Group #14563674 — subgroups

Subgroups — #14563674

Order 2432.

272 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 93 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×#64515	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597276	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926507	C₂	1	2	yes	maximal
4	#11926308	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#64515	—	2	2	no	—
12	C₂×#64515	—	2	2	no	—
13	C₂×#64515	C₄	1	4	yes	—
14	C₁₉×#108	—	2	2	no	—
15	(C₂×D₁₉)⋊C₈	—	2	4	no	—
16	#10597276	—	2	2	no	—
17	C₂³×D₁₉	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₁₉	—	2	1	no	—
21	C₂×C₄×D₁₉	—	2	1	no	—
22	C₂×C₄×D₁₉	—	2	1	no	—
23	C₂×C₄×D₁₉	—	2	1	no	—
24	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄×D₁₉	D₄	1	2	yes	—
26	M₁₆×C₁₉	—	2	2	no	—
27	M₁₆×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₁₉	D₄	1	2	yes	—
31	C₂×C₈×C₁₉	D₄	1	2	yes	—
32	#64520	—	2	2	no	—
33	#64520	—	2	2	no	—
34	C₂×C₁₉⋊C₈	—	2	1	no	—
35	C₂×C₁₉⋊C₈	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
38	#64515	—	2	8	no	—
39	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	1	no	—
41	C₂²×D₁₉	—	2	1	no	—
42	C₂²×D₁₉	—	4	2	no	—
43	C₂²×D₁₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂×Dic₁₉	—	2	1	no	—
51	C₂×Dic₁₉	—	2	1	no	—
52	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
53	C₄×D₁₉	—	2	2	no	—
54	C₄×D₁₉	—	2	2	no	—
55	C₄×D₁₉	—	2	2	no	—
56	C₄×D₁₉	—	2	2	no	—
57	C₈×C₁₉	—	4	2	no	—
58	C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
59	C₁₉⋊C₈	—	2	2	no	—
60	C₁₉⋊C₈	—	4	2	no	—
61	#1811	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
66	C₂×D₁₉	—	2	2	no	—
67	C₂×D₁₉	—	2	4	no	—
68	C₂×D₁₉	—	4	2	no	—
69	C₂×D₁₉	—	4	2	no	—
70	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₄×C₁₉	#117	1	1	yes	characteristic
72	C₄×C₁₉	#121	1	1	yes	characteristic
73	C₄×C₁₉	#121	1	1	yes	characteristic
74	Dic₁₉	—	2	2	no	—
75	C₂²×M₁₆	—	19	1	no	—
76	C₂×#108	—	19	1	no	—
77	C₂×#108	D₁₉	1	1	yes	characteristic, complemented
78	#407	—	19	2	no	—
79	#341	—	19	2	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	#380	1	1	yes	characteristic
83	C₂×C₁₉	#430	1	2	yes	—
84	D₁₉	—	4	2	no	—
85	C₂³×C₄	—	19	1	no	—
86	C₂×M₁₆	—	19	4	no	—
87	C₂×M₁₆	—	19	2	no	—
88	C₂×M₁₆	—	38	2	no	—
89	C₂×M₁₆	—	38	2	no	—
90	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
91	C₂²×C₈	—	19	1	no	—
92	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
93	#108	—	2	2	no	—
94	#108	—	38	2	no	—
95	C₂²⋊C₈	—	38	4	no	—
96	C₁₉	#1811	1	1	yes	characteristic, complemented, Sylow
97	C₂⁴	—	19	1	no	—
98	C₂²×C₄	—	19	1	no	—
99	C₂²×C₄	—	19	2	no	—
100	C₂²×C₄	—	19	2	no	—
101	C₂²×C₄	—	38	1	no	—
102	C₂²×C₄	—	38	1	no	—
103	C₂²×C₄	—	38	1	no	—
104	C₂²×C₄	—	38	1	no	—
105	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
106	M₁₆	—	2	2	no	—
107	M₁₆	—	2	2	no	—
108	M₁₆	—	38	8	no	—
109	M₁₆	—	38	2	no	—
110	M₁₆	—	38	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	19	2	no	—
113	C₂×C₈	—	38	1	no	—
114	C₂×C₈	—	38	1	no	—
115	C₂×C₈	—	38	2	no	—
116	C₂×C₈	C₄×D₁₉	1	2	yes	—
117	C₂×C₈	D₇₆	1	2	yes	—
118	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
119	C₂³	—	19	2	no	—
120	C₂³	—	38	1	no	—
121	C₂³	—	38	1	no	—
122	C₂³	—	76	2	no	—
123	C₂³	Q₈×D₁₉	1	1	yes	characteristic
124	C₂×C₄	—	19	2	no	—
125	C₂×C₄	—	38	1	no	—
126	C₂×C₄	—	38	1	no	—
127	C₂×C₄	—	38	2	no	—
128	C₂×C₄	—	38	2	no	—
129	C₂×C₄	—	38	2	no	—
130	C₂×C₄	—	38	2	no	—
131	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
132	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
133	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
134	C₂×C₄	#64543	1	1	yes	characteristic
135	C₂×C₄	#64545	1	1	yes	characteristic
136	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
137	C₈	—	4	2	no	—
138	C₈	—	38	2	no	—
139	C₈	—	76	2	no	—
140	C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
141	C₂²	—	2	2	no	—
142	C₂²	—	38	4	no	—
143	C₂²	—	38	2	no	—
144	C₂²	—	76	2	no	—
145	C₂²	—	76	2	no	—
146	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
147	C₂²	#10597343	1	1	yes	characteristic
148	C₂²	#10597392	1	1	yes	characteristic
149	C₄	—	38	2	no	—
150	C₄	#10597338	1	1	yes	characteristic
151	C₄	#10597341	1	1	yes	characteristic
152	C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
153	C₄	#10597384	1	1	yes	characteristic
154	C₂	—	2	1	no	—
155	C₂	—	2	1	no	—
156	C₂	—	76	2	no	—
157	C₂	#11926401	1	1	yes	characteristic
158	C₂	#11926591	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64515

