Group #14574286 — subgroups

Subgroups — #14574286

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	#11927150	C₂	1	2	yes	maximal, complemented
2	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926910	C₂	1	2	yes	maximal, complemented
4	#11926798	C₂	1	2	yes	maximal, complemented
5	#11926781	C₂	1	2	yes	maximal, complemented
6	#11926655	C₂	1	2	yes	maximal, complemented
7	#11926626	C₂	1	2	yes	maximal, complemented
8	#11926498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#125	C₂²	1	2	yes	—
11	C₂×D₁₅₂	C₂²	1	2	yes	—
12	C₂×D₁₅₂	C₂²	1	2	yes	—
13	C₂×#64515	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
15	#10597341	—	2	4	no	—
16	#10597341	C₂²	1	4	yes	—
17	#10597340	—	2	4	no	—
18	#10597339	C₂²	1	4	yes	—
19	#10597320	C₂²	1	2	yes	—
20	#10597318	C₂²	1	1	yes	characteristic
21	C₁₉×#107	C₂²	1	2	yes	—
22	C₁₉×#106	C₂²	1	2	yes	—
23	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	#10597272	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
26	#10597266	C₂²	1	4	yes	—
27	#10597266	C₂²	1	4	yes	—
28	#10597260	C₂²	1	1	yes	characteristic
29	C₂×D₇₆	—	2	4	no	—
30	C₂×D₇₆	—	2	4	no	—
31	C₂×D₇₆	C₂³	1	4	yes	—
32	C₂×C₄×D₁₉	—	2	4	no	—
33	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
36	C₄⋊C₄×C₁₉	—	2	4	no	—
37	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
38	C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	(C₂×D₁₉)⋊C₄	—	2	4	no	—
40	(C₂×D₁₉)⋊C₄	—	2	4	no	—
41	(C₂×D₁₉)⋊C₄	D₄	1	2	yes	—
42	Dic₁₉⋊C₄	D₄	1	2	yes	—
43	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
45	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
46	D₁₅₂	—	2	4	no	—
47	D₁₅₂	—	2	4	no	—
48	#64515	—	2	2	no	—
49	C₈×D₁₉	—	2	2	no	—
50	C₂²×D₁₉	—	2	4	no	—
51	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
55	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
56	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
57	D₇₆	—	2	4	no	—
58	D₇₆	—	2	4	no	—
59	D₇₆	—	8	4	no	—
60	D₇₆	—	8	4	no	—
61	C₄×D₁₉	—	2	1	no	—
62	C₄×D₁₉	—	2	1	no	—
63	C₄×D₁₉	—	8	4	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	C₂²×D₄	1	1	yes	characteristic
70	C₂×D₁₉	—	2	1	no	—
71	C₂×D₁₉	—	2	2	no	—
72	C₂×D₁₉	—	4	4	no	—
73	C₂×D₁₉	—	4	4	no	—
74	C₂×D₁₉	—	4	4	no	—
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	—	4	4	no	—
77	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
78	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
79	Dic₁₉	—	2	1	no	—
80	Dic₁₉	—	2	2	no	—
81	#540	—	19	2	no	—
82	#499	D₁₉	1	1	yes	characteristic, complemented
83	#493	—	19	1	no	—
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	#532	1	1	yes	characteristic
91	C₂×C₁₉	#576	1	2	yes	—
92	D₁₉	—	4	1	no	—
93	D₁₉	—	8	4	no	—
94	C₂×D₈	—	19	2	no	—
95	C₂×D₈	—	19	2	no	—
96	C₂×M₁₆	—	19	1	no	—
97	C₂²×C₈	—	19	1	no	—
98	#127	—	19	2	no	—
99	#125	C₂×D₁₉	1	2	yes	—
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	C₂×D₁₉	1	2	yes	—
106	#106	C₂×D₁₉	1	2	yes	—
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	—	19	4	no	—
115	C₂×D₄	—	38	4	no	—
116	C₂×D₄	—	38	4	no	—
117	C₂²×C₄	—	19	1	no	—
118	C₂²×C₄	—	38	4	no	—
119	D₈	—	38	4	no	—
120	D₈	—	38	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	—	2	4	no	—
128	C₄⋊C₄	—	19	2	no	—
129	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
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	—	19	1	no	—
136	C₂³	—	38	4	no	—
137	D₄	—	38	4	no	—
138	D₄	—	38	4	no	—
139	D₄	—	152	4	no	—
140	D₄	—	152	4	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	19	2	no	—
143	C₂×C₄	—	19	1	no	—
144	C₂×C₄	—	38	1	no	—
145	C₂×C₄	—	38	1	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	#64545	1	2	yes	—
152	C₈	#64545	1	2	yes	—
153	C₂²	—	38	2	no	—
154	C₂²	—	38	1	no	—
155	C₂²	—	76	4	no	—
156	C₂²	—	76	4	no	—
157	C₂²	—	76	4	no	—
158	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	4	4	no	—
161	C₄	—	38	2	no	—
162	C₄	—	38	1	no	—
163	C₄	C₂×#64545	1	1	yes	characteristic
164	C₄	C₂×#64545	1	1	yes	characteristic
165	C₂	—	76	1	no	—
166	C₂	—	152	4	no	—
167	C₂	#11927095	1	1	yes	characteristic
168	C₂	#11927346	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927150

