Group #14563650 — subgroups

Subgroups — #14563650

Order 2432.

292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597292	C₂	1	2	yes	maximal
3	#11926410	C₂	1	1	yes	maximal, characteristic
4	#11926306	C₂	1	2	yes	maximal
5	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₄×Q₈×C₁₉	—	2	2	no	—
8	C₄×Q₈×C₁₉	C₄	1	4	yes	complemented
9	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	—	2	1	no	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597292	—	2	4	no	—
16	C₁₉⋊#95	—	2	1	no	—
17	C₁₉⋊#95	—	2	1	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	C₂×Q₈×C₁₉	—	2	1	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×Q₈×C₁₉	D₄	1	2	yes	—
24	C₂×Q₈×C₁₉	Q₈	1	2	yes	—
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	C₂²×Dic₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	—	2	4	no	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₄²×C₁₉	—	2	4	no	—
35	C₄²×C₁₉	C₂×C₄	1	2	yes	—
36	C₄²×C₁₉	D₄	1	2	yes	—
37	C₄⋊Dic₁₉	—	2	2	no	—
38	C₄⋊Dic₁₉	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
43	Q₈×C₁₉	—	2	2	no	—
44	Q₈×C₁₉	—	2	2	no	—
45	Q₈×C₁₉	—	2	2	no	—
46	Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
47	C₂×C₄×C₁₉	—	2	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	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂×Dic₁₉	—	4	2	no	—
63	C₂×Dic₁₉	—	4	2	no	—
64	C₂×Dic₁₉	—	4	2	no	—
65	C₁₉⋊C₈	—	4	2	no	—
66	#1805	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₁₉	#121	1	1	yes	characteristic
69	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
70	C₂²×C₁₉	#135	1	2	yes	—
71	C₂²×C₁₉	#137	1	2	yes	—
72	C₄×C₁₉	—	2	4	no	—
73	C₄×C₁₉	—	2	2	no	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	4	2	no	—
76	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₄×C₁₉	#117	1	1	yes	characteristic
78	C₄×C₁₉	#121	1	1	yes	characteristic
79	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
80	Dic₁₉	—	8	2	no	—
81	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic
82	C₂×C₄⋊C₈	—	19	1	no	—
83	C₂×#103	—	19	2	no	—
84	#382	—	19	1	no	—
85	#340	—	19	2	no	—
86	C₂×C₁₉	#380	1	1	yes	characteristic
87	C₂×C₁₉	#416	1	1	yes	characteristic
88	C₂×C₁₉	#419	1	1	yes	characteristic
89	C₂×C₁₉	#464	1	2	yes	—
90	C₂×C₁₉	#479	1	2	yes	—
91	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
92	C₂²×C₈	—	19	2	no	—
93	C₄×Q₈	—	2	2	no	—
94	C₄×Q₈	Dic₁₉	1	4	yes	complemented
95	C₂×C₄⋊C₄	—	2	1	no	—
96	C₂×C₄⋊C₄	—	19	2	no	—
97	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
98	C₂×C₄²	—	2	1	no	—
99	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
100	C₄⋊C₈	—	38	2	no	—
101	#103	—	38	4	no	—
102	#95	—	38	1	no	—
103	#95	—	38	1	no	—
104	C₁₉	#1805	1	1	yes	characteristic, complemented, Sylow
105	C₂×Q₈	—	2	1	no	—
106	C₂×Q₈	—	2	1	no	—
107	C₂×Q₈	—	2	1	no	—
108	C₂×Q₈	Dic₃₈	1	2	yes	—
109	C₂×Q₈	D₇₆	1	2	yes	—
110	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
111	C₂²×C₄	—	2	1	no	—
112	C₂²×C₄	—	2	1	no	—
113	C₂²×C₄	—	38	2	no	—
114	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	—	38	2	no	—
119	C₂×C₈	—	38	2	no	—
120	C₄⋊C₄	—	2	4	no	—
121	C₄⋊C₄	—	2	1	no	—
122	C₄⋊C₄	—	38	2	no	—
123	C₄⋊C₄	—	38	2	no	—
124	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
125	C₄²	—	2	4	no	—
126	C₄²	C₂×Dic₁₉	1	2	yes	—
127	C₄²	C₂²⋊D₁₉	1	2	yes	—
128	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
129	Q₈	—	2	2	no	—
130	Q₈	—	2	2	no	—
131	Q₈	—	2	2	no	—
132	Q₈	C₄⋊Dic₁₉	1	4	yes	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	4	2	no	—
140	C₂×C₄	—	76	2	no	—
141	C₂×C₄	—	76	2	no	—
142	C₂×C₄	—	76	2	no	—
143	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
144	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
145	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
146	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
147	C₂×C₄	#64541	1	1	yes	characteristic
148	C₂×C₄	#64541	1	1	yes	characteristic
149	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
150	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
151	C₈	—	76	2	no	—
152	C₂²	#10597370	1	1	yes	characteristic
153	C₂²	#10597376	1	1	yes	characteristic
154	C₂²	#10597388	1	2	yes	—
155	C₂²	#10597396	1	2	yes	—
156	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
157	C₄	—	2	2	no	—
158	C₄	—	2	2	no	—
159	C₄	—	2	4	no	—
160	C₄	—	4	2	no	—
161	C₄	—	152	2	no	—
162	C₄	#10597370	1	1	yes	characteristic
163	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
164	C₄	#10597372	1	1	yes	characteristic
165	C₄	#10597376	1	1	yes	characteristic
166	C₂	#11926404	1	1	yes	characteristic
167	C₂	#11926540	1	1	yes	characteristic
168	C₂	#11926553	1	1	yes	characteristic
169	C₂	#11926766	1	2	yes	—
170	C₂	#11926851	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