C₂

yes

maximal, characteristic

C₂×#10597276

C₂

yes

maximal, characteristic, complemented

#11926507

C₂

yes

maximal

#11926308

C₂

yes

maximal, complemented

C₂×C₁₉×#108

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

—

C₄

yes

—

C₁₉×#108

—

(C₂×D₁₉)⋊C₈

—

#10597276

—

C₂³×D₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

Q₈

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

#64515

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₄⋊C₄

yes

—

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

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1811

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂²×M₁₆

—

C₂×#108

—

C₂×#108

D₁₉

yes

characteristic, complemented

#407

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#380

yes

characteristic

C₂×C₁₉

#430

yes

—

D₁₉

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#108

—

#108

—

C₂²⋊C₈

—

C₁₉

#1811

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₂²×D₁₉

yes

characteristic

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₄×D₁₉

yes

—

117

C₂×C₈

D₇₆

yes

—

118

C₂×C₈

C₂²⋊D₁₉

yes

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

Q₈×D₁₉

yes

characteristic

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

132

C₂×C₄

C₂×D₇₆

yes

characteristic

133

C₂×C₄

D₄×D₁₉

yes

characteristic

134

C₂×C₄

#64543

yes

characteristic

135

C₂×C₄

#64545

yes

characteristic

136

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

(C₂×D₁₉)⋊C₄

yes

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

147

C₂²

#10597343

yes

characteristic

148

C₂²

#10597392

yes

characteristic

149

C₄

—

150

C₄

#10597338

yes

characteristic

151

C₄

#10597341

yes

characteristic

152

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

153

C₄

#10597384

yes

characteristic

154

C₂

—

155

C₂

—

156

C₂

—

157

C₂

#11926401

yes

characteristic

158

C₂

#11926591

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	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#1811
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

C₂×C₄⋊C₄

prime radical

C₂³×D₁₉

Q₈

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×#10597276	C₂	semidirect
4. #11926308	C₂	semidirect
5. C₂×C₁₉×#108	C₂	semidirect
77. C₂×#108	D₁₉	semidirect
96. C₁₉	#1811	semidirect

H ≅ G/N

type

2. C₂×#10597276

C₂

semidirect

4. #11926308

C₂

semidirect

5. C₂×C₁₉×#108

C₂

semidirect

77. C₂×#108

D₁₉

semidirect

96. C₁₉

#1811

semidirect

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

subgroup	index
C₂²×#64515	2
C₂×#10597276	2
#11926507	2
#11926308	2
C₂×C₁₉×#108	2
#1811	19

subgroup

index

C₂²×#64515

C₂×C₁₉×#108

Subgroups — #14563674

Conjugacy classes of subgroups

Complements

Maximal subgroups