Group #14574282 — subgroups

Subgroups — #14574282

Order 2432.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927148	C₂	1	2	yes	maximal, complemented
2	#11926946	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926908	C₂	1	2	yes	maximal, complemented
4	#11926794	C₂	1	2	yes	maximal, complemented
5	#11926777	C₂	1	2	yes	maximal, complemented
6	#11926656	C₂	1	2	yes	maximal, complemented
7	D₈×Dic₁₉	C₂	1	2	yes	maximal, complemented
8	#11926498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₈×C₁₉	C₂²	1	2	yes	—
11	C₂×D₈×C₁₉	C₂²	1	2	yes	—
12	C₁₉×#127	C₂²	1	2	yes	—
13	#10597385	—	2	4	no	—
14	#10597384	C₂²	1	4	yes	—
15	#10597381	—	2	4	no	—
16	D₄×Dic₁₉	C₂²	1	4	yes	—
17	C₂×#64515	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
19	#10597318	C₂²	1	1	yes	characteristic
20	#10597316	C₂²	1	2	yes	—
21	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	#10597289	C₂²	1	4	yes	—
23	#10597289	C₂²	1	4	yes	—
24	#10597275	C₂²	1	2	yes	—
25	#10597274	C₂²	1	2	yes	—
26	#10597272	C₂²	1	1	yes	characteristic
27	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
28	#10597260	C₂²	1	1	yes	characteristic
29	C₂×D₄×C₁₉	—	2	4	no	—
30	C₂×D₄×C₁₉	C₂³	1	4	yes	—
31	C₂×C₂²⋊D₁₉	—	2	4	no	—
32	C₂²×Dic₁₉	—	2	4	no	—
33	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
34	D₈×C₁₉	—	2	4	no	—
35	D₈×C₁₉	—	2	4	no	—
36	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
38	C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²⋊Dic₁₉	—	2	4	no	—
40	C₂²⋊Dic₁₉	—	2	4	no	—
41	(C₂×D₁₉)⋊C₄	D₄	1	2	yes	—
42	C₄⋊Dic₁₉	C₂³	1	4	yes	—
43	Dic₁₉⋊C₄	—	2	4	no	—
44	Dic₁₉⋊C₄	D₄	1	2	yes	—
45	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
46	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
48	#64515	—	2	2	no	—
49	C₈×D₁₉	—	2	2	no	—
50	C₂³×C₁₉	—	2	4	no	—
51	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
52	D₄×C₁₉	—	2	4	no	—
53	D₄×C₁₉	—	2	4	no	—
54	D₄×C₁₉	—	8	4	no	—
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
57	C₂²⋊D₁₉	—	8	4	no	—
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	—	8	4	no	—
60	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
61	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
62	C₄×D₁₉	—	2	1	no	—
63	C₄×D₁₉	—	2	1	no	—
64	C₈×C₁₉	#41	1	2	yes	—
65	C₈×C₁₉	#41	1	2	yes	—
66	C₁₉⋊C₈	—	2	1	no	—
67	C₁₉⋊C₈	—	2	1	no	—
68	#3176	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	—	4	4	no	—
70	C₂²×C₁₉	—	4	4	no	—
71	C₂²×C₁₉	—	4	4	no	—
72	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
