Group #14564353 — subgroups

Subgroups — #14564353

Order 2432.

260 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 133 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×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉⋊C₈	C₂	1	2	yes	maximal
3	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#11926298	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
12	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
13	C₄×C₈×C₁₉	—	2	2	no	—
14	C₁₉⋊#95	C₄	1	2	yes	—
15	Dic₁₉⋊C₈	—	2	4	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
21	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	—	2	1	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	D₄	1	2	yes	—
27	C₂×C₈×C₁₉	Q₈	1	2	yes	—
28	C₄²×C₁₉	D₄	1	2	yes	—
29	C₄²×C₁₉	Q₈	1	2	yes	—
30	C₄⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	C₈	1	4	yes	complemented
32	C₄×Dic₁₉	—	2	2	no	—
33	C₄×Dic₁₉	—	2	2	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
43	C₂×C₄×C₁₉	M₁₆	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×Q₈	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	2	no	—
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	2	2	no	—
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	C₂×C₈	1	4	yes	—
56	C₈×C₁₉	—	2	2	no	—
57	C₈×C₁₉	—	2	2	no	—
58	C₁₉⋊C₈	—	4	2	no	—
59	#1939	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
62	C₂²×C₁₉	C₄×Q₈	1	1	yes	characteristic
63	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
64	C₂²×C₁₉	C₂×M₁₆	1	1	yes	characteristic
65	C₂²×C₁₉	#131	1	1	yes	characteristic
66	C₂²×C₁₉	#131	1	1	yes	characteristic
67	C₄×C₁₉	—	2	2	no	—
68	C₄×C₁₉	C₄⋊C₈	1	4	yes	complemented
69	C₄×C₁₉	#121	1	1	yes	characteristic
70	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
71	C₄×C₁₉	#125	1	1	yes	characteristic
72	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
73	Dic₁₉	—	2	4	no	—
74	Dic₁₉	—	4	2	no	—
75	C₂×C₄⋊C₈	—	19	2	no	—
76	C₂×C₄⋊C₈	—	19	1	no	—
77	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic
78	C₄×C₄⋊C₄	—	19	1	no	—
79	#336	—	19	2	no	—
80	C₂×C₁₉	#389	1	1	yes	characteristic
81	C₂×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
82	C₂×C₁₉	#424	1	1	yes	characteristic
83	C₂×C₁₉	C₈×D₄	1	1	yes	characteristic
84	C₂×C₁₉	#436	1	1	yes	characteristic
85	C₂×C₁₉	C₈×Q₈	1	1	yes	characteristic
86	C₂×C₁₉	#446	1	1	yes	characteristic
87	C₂²×C₈	—	19	2	no	—
88	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
89	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
90	C₂×C₄⋊C₄	—	19	1	no	—
91	C₂×C₄⋊C₄	—	19	1	no	—
92	C₂×C₄²	—	19	2	no	—
93	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
94	C₄⋊C₈	—	38	4	no	—
95	C₄⋊C₈	—	38	2	no	—
96	C₄×C₈	—	2	2	no	—
97	#95	—	19	2	no	—
98	C₁₉	#1939	1	1	yes	characteristic, complemented, Sylow
99	C₂²×C₄	—	19	2	no	—
100	C₂²×C₄	—	19	2	no	—
101	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
102	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
103	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	38	2	no	—
109	C₂×C₈	—	38	2	no	—
110	C₂×C₈	—	38	2	no	—
111	C₂×C₈	Dic₃₈	1	2	yes	—
112	C₂×C₈	D₇₆	1	2	yes	—
113	C₄⋊C₄	—	19	4	no	—
114	C₄⋊C₄	—	38	2	no	—
115	C₄²	—	38	2	no	—
116	C₄²	—	38	2	no	—
117	C₄²	Dic₃₈	1	2	yes	—
118	C₄²	C₂²⋊D₁₉	1	2	yes	—
119	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	19	4	no	—
123	C₂×C₄	—	38	2	no	—
124	C₂×C₄	—	38	2	no	—
125	C₂×C₄	—	38	2	no	—
126	C₂×C₄	—	38	2	no	—
127	C₂×C₄	—	38	2	no	—
128	C₂×C₄	C₈×D₁₉	1	2	yes	—
129	C₂×C₄	#64515	1	2	yes	—
130	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
131	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
132	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
133	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
134	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
135	C₂×C₄	#64541	1	1	yes	characteristic
136	C₂×C₄	#64541	1	1	yes	characteristic
137	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
138	C₈	—	2	2	no	—
139	C₈	—	2	2	no	—
140	C₈	—	76	2	no	—
141	C₂²	C₄×Dic₃₈	1	1	yes	characteristic
142	C₂²	C₄×D₇₆	1	1	yes	characteristic
143	C₂²	C₂×C₈×D₁₉	1	1	yes	characteristic
144	C₂²	C₂×#64515	1	1	yes	characteristic
145	C₂²	#10597347	1	1	yes	characteristic
146	C₂²	#10597347	1	1	yes	characteristic
147	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
148	C₄	—	2	2	no	—
149	C₄	—	38	4	no	—
150	C₄	—	76	2	no	—
151	C₄	Dic₁₉⋊C₈	1	4	yes	complemented
152	C₄	#10597315	1	1	yes	characteristic
153	C₄	#10597316	1	1	yes	characteristic
154	C₄	#10597370	1	1	yes	characteristic
155	C₄	#10597376	1	1	yes	characteristic
156	C₂	#11926442	1	1	yes	characteristic
157	C₂	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
158	C₂	#11926570	1	1	yes	characteristic
159	C₂	C₈×D₇₆	1	1	yes	characteristic
160	C₂	#11926623	1	1	yes	characteristic
161	C₂	C₈×Dic₃₈	1	1	yes	characteristic
162	C₂	#11926674	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal

