Group #14559881 — subgroups

Subgroups — C₁₉×#2024 #14559881

Order 2432.

290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 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×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#103	C₂	1	2	yes	maximal
3	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#340	C₂	1	2	yes	maximal
5	C₁₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	—	2	1	no	—
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
9	C₁₉×C₄⋊Q₈	—	2	4	no	—
10	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#103	—	2	4	no	—
15	C₁₉×#95	—	2	1	no	—
16	C₁₉×#95	—	2	1	no	—
17	C₂×Q₈×C₁₉	—	2	4	no	—
18	C₂×Q₈×C₁₉	—	2	1	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	4	2	no	—
22	C₂×Q₈×C₁₉	—	4	2	no	—
23	C₂×Q₈×C₁₉	Q₈	1	2	yes	complemented
24	C₂²×C₄×C₁₉	—	2	2	no	—
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	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	C₂×C₈×C₁₉	—	2	2	no	—
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₄⋊C₄×C₁₉	—	2	4	no	—
34	C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₄⋊C₄×C₁₉	D₄	1	4	yes	—
37	C₄²×C₁₉	—	2	2	no	—
38	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
39	Q₈×C₁₉	—	2	4	no	—
40	Q₈×C₁₉	—	4	8	no	—
41	Q₈×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	—	4	2	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
56	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#41	1	2	yes	—
60	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₈×C₁₉	—	4	2	no	—
62	#2024	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₁₉	#120	1	1	yes	characteristic
64	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂²×C₁₉	#124	1	1	yes	characteristic
66	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
67	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
68	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
69	C₂²×C₁₉	#137	1	1	yes	characteristic
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	4	2	no	—
73	C₄×C₁₉	—	4	4	no	—
74	C₄×C₁₉	—	8	1	no	—
75	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
76	C₄×C₁₉	#124	1	2	yes	—
77	C₂×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
78	C₂×#103	C₂×C₁₉	1	2	yes	—
79	#391	C₂×C₁₉	1	1	yes	characteristic
80	#340	C₂×C₁₉	1	2	yes	—
81	#336	C₂×C₁₉	1	1	yes	characteristic
82	C₂×C₁₉	#393	1	1	yes	characteristic
83	C₂×C₁₉	#450	1	1	yes	characteristic
84	C₂×C₁₉	#451	1	1	yes	characteristic
85	C₂×C₁₉	#475	1	1	yes	characteristic
86	C₂×C₁₉	#477	1	1	yes	characteristic
87	C₂×C₁₉	#487	1	1	yes	characteristic
88	C₂×C₁₉	#489	1	1	yes	characteristic
89	C₂²×Q₈	—	2	1	no	—
90	C₂²×Q₈	C₂²×C₁₉	1	1	yes	characteristic
91	C₂²×C₈	C₂²×C₁₉	1	2	yes	—
92	C₄⋊Q₈	—	2	4	no	—
93	C₂×C₄⋊C₄	—	2	1	no	—
94	C₂×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
95	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
96	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
97	#103	—	2	4	no	—
98	#95	—	2	1	no	—
99	#95	—	2	1	no	—
100	C₁₉	#2024	1	1	yes	characteristic, direct product factor, Sylow
101	C₂×Q₈	—	2	4	no	—
102	C₂×Q₈	—	2	1	no	—
103	C₂×Q₈	—	2	2	no	—
104	C₂×Q₈	—	2	2	no	—
105	C₂×Q₈	—	4	2	no	—
106	C₂×Q₈	—	4	2	no	—
107	C₂×Q₈	Q₈×C₁₉	1	2	yes	complemented
108	C₂²×C₄	—	2	1	no	—
109	C₂²×C₄	—	2	2	no	—
110	C₂²×C₄	—	2	1	no	—
111	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
112	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₄⋊C₄	—	2	4	no	—
118	C₄⋊C₄	—	2	2	no	—
119	C₄⋊C₄	—	2	2	no	—
120	C₄⋊C₄	D₄×C₁₉	1	4	yes	—
121	C₄²	—	2	2	no	—
122	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
123	Q₈	—	2	4	no	—
124	Q₈	—	4	8	no	—
125	Q₈	—	4	2	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	4	2	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	4	1	no	—
138	C₂×C₄	—	4	1	no	—
139	C₂×C₄	SD₁₆×C₁₉	1	2	yes	—
140	C₂×C₄	Q₁₆×C₁₉	1	2	yes	—
141	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
142	C₂×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
143	C₂×C₄	#41×C₁₉	1	2	yes	—
144	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
145	C₈	—	4	2	no	—
146	C₂²	C₁₉×#120	1	1	yes	characteristic
147	C₂²	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
148	C₂²	C₁₉×#124	1	1	yes	characteristic
149	C₂²	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
150	C₂²	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
151	C₂²	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂²	C₁₉×#137	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	2	no	—
156	C₄	—	4	4	no	—
157	C₄	—	8	1	no	—
158	C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
159	C₄	C₁₉×#124	1	2	yes	—
160	C₂	C₁₉×#393	1	1	yes	characteristic
161	C₂	C₁₉×#450	1	1	yes	characteristic
162	C₂	C₁₉×#451	1	1	yes	characteristic
163	C₂	C₁₉×#475	1	1	yes	characteristic
164	C₂	C₁₉×#477	1	1	yes	characteristic
165	C₂	C₁₉×#487	1	1	yes	characteristic
166	C₂	C₁₉×#489	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×C₁₉×#103

