Group #14563629 — subgroups

Subgroups — #14563629

Order 2432.

272 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 95 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×Q₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926567	C₂	1	2	yes	maximal
3	C₂×#10597293	C₂	1	1	yes	maximal, characteristic
4	#11926312	C₂	1	2	yes	maximal
5	C₂×C₁₉×#101	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	Q₈×Dic₁₉	—	2	2	no	—
9	Q₈×Dic₁₉	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	C₄	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₉	C₄	1	2	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×#64520	C₂²	1	2	yes	—
15	C₁₉×#101	—	2	2	no	—
16	#10597293	—	2	2	no	—
17	Dic₁₉⋊C₈	—	2	2	no	—
18	Dic₁₉⋊C₈	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	D₄	1	2	yes	—
22	C₂×Q₈×C₁₉	Q₈	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
27	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
28	M₁₆×C₁₉	—	2	2	no	—
29	M₁₆×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	4	no	—
33	C₄×Dic₁₉	—	2	2	no	—
34	C₄×Dic₁₉	—	2	2	no	—
35	C₄×Dic₁₉	D₄	1	2	yes	—
36	C₄×Dic₁₉	D₄	1	2	yes	—
37	#64520	—	2	2	no	—
38	#64520	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	Q₈×C₁₉	—	2	4	no	—
42	Q₈×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
46	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#41	1	2	yes	—
50	C₂×Dic₁₉	—	2	2	no	—
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	4	1	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	C₂×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×Dic₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₈×C₁₉	—	4	2	no	—
58	C₁₉⋊C₈	—	4	2	no	—
59	#1801	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₁₉	#117	1	1	yes	characteristic
65	C₄×C₁₉	—	2	4	no	—
66	C₄×C₁₉	#121	1	2	yes	—
67	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
68	Dic₁₉	—	2	1	no	—
69	Dic₁₉	—	2	2	no	—
70	Dic₁₉	—	4	2	no	—
71	Dic₁₉	#101	1	2	yes	complemented
72	C₂×C₄×Q₈	—	19	1	no	—
73	#423	—	19	2	no	—
74	C₂×#101	—	19	1	no	—
75	C₂×#101	D₁₉	1	1	yes	characteristic
76	#343	—	19	2	no	—
77	C₂×C₁₉	—	2	1	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	#380	1	1	yes	characteristic
80	C₂×C₁₉	C₂×#101	1	1	yes	characteristic
81	C₂×C₁₉	#413	1	1	yes	characteristic
82	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
83	C₂×M₁₆	—	19	2	no	—
84	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
85	C₄×Q₈	—	38	2	no	—
86	C₄×Q₈	—	38	2	no	—
87	C₂×C₄⋊C₄	—	19	2	no	—
88	C₂×C₄⋊C₄	—	19	1	no	—
89	C₂×C₄²	—	19	1	no	—
90	C₂×C₄²	—	19	2	no	—
91	C₄⋊C₈	—	38	2	no	—
92	C₄⋊C₈	—	38	2	no	—
93	#101	—	2	2	no	—
94	#101	—	38	2	no	—
95	C₁₉	#1801	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	2	2	no	—
97	C₂×Q₈	—	2	2	no	—
98	C₂×Q₈	Dic₃₈	1	2	yes	—
99	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
100	C₂²×C₄	—	19	1	no	—
101	C₂²×C₄	—	19	1	no	—
102	C₂²×C₄	—	19	2	no	—
103	C₂²×C₄	C₄×D₁₉	1	2	yes	—
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	M₁₆	—	2	2	no	—
106	M₁₆	—	2	2	no	—
107	M₁₆	—	38	2	no	—
108	M₁₆	—	38	2	no	—
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	38	2	no	—
111	C₄⋊C₄	—	38	4	no	—
112	C₄⋊C₄	—	38	2	no	—
113	C₄²	—	19	2	no	—
114	C₄²	—	19	2	no	—
115	C₄²	—	38	2	no	—
116	C₄²	—	38	2	no	—
117	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
118	Q₈	—	2	4	no	—
119	Q₈	—	2	4	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	19	1	no	—
123	C₂×C₄	—	19	1	no	—
124	C₂×C₄	—	19	2	no	—
125	C₂×C₄	—	38	2	no	—
126	C₂×C₄	—	38	2	no	—
127	C₂×C₄	—	76	1	no	—
128	C₂×C₄	—	76	2	no	—
129	C₂×C₄	Dic₁₉⋊C₄	1	4	yes	—
130	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
131	C₂×C₄	D₄×D₁₉	1	2	yes	—
132	C₂×C₄	#64543	1	2	yes	—
133	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
134	C₈	—	4	2	no	—
135	C₈	—	76	2	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	#10597323	1	1	yes	characteristic
139	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
140	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	19	2	no	—
143	C₄	—	38	1	no	—
144	C₄	—	38	2	no	—
145	C₄	—	76	2	no	—
146	C₄	#10597324	1	2	yes	—
147	C₄	#10597385	1	2	yes	—
148	C₂	—	2	1	no	—
149	C₂	—	2	1	no	—
150	C₂	#11926402	1	1	yes	characteristic
151	C₂	#101×D₁₉	1	1	yes	characteristic
152	C₂	#11926527	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₁₉

C₂

yes

maximal, characteristic

#11926567

C₂

yes

maximal

C₂×#10597293

C₂

yes

maximal, characteristic

#11926312

C₂

yes

maximal

C₂×C₁₉×#101

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

Q₈×Dic₁₉

—

Q₈×Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₄

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₁₉×#101

—

#10597293

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₉

C₂²⋊C₄

yes

—

C₂×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

#1801

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#101

yes

complemented

C₂×C₄×Q₈

—

#423

—

C₂×#101

—

C₂×#101

D₁₉

yes

characteristic

#343

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

#101

—

#101

—

C₁₉

#1801

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₃₈

yes

—

C₂×Q₈

C₂²⋊D₁₉

yes

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₄×D₁₉

yes

—

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

M₁₆

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₂³

C₂×C₄×D₁₉

yes

characteristic

118

Q₈

—

119

Q₈

—

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

—

129

C₂×C₄

Dic₁₉⋊C₄

yes

—

130

C₂×C₄

C₂×Dic₃₈

yes

characteristic

131

C₂×C₄

D₄×D₁₉

yes

—

132

C₂×C₄

#64543

yes

—

133

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

—

138

C₂²

#10597323

yes

characteristic

139

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

140

C₂²

C₂×Dic₁₉⋊C₄

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

#10597324

yes

—

147

C₄

#10597385

yes

—

148

C₂

—

149

C₂

—

150

C₂

#11926402

yes

characteristic

151

C₂

#101×D₁₉

yes

characteristic

152

C₂

#11926527

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₁₉
commutator, prime radical	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#101	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#101	D₁₉
hypocenter	C₁₉	#1801
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₁₉

commutator, prime radical

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#101

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
71. Dic₁₉	#101	semidirect
95. C₁₉	#1801	semidirect

H ≅ G/N

type

71. Dic₁₉

#101

semidirect

95. C₁₉

#1801

semidirect

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

subgroup	index
C₂×Q₈×Dic₁₉	2
#11926567	2
C₂×#10597293	2
#11926312	2
C₂×C₁₉×#101	2
#1801	19

subgroup

index

C₂×Q₈×Dic₁₉

C₂×C₁₉×#101

Subgroups — #14563629

Conjugacy classes of subgroups

Complements

Maximal subgroups