C₂

yes

maximal, complemented

#11926921

C₂

yes

maximal, characteristic, complemented

#11926910

C₂

yes

maximal, complemented

#11926798

C₂

yes

maximal, complemented

#11926781

C₂

yes

maximal, complemented

#11926655

C₂

yes

maximal, complemented

#11926626

C₂

yes

maximal, complemented

#11926498

C₂

yes

maximal, characteristic, complemented

C₁₉×#499

C₂

yes

maximal, characteristic, complemented

C₁₉×#125

C₂²

yes

—

C₂×D₁₅₂

C₂²

yes

—

C₂×D₁₅₂

C₂²

yes

—

C₂×#64515

C₂²

yes

characteristic

C₂×C₈×D₁₉

C₂²

yes

characteristic

#10597341

—

#10597341

C₂²

yes

—

#10597340

—

#10597339

C₂²

yes

—

#10597320

C₂²

yes

—

#10597318

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

—

C₁₉×#106

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597272

C₂²

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

#10597266

C₂²

yes

—

#10597266

C₂²

yes

—

#10597260

C₂²

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

D₄

yes

—

Dic₁₉⋊C₄

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

D₁₅₂

—

D₁₅₂

—

#64515

—

C₈×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

#41

yes

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3176

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#41

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

#540

—

#499

D₁₉

yes

characteristic, complemented

—

—

—

—

—

C₄×D₈

—

#405

—

C₂×C₁₉

#532

yes

characteristic

C₂×C₁₉

#576

yes

—

D₁₉

—

D₁₉

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

—

#127

—

#125

C₂×D₁₉

yes

—

100

#123

—

101

#121

—

102

#121

—

103

C₄×D₄

—

104

#117

—

105

#107

C₂×D₁₉

yes

—

106

#106

C₂×D₁₉

yes

—

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

—

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

C₂²×D₁₉

yes

—

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

—

152

—

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

#64545

yes

—

152

C₈

#64545

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×#64545

yes

characteristic

164

C₄

C₂×#64545

yes

characteristic

165

C₂

—

166

C₂

—

152

—

167

C₂

#11927095

yes

characteristic

168

C₂

#11927346

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#499	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#499	D₁₉
hypocenter	C₁₉	#3176
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #499

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#499

C₂

socle

C₂²×C₁₉

C₂²×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #499

N	H ≅ G/N	type
1. #11927150	C₂	semidirect
2. #11926921	C₂	semidirect
3. #11926910	C₂	semidirect
4. #11926798	C₂	semidirect
5. #11926781	C₂	semidirect
6. #11926655	C₂	semidirect
7. #11926626	C₂	semidirect
8. #11926498	C₂	semidirect
9. C₁₉×#499	C₂	semidirect
82. #499	D₁₉	semidirect
113. C₁₉	#3176	semidirect

H ≅ G/N

type

1. #11927150

C₂

semidirect

2. #11926921

C₂

semidirect

3. #11926910

C₂

semidirect

4. #11926798

C₂

semidirect

5. #11926781

C₂

semidirect

6. #11926655

C₂

semidirect

7. #11926626

C₂

semidirect

8. #11926498

C₂

semidirect

9. C₁₉×#499

C₂

semidirect

82. #499

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
#11927150	2
#11926921	2
#11926910	2
#11926798	2
#11926781	2
#11926655	2
#11926626	2
#11926498	2
C₁₉×#499	2
#3176	19

subgroup

index

C₁₉×#499

Subgroups — #14574286

Conjugacy classes of subgroups

Complements

Maximal subgroups