Group #14562143 — subgroups

Subgroups — #14562143

Order 2432.

272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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	#11926601	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926390	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926278	C₂	1	4	yes	maximal, complemented
4	C₁₉×#532	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₁₉	—	2	1	no	—
6	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
7	C₁₉×#127	C₄	1	1	yes	characteristic, complemented
8	C₁₉×#124	—	2	1	no	—
9	C₁₉×#121	—	2	1	no	—
10	C₁₉×#121	C₂²	1	2	yes	—
11	C₄×D₄×C₁₉	—	2	1	no	—
12	C₄×D₄×C₁₉	C₄	1	2	yes	complemented
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	—	2	1	no	—
15	C₁₉⋊#95	—	2	1	no	—
16	C₁₉⋊#95	C₂²	1	2	yes	—
17	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
18	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
19	#10597260	—	2	1	no	—
20	#41×C₁₉	—	4	4	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	2	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	—	2	2	no	—
27	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₄×Dic₁₉	—	2	4	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
43	Q₈×C₁₉	—	4	2	no	—
44	D₄×C₁₉	—	4	2	no	—
45	D₄×C₁₉	—	4	2	no	—
46	D₄×C₁₉	—	4	4	no	—
47	D₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	4	no	—
53	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×Dic₁₉	—	2	4	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	C₂×Dic₁₉	—	4	2	no	—
62	C₁₉⋊C₈	—	4	2	no	—
63	#1505	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	—	4	2	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	4	2	no	—
77	C₄×C₁₉	#104	1	2	yes	—
78	Dic₁₉	—	4	4	no	—
79	#532	D₁₉	1	1	yes	characteristic
80	#432	—	19	1	no	—
81	#376	—	19	1	no	—
82	#327	—	19	4	no	—
83	C₂×C₁₉	—	2	2	no	—
84	C₂×C₁₉	—	8	2	no	—
85	C₂×C₁₉	#410	1	1	yes	characteristic
86	C₂×C₁₉	#418	1	1	yes	characteristic
87	C₂×C₁₉	C₂×#104	1	1	yes	characteristic
88	C₂×#41	—	2	1	no	—
89	C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic, complemented
90	#127	Dic₁₉	1	1	yes	characteristic, complemented
91	#124	—	2	1	no	—
92	#121	—	2	1	no	—
93	#121	C₂×D₁₉	1	2	yes	—
94	C₄×D₄	—	2	1	no	—
95	C₄×D₄	Dic₁₉	1	2	yes	complemented
96	C₂×C₄²	—	38	1	no	—
97	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
98	C₄⋊C₈	—	38	1	no	—
99	C₂²⋊C₈	—	19	2	no	—
100	#97	—	38	1	no	—
101	#95	—	19	2	no	—
102	#95	—	38	1	no	—
103	C₁₉	#1505	1	1	yes	characteristic, complemented, Sylow
104	#41	—	4	4	no	—
105	C₂×Q₈	—	2	1	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	2	1	no	—
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
110	C₂²×C₄	—	2	2	no	—
111	C₂²×C₄	—	38	2	no	—
112	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
114	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
115	C₂×C₈	—	38	2	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
118	C₂²⋊C₄	—	2	2	no	—
119	C₂²⋊C₄	—	2	2	no	—
120	C₄²	—	38	4	no	—
121	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
122	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
123	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
124	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
125	C₂³	—	2	2	no	—
126	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	Q₈	—	4	2	no	—
128	D₄	—	4	2	no	—
129	D₄	—	4	2	no	—
130	D₄	—	4	4	no	—
131	D₄	—	4	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	—	4	4	no	—
137	C₂×C₄	—	38	4	no	—
138	C₂×C₄	—	76	2	no	—
139	C₂×C₄	—	76	2	no	—
140	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
141	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
142	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
143	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
144	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
145	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
146	C₈	—	76	2	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	4	2	no	—
150	C₂²	—	4	2	no	—
151	C₂²	—	4	2	no	—
152	C₂²	#10597378	1	2	yes	—
153	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
154	C₄	—	2	1	no	—
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	—	2	1	no	—
159	C₄	—	4	2	no	—
160	C₄	—	76	4	no	—
161	C₄	#10597294	1	2	yes	—
162	C₂	—	2	2	no	—
163	C₂	—	8	2	no	—
164	C₂	#11926518	1	1	yes	characteristic
165	C₂	#11926549	1	1	yes	characteristic
166	C₂	C₂×#10597294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, characteristic, complemented

#11926390

C₂

yes

maximal, characteristic, complemented

#11926278

C₂

yes

maximal, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

—

C₁₉×C₄⋊Q₈

C₄

yes

characteristic, complemented

C₁₉×#127

C₄

yes

characteristic, complemented

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

C₂²

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

C₄

yes

complemented

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1505

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#104

yes

—

Dic₁₉

—

#532

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×#41

—

C₄⋊Q₈

Dic₁₉

yes

characteristic, complemented

#127

Dic₁₉

yes

characteristic, complemented

#124

—

#121

—

#121

C₂×D₁₉

yes

—

C₄×D₄

—

C₄×D₄

Dic₁₉

yes

complemented

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

100

#97

—

101

#95

—

102

#95

—

103

C₁₉

#1505

yes

characteristic, complemented, Sylow

104

#41

—

105

C₂×Q₈

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

C₂×Dic₁₉

yes

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

113

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

114

C₂²×C₄

C₂²×D₁₉

yes

characteristic

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

C₂×Dic₁₉

yes

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

—

121

C₄²

C₂×Dic₁₉

yes

characteristic

122

C₄²

C₂×Dic₁₉

yes

characteristic

123

C₄²

C₂²⋊D₁₉

yes

characteristic

124

C₄²

C₂²⋊D₁₉

yes

characteristic

125

C₂³

—

126

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

127

Q₈

—

128

D₄

—

129

D₄

—

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

—

139

C₂×C₄

—

140

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

141

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

142

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

143

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

144

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

145

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

#10597378

yes

—

153

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

#10597294

yes

—

162

C₂

—

163

C₂

—

164

C₂

#11926518

yes

characteristic

165

C₂

#11926549

yes

characteristic

166

C₂

C₂×#10597294

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#532	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#532	D₁₉
hypocenter	C₁₉	#1505
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting, prime radical

C₁₉×#532

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. #11926601	C₂	semidirect
2. #11926390	C₂	semidirect
3. #11926278	C₂	semidirect
6. C₁₉×C₄⋊Q₈	C₄	semidirect
7. C₁₉×#127	C₄	semidirect
12. C₄×D₄×C₁₉	C₄	semidirect
89. C₄⋊Q₈	Dic₁₉	semidirect
90. #127	Dic₁₉	semidirect
95. C₄×D₄	Dic₁₉	semidirect
103. C₁₉	#1505	semidirect

H ≅ G/N

type

1. #11926601

C₂

semidirect

2. #11926390

C₂

semidirect

3. #11926278

C₂

semidirect

6. C₁₉×C₄⋊Q₈

C₄

semidirect

7. C₁₉×#127

C₄

semidirect

12. C₄×D₄×C₁₉

C₄

semidirect

89. C₄⋊Q₈

Dic₁₉

semidirect

90. #127

Dic₁₉

semidirect

95. C₄×D₄

Dic₁₉

semidirect

103. C₁₉

#1505

semidirect

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

subgroup	index
#11926601	2
#11926390	2
#11926278	2
C₁₉×#532	2
#1505	19

subgroup

index

C₁₉×#532

Subgroups — #14562143

Conjugacy classes of subgroups

Complements

Maximal subgroups