C₄×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal

C₂×C₄×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

C₄

yes

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

Q₈

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₈

yes

complemented

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×C₈

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1939

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

C₄×Q₈

yes

characteristic

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₂²×C₁₉

C₂×M₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

C₄⋊C₈

yes

complemented

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#125

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

D₁₉

yes

characteristic

C₄×C₄⋊C₄

—

#336

—

C₂×C₁₉

#389

yes

characteristic

C₂×C₁₉

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₉

#424

yes

characteristic

C₂×C₁₉

C₈×D₄

yes

characteristic

C₂×C₁₉

#436

yes

characteristic

C₂×C₁₉

C₈×Q₈

yes

characteristic

C₂×C₁₉

#446

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

#95

—

C₁₉

#1939

yes

characteristic, complemented, Sylow

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₄×D₁₉

yes

characteristic

102

C₂²×C₄

C₄×D₁₉

yes

characteristic

103

C₂²×C₄

C₂²×D₁₉

yes

characteristic

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

Dic₃₈

yes

—

112

C₂×C₈

D₇₆

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄²

—

116

C₄²

—

117

C₄²

Dic₃₈

yes

—

118

C₄²

C₂²⋊D₁₉

yes

—

119

C₂³

C₂×C₄×D₁₉

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₈×D₁₉

yes

—

129

C₂×C₄

#64515

yes

—

130

C₂×C₄

Dic₁₉⋊C₄

yes

—

131

C₂×C₄

Dic₁₉⋊C₄

yes

—

132

C₂×C₄

C₂×Dic₃₈

yes

characteristic

133

C₂×C₄

C₂×Dic₃₈

yes

characteristic

134

C₂×C₄

C₂×D₇₆

yes

characteristic

135

C₂×C₄

#64541

yes

characteristic

136

C₂×C₄

#64541

yes

characteristic

137

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

C₄×Dic₃₈

yes

characteristic

142

C₂²

C₄×D₇₆

yes

characteristic

143

C₂²

C₂×C₈×D₁₉

yes

characteristic

144

C₂²

C₂×#64515

yes

characteristic

145

C₂²

#10597347

yes

characteristic

146

C₂²

#10597347

yes

characteristic

147

C₂²

C₂×Dic₁₉⋊C₄

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

Dic₁₉⋊C₈

yes

complemented

152

C₄

#10597315

yes

characteristic

153

C₄

#10597316

yes

characteristic

154

C₄

#10597370

yes

characteristic

155

C₄

#10597376

yes

characteristic

156

C₂

#11926442

yes

characteristic

157

C₂

C₂×Dic₁₉⋊C₈

yes

characteristic

158

C₂

#11926570

yes

characteristic

159

C₂

C₈×D₇₆

yes

characteristic

160

C₂

#11926623

yes

characteristic

161

C₂

C₈×Dic₃₈

yes

characteristic

162

C₂

#11926674

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂²×C₈
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	#1939
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂²×C₈

Fitting

C₂×C₄×C₈×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂²×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₄×C₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
31. C₄⋊Dic₁₉	C₈	semidirect
68. C₄×C₁₉	C₄⋊C₈	semidirect
98. C₁₉	#1939	semidirect
151. C₄	Dic₁₉⋊C₈	semidirect

H ≅ G/N

type

31. C₄⋊Dic₁₉

C₈

semidirect

68. C₄×C₁₉

C₄⋊C₈

semidirect

98. C₁₉

#1939

semidirect

151. C₄

Dic₁₉⋊C₈

semidirect

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

subgroup	index
C₂×C₄⋊(C₁₉⋊C₈)	2
C₂×Dic₁₉⋊C₈	2
C₄×C₄⋊Dic₁₉	2
#11926298	2
C₂×C₄×C₈×C₁₉	2
#1939	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₂×Dic₁₉⋊C₈

C₄×C₄⋊Dic₁₉

#11926298

C₂×C₄×C₈×C₁₉

#1939

Subgroups — #14564353

Conjugacy classes of subgroups

Complements

Maximal subgroups