73	C₂×D₁₉	—	2	1	no	—
74	C₂×D₁₉	—	2	2	no	—
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
77	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
78	Dic₁₉	—	2	1	no	—
79	Dic₁₉	—	2	2	no	—
80	Dic₁₉	—	4	4	no	—
81	#540	—	19	2	no	—
82	#499	—	19	1	no	—
83	#493	D₁₉	1	1	yes	characteristic, complemented
84	#490	—	19	2	no	—
85	#469	—	19	2	no	—
86	#466	—	19	2	no	—
87	#442	—	19	2	no	—
88	C₄×D₈	—	19	2	no	—
89	#405	—	19	1	no	—
90	C₂×C₁₉	—	8	4	no	—
91	C₂×C₁₉	#532	1	1	yes	characteristic
92	C₂×C₁₉	#576	1	2	yes	—
93	D₁₉	—	4	1	no	—
94	C₂×D₈	C₂×D₁₉	1	2	yes	—
95	C₂×D₈	C₂×D₁₉	1	2	yes	—
96	C₂×M₁₆	—	19	1	no	—
97	C₂²×C₈	—	19	1	no	—
98	#127	C₂×D₁₉	1	2	yes	—
99	#125	—	19	2	no	—
100	#123	—	38	4	no	—
101	#121	—	19	4	no	—
102	#121	—	38	4	no	—
103	C₄×D₄	—	19	4	no	—
104	#117	—	19	1	no	—
105	#107	—	19	2	no	—
106	#106	—	19	2	no	—
107	#102	—	19	4	no	—
108	#102	—	19	4	no	—
109	#97	—	19	1	no	—
110	#97	—	19	1	no	—
111	C₄×C₈	—	19	1	no	—
112	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
113	C₁₉	#3176	1	1	yes	characteristic, complemented, Sylow
114	C₂×D₄	—	2	4	no	—
115	C₂×D₄	—	38	4	no	—
116	C₂×D₄	C₂²×D₁₉	1	4	yes	—
117	C₂²×C₄	—	19	1	no	—
118	C₂²×C₄	—	38	4	no	—
119	D₈	—	2	4	no	—
120	D₈	—	2	4	no	—
121	M₁₆	—	38	2	no	—
122	C₂×C₈	—	19	1	no	—
123	C₂×C₈	—	19	1	no	—
124	C₂×C₈	—	38	2	no	—
125	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
126	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
127	C₄⋊C₄	—	19	2	no	—
128	C₄⋊C₄	—	19	4	no	—
129	C₄⋊C₄	—	38	4	no	—
130	C₂²⋊C₄	—	19	2	no	—
131	C₂²⋊C₄	—	38	4	no	—
132	C₂²⋊C₄	—	38	4	no	—
133	C₄²	—	19	1	no	—
134	C₄²	C₂²×D₁₉	1	1	yes	characteristic
135	C₂³	—	2	4	no	—
136	C₂³	—	19	1	no	—
137	D₄	—	2	4	no	—
138	D₄	—	2	4	no	—
139	D₄	—	8	4	no	—
140	D₄	—	152	4	no	—
141	C₂×C₄	—	19	2	no	—
142	C₂×C₄	—	19	1	no	—
143	C₂×C₄	—	38	1	no	—
144	C₂×C₄	—	38	1	no	—
145	C₂×C₄	—	38	4	no	—
146	C₂×C₄	—	152	4	no	—
147	C₂×C₄	D₄×D₁₉	1	2	yes	—
148	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
149	C₈	—	38	1	no	—
150	C₈	—	38	1	no	—
151	C₈	#64543	1	2	yes	—
152	C₈	#64543	1	2	yes	—
153	C₂²	—	4	4	no	—
154	C₂²	—	4	4	no	—
155	C₂²	—	4	4	no	—
156	C₂²	—	38	2	no	—
157	C₂²	—	38	1	no	—
158	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	38	2	no	—
161	C₄	—	38	1	no	—
162	C₄	—	76	4	no	—
163	C₄	C₂×#64543	1	1	yes	characteristic
164	C₄	C₂×#64543	1	1	yes	characteristic
165	C₂	—	8	4	no	—
166	C₂	—	76	1	no	—
167	C₂	#11927092	1	1	yes	characteristic
168	C₂	#11927345	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927148