C₂

yes

maximal

C₁₉×#391

C₂

yes

maximal, characteristic

C₁₉×#340

C₂

yes

maximal

C₁₉×#336

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#103

—

C₁₉×#95

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₈×C₁₉

—

#2024

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#124

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#124

yes

—

C₂×C₄⋊Q₈

C₂×C₁₉

yes

characteristic

C₂×#103

C₂×C₁₉

yes

—

#391

C₂×C₁₉

yes

characteristic

#340

C₂×C₁₉

yes

—

#336

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×Q₈

C₂²×C₁₉

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²×C₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

C₂×C₄²

C₂²×C₁₉

yes

—

—

—

100

C₁₉

#2024

yes

characteristic, direct product factor, Sylow

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

Q₈×C₁₉

yes

complemented

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

D₄×C₁₉

yes

characteristic

112

C₂²×C₄

D₄×C₁₉

yes

characteristic

113

C₂²×C₄

C₂³×C₁₉

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

D₄×C₁₉

yes

—

121

C₄²

—

122

C₂³

C₂×D₄×C₁₉

yes

characteristic

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

SD₁₆×C₁₉

yes

—

140

C₂×C₄

Q₁₆×C₁₉

yes

—

141

C₂×C₄

C₂×D₄×C₁₉

yes

—

142

C₂×C₄

C₂×Q₈×C₁₉

yes

characteristic

143

C₂×C₄

#41×C₁₉

yes

—

144

C₂×C₄

#41×C₁₉

yes

characteristic

145

C₈

—

146

C₂²

C₁₉×#120

yes

characteristic

147

C₂²

C₁₉×C₂²⋊Q₈

yes

characteristic

148

C₂²

C₁₉×#124

yes

characteristic

149

C₂²

C₂×SD₁₆×C₁₉

yes

characteristic

150

C₂²

C₂×Q₁₆×C₁₉

yes

characteristic

151

C₂²

C₁₉×AGL(1,ℤ/8)

yes

characteristic

152

C₂²

C₁₉×#137

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

C₁₉×C₂²⋊Q₈

yes

—

159

C₄

C₁₉×#124

yes

—

160

C₂

C₁₉×#393

yes

characteristic

161

C₂

C₁₉×#450

yes

characteristic

162

C₂

C₁₉×#451

yes

characteristic

163

C₂

C₁₉×#475

yes

characteristic

164

C₂

C₁₉×#477

yes

characteristic

165

C₂

C₁₉×#487

yes

characteristic

166

C₂

C₁₉×#489

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₉

C₂×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₉

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
23. C₂×Q₈×C₁₉	Q₈	semidirect
62. #2024	C₁₉	direct (N × H)
100. C₁₉	#2024	direct (N × H)
107. C₂×Q₈	Q₈×C₁₉	semidirect

H ≅ G/N

type

23. C₂×Q₈×C₁₉

Q₈

semidirect

62. #2024

C₁₉

direct (N × H)

100. C₁₉

#2024

direct (N × H)

107. C₂×Q₈

Q₈×C₁₉

semidirect

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

subgroup	index
C₂×C₁₉×C₄⋊Q₈	2
C₂×C₁₉×#103	2
C₁₉×#391	2
C₁₉×#340	2
C₁₉×#336	2
#2024	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

C₂×C₁₉×#103

C₁₉×#391

C₁₉×#340

C₁₉×#336

#2024

Subgroups — C₁₉×#2024 #14559881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2024 #14559881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2024 #14559881