C₂×C₄×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

C₄

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

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

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1805

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#135

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

Dic₁₉

—

C₂×C₄×Q₈

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₂×#103

—

#382

—

#340

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#479

yes

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

Dic₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

100

C₄⋊C₈

—

101

#103

—

102

#95

—

103

#95

—

104

C₁₉

#1805

yes

characteristic, complemented, Sylow

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

Dic₃₈

yes

—

109

C₂×Q₈

D₇₆

yes

—

110

C₂×Q₈

C₂×Dic₁₉

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

115

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

116

C₂²×C₄

C₂²×D₁₉

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

C₂×Dic₁₉

yes

—

125

C₄²

—

126

C₄²

C₂×Dic₁₉

yes

—

127

C₄²

C₂²⋊D₁₉

yes

—

128

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

129

Q₈

—

130

Q₈

—

131

Q₈

—

132

Q₈

C₄⋊Dic₁₉

yes

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

C₂²⋊Dic₁₉

yes

—

144

C₂×C₄

C₂²⋊Dic₁₉

yes

—

145

C₂×C₄

C₂×Dic₃₈

yes

characteristic

146

C₂×C₄

C₂×D₇₆

yes

characteristic

147

C₂×C₄

#64541

yes

characteristic

148

C₂×C₄

#64541

yes

characteristic

149

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

150

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

151

C₈

—

152

C₂²

#10597370

yes

characteristic

153

C₂²

#10597376

yes

characteristic

154

C₂²

#10597388

yes

—

155

C₂²

#10597396

yes

—

156

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

—

152

—

162

C₄

#10597370

yes

characteristic

163

C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

164

C₄

#10597372

yes

characteristic

165

C₄

#10597376

yes

characteristic

166

C₂

#11926404

yes

characteristic

167

C₂

#11926540

yes

characteristic

168

C₂

#11926553

yes

characteristic

169

C₂

#11926766

yes

—

170

C₂

#11926851

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₄×Q₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	#1805
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₄×Q₈×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₄×Q₈

D₁₉

hypocenter

C₁₉

#1805

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
8. C₄×Q₈×C₁₉	C₄	semidirect
94. C₄×Q₈	Dic₁₉	semidirect
104. C₁₉	#1805	semidirect

H ≅ G/N

type

8. C₄×Q₈×C₁₉

C₄

semidirect

94. C₄×Q₈

Dic₁₉

semidirect

104. C₁₉

#1805

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×#10597292	2
#11926410	2
#11926306	2
C₂×C₄×Q₈×C₁₉	2
#1805	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₂×C₄×Q₈×C₁₉

Subgroups — #14563650

Conjugacy classes of subgroups

Complements

Maximal subgroups