C₂

yes

maximal, complemented

#11926946

C₂

yes

maximal, characteristic, complemented

#11926908

C₂

yes

maximal, complemented

#11926794

C₂

yes

maximal, complemented

#11926777

C₂

yes

maximal, complemented

#11926656

C₂

yes

maximal, complemented

D₈×Dic₁₉

C₂

yes

maximal, complemented

#11926498

C₂

yes

maximal, characteristic, complemented

C₁₉×#493

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

C₂²

yes

—

C₂×D₈×C₁₉

C₂²

yes

—

C₁₉×#127

C₂²

yes

—

#10597385

—

#10597384

C₂²

yes

—

#10597381

—

D₄×Dic₁₉

C₂²

yes

—

C₂×#64515

C₂²

yes

characteristic

C₂×C₈×D₁₉

C₂²

yes

characteristic

#10597318

C₂²

yes

characteristic

#10597316

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597289

C₂²

yes

—

#10597289

C₂²

yes

—

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

#10597272

C₂²

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

#10597260

C₂²

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂×C₄×D₁₉

C₂³

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

D₄

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

#64515

—

C₈×D₁₉

—

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

#41

yes

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3176

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#41

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#540

—

#499

—

#493

D₁₉

yes

characteristic, complemented

—

—

—

—

C₄×D₈

—

#405

—

C₂×C₁₉

—

C₂×C₁₉

#532

yes

characteristic

C₂×C₁₉

#576

yes

—

D₁₉

—

C₂×D₈

C₂×D₁₉

yes

—

C₂×D₈

C₂×D₁₉

yes

—

C₂×M₁₆

—

C₂²×C₈

—

#127

C₂×D₁₉

yes

—

#125

—

100

#123

—

101

#121

—

102

#121

—

103

C₄×D₄

—

104

#117

—

105

#107

—

106

#106

—

107

#102

—

108

#102

—

109

#97

—

110

#97

—

111

C₄×C₈

—

112

C₄×C₈

C₂×D₁₉

yes

characteristic

113

C₁₉

#3176

yes

characteristic, complemented, Sylow

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

C₂²×D₁₉

yes

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

D₈

—

120

D₈

—

121

M₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₂²×D₁₉

yes

characteristic

126

C₂×C₈

C₂²×D₁₉

yes

characteristic

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₂²⋊C₄

—

131

C₂²⋊C₄

—

132

C₂²⋊C₄

—

133

C₄²

—

134

C₄²

C₂²×D₁₉

yes

characteristic

135

C₂³

—

136

C₂³

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

152

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

152

—

147

C₂×C₄

D₄×D₁₉

yes

—

148

C₂×C₄

C₂³×D₁₉

yes

characteristic

149

C₈

—

150

C₈

—

151

C₈

#64543

yes

—

152

C₈

#64543

yes

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

C₂×D₄×D₁₉

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

C₂×#64543

yes

characteristic

164

C₄

C₂×#64543

yes

characteristic

165

C₂

—

166

C₂

—

167

C₂

#11927092

yes

characteristic

168

C₂

#11927345

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#493	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#493	D₁₉
hypocenter	C₁₉	#3176
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#493

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #11927148	C₂	semidirect
2. #11926946	C₂	semidirect
3. #11926908	C₂	semidirect
4. #11926794	C₂	semidirect
5. #11926777	C₂	semidirect
6. #11926656	C₂	semidirect
7. D₈×Dic₁₉	C₂	semidirect
8. #11926498	C₂	semidirect
9. C₁₉×#493	C₂	semidirect
83. #493	D₁₉	semidirect
113. C₁₉	#3176	semidirect

H ≅ G/N

type

1. #11927148

C₂

semidirect

2. #11926946

C₂

semidirect

3. #11926908

C₂

semidirect

4. #11926794

C₂

semidirect

5. #11926777

C₂

semidirect

6. #11926656

C₂

semidirect

7. D₈×Dic₁₉

C₂

semidirect

8. #11926498

C₂

semidirect

9. C₁₉×#493

C₂

semidirect

83. #493

D₁₉

semidirect

113. C₁₉

#3176

semidirect

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

subgroup	index
#11927148	2
#11926946	2
#11926908	2
#11926794	2
#11926777	2
#11926656	2
D₈×Dic₁₉	2
#11926498	2
C₁₉×#493	2
#3176	19

subgroup

index

D₈×Dic₁₉

C₁₉×#493

Subgroups — #14574282

Conjugacy classes of subgroups

Complements

Maximal subgroups