	—	2	4	no	—
90	C₂×Q₁₆	—	2	2	no	—
91	C₂×Q₁₆	—	38	2	no	—
92	C₂×SD₁₆	—	38	2	no	—
93	C₂×M₁₆	—	19	2	no	—
94	C₂×M₁₆	—	19	1	no	—
95	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
96	#101	—	38	4	no	—
97	C₂²⋊C₈	—	38	2	no	—
98	C₁₉	#2020	1	1	yes	characteristic, complemented, Sylow
99	#41	—	38	2	no	—
100	#41	—	38	2	no	—
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	—	2	2	no	—
103	C₂×Q₈	—	2	2	no	—
104	C₂×Q₈	—	2	2	no	—
105	C₂×Q₈	—	2	2	no	—
106	C₂×Q₈	—	19	1	no	—
107	C₂×Q₈	C₂²⋊D₁₉	1	4	yes	—
108	C₂×D₄	—	19	1	no	—
109	C₂×D₄	—	38	1	no	—
110	C₂²×C₄	—	2	2	no	—
111	C₂²×C₄	—	38	1	no	—
112	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
113	Q₁₆	—	2	8	no	—
114	Q₁₆	—	38	8	no	—
115	SD₁₆	—	38	8	no	—
116	M₁₆	—	19	4	no	—
117	M₁₆	—	38	2	no	—
118	M₁₆	—	38	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	38	2	no	—
121	C₂×C₈	—	38	1	no	—
122	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
123	C₂³	—	38	1	no	—
124	C₂³	#64543	1	1	yes	characteristic
125	Q₈	—	2	4	no	—
126	Q₈	—	2	4	no	—
127	Q₈	—	4	2	no	—
128	Q₈	—	4	2	no	—
129	Q₈	—	38	2	no	—
130	D₄	—	38	2	no	—
131	D₄	—	76	2	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	38	1	no	—
136	C₂×C₄	—	76	1	no	—
137	C₂×C₄	—	76	1	no	—
138	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
139	C₂×C₄	D₄×D₁₉	1	2	yes	—
140	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
141	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	38	4	no	—
144	C₈	—	76	1	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	76	2	no	—
147	C₂²	—	76	1	no	—
148	C₂²	#10597384	1	1	yes	characteristic
149	C₂²	#10597385	1	2	yes	—
150	C₄	—	4	4	no	—
151	C₄	—	76	1	no	—
152	C₄	#10597383	1	2	yes	—
153	C₄	#10597386	1	1	yes	characteristic
154	C₄	#10597399	1	1	yes	characteristic
155	C₂	—	2	2	no	—
156	C₂	—	152	1	no	—
157	C₂	#11926452	1	1	yes	characteristic
158	C₂	#11926816	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597388

C₂

yes

maximal

C₂×#10597293

C₂

yes

maximal, complemented

#11926510

C₂

yes

maximal, characteristic

#11926309

C₂

yes

maximal, characteristic, complemented

C₂²×Q₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂×#64541

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597293

—

(C₂×D₁₉)⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

characteristic

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

—

—

—

—

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2020

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×#137

—

C₂²×Q₁₆

D₁₉

yes

characteristic, complemented

C₂×#101

—

#408

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

#392

yes

characteristic

C₂×C₁₉

#473

yes

—

D₁₉

—

C₂×#41

—

C₂²×Q₈

C₂×D₁₉

yes

—

#137

—

#137

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#101

—

C₂²⋊C₈

—

C₁₉

#2020

yes

characteristic, complemented, Sylow

#41

—

100

#41

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

C₂²⋊D₁₉

yes

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₂²×D₁₉

yes

characteristic

113

Q₁₆

—

114

Q₁₆

—

115

SD₁₆

—

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

C₂²⋊D₁₉

yes

—

123

C₂³

—

124

C₂³

#64543

yes

characteristic

125

Q₈

—

126

Q₈

—

127

Q₈

—

128

Q₈

—

129

Q₈

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

D₄×D₁₉

yes

characteristic

139

C₂×C₄

D₄×D₁₉

yes

—

140

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

141

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

#10597384

yes

characteristic

149

C₂²

#10597385

yes

—

150

C₄

—

151

C₄

—

152

C₄

#10597383

yes

—

153

C₄

#10597386

yes

characteristic

154

C₄

#10597399

yes

characteristic

155

C₂

—

156

C₂

—

152

—

157

C₂

#11926452

yes

characteristic

158

C₂

#11926816

yes

—

	subgroup	G/H
center	C₂²	#10597384
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂²×Q₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂×#64541	C₂²
hypercenter	C₂²×Q₁₆	D₁₉
hypocenter	C₁₉	#2020
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

#10597384

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂²×Q₁₆×C₁₉

C₂

C₂²×C₁₉

C₂²

C₂²×Q₁₆

D₁₉

hypocenter

C₁₉

#2020

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
2. C₂×#10597293	C₂	semidirect
4. #11926309	C₂	semidirect
5. C₂²×Q₁₆×C₁₉	C₂	semidirect
77. C₂²×Q₁₆	D₁₉	semidirect
98. C₁₉	#2020	semidirect

H ≅ G/N

type

2. C₂×#10597293

C₂

semidirect

4. #11926309

C₂

semidirect

5. C₂²×Q₁₆×C₁₉

C₂

semidirect

77. C₂²×Q₁₆

D₁₉

semidirect

98. C₁₉

#2020

semidirect

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

subgroup	index
C₂×#10597388	2
C₂×#10597293	2
#11926510	2
#11926309	2
C₂²×Q₁₆×C₁₉	2
#2020	19

subgroup

index

C₂²×Q₁₆×C₁₉

Subgroups — #14564754

Conjugacy classes of subgroups

Complements

Maximal subgroups