Group #14563717 — subgroups

Subgroups — #14563717

Order 2432.

272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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×#10597338	C₂	1	1	yes	maximal, characteristic
2	#11926507	C₂	1	2	yes	maximal
3	#11926313	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926312	C₂	1	2	yes	maximal, complemented
5	C₁₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×(C₂×D₁₉)⋊C₄	C₄	1	2	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₉	C₄	1	2	yes	—
12	C₂×#64520	C₂²	1	2	yes	—
13	#10597338	—	2	4	no	—
14	(C₂×D₁₉)⋊C₈	—	2	4	no	—
15	C₂³×D₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄×D₁₉	—	2	2	no	—
21	C₂×C₄×D₁₉	—	2	1	no	—
22	C₂×C₄×D₁₉	—	2	1	no	—
23	C₂×C₄×D₁₉	D₄	1	4	yes	—
24	M₁₆×C₁₉	—	2	2	no	—
25	M₁₆×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	(C₂×D₁₉)⋊C₄	—	2	4	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄×Dic₁₉	—	2	4	no	—
31	#64520	—	2	2	no	—
32	#64520	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	2	2	no	—
34	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂²×D₁₉	—	2	1	no	—
36	C₂²×D₁₉	—	2	1	no	—
37	C₂²×D₁₉	—	4	1	no	—
38	C₂²×D₁₉	—	4	1	no	—
39	C₂²×D₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₉	#41	1	2	yes	—
44	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×Dic₁₉	—	2	1	no	—
47	C₂×Dic₁₉	—	2	1	no	—
48	C₂×Dic₁₉	—	2	2	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	C₂²⋊C₄	1	2	yes	—
51	C₄×D₁₉	—	2	4	no	—
52	C₄×D₁₉	—	2	4	no	—
53	C₈×C₁₉	—	4	2	no	—
54	C₁₉⋊C₈	—	4	2	no	—
55	#1822	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₁₉	#117	1	1	yes	characteristic
60	C₂²×C₁₉	#117	1	1	yes	characteristic
61	C₂×D₁₉	—	2	2	no	—
62	C₂×D₁₉	—	2	2	no	—
63	C₂×D₁₉	—	2	2	no	—
64	C₂×D₁₉	—	4	2	no	—
65	C₂×D₁₉	—	4	2	no	—
66	C₄×C₁₉	—	4	2	no	—
67	C₄×C₁₉	#123	1	2	yes	—
68	C₄×C₁₉	#123	1	2	yes	—
69	Dic₁₉	—	2	2	no	—
70	Dic₁₉	—	4	2	no	—
71	C₂×#117	—	19	1	no	—
72	#407	—	19	2	no	—
73	#343	—	19	2	no	—
74	#343	—	19	1	no	—
75	#343	D₁₉	1	1	yes	characteristic, complemented
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	—	2	1	no	—
78	C₂×C₁₉	#381	1	1	yes	characteristic
79	C₂×C₁₉	#413	1	1	yes	characteristic
80	C₂×C₁₉	#413	1	1	yes	characteristic
81	D₁₉	—	4	2	no	—
82	C₂³×C₄	—	19	1	no	—
83	C₂×M₁₆	—	19	2	no	—
84	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
85	#117	—	38	4	no	—
86	C₂×C₄⋊C₄	—	19	1	no	—
87	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
88	C₂×C₂²⋊C₄	—	19	2	no	—
89	C₂×C₄²	—	19	2	no	—
90	C₂²⋊C₈	—	38	4	no	—
91	C₁₉	#1822	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	—	19	1	no	—
93	C₂²×C₄	—	19	1	no	—
94	C₂²×C₄	—	19	4	no	—
95	C₂²×C₄	—	19	2	no	—
96	C₂²×C₄	—	38	2	no	—
97	C₂²×C₄	—	38	1	no	—
98	C₂²×C₄	—	38	1	no	—
99	C₂²×C₄	C₄×D₁₉	1	2	yes	—
100	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
101	M₁₆	—	2	2	no	—
102	M₁₆	—	2	2	no	—
103	M₁₆	—	38	2	no	—
104	M₁₆	—	38	2	no	—
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	38	2	no	—
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	38	2	no	—
109	C₂²⋊C₄	—	38	4	no	—
110	C₄²	—	38	4	no	—
111	C₂³	—	19	2	no	—
112	C₂³	—	38	1	no	—
113	C₂³	—	38	1	no	—
114	C₂³	—	76	1	no	—
115	C₂³	—	76	1	no	—
116	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	19	2	no	—
120	C₂×C₄	—	38	1	no	—
121	C₂×C₄	—	38	1	no	—
122	C₂×C₄	—	38	4	no	—
123	C₂×C₄	—	38	4	no	—
124	C₂×C₄	—	38	2	no	—
125	C₂×C₄	—	76	2	no	—
126	C₂×C₄	#64541	1	2	yes	—
127	C₂×C₄	D₄×D₁₉	1	2	yes	—
128	C₂×C₄	#64543	1	1	yes	characteristic
129	C₂×C₄	#64545	1	1	yes	characteristic
130	C₈	—	4	2	no	—
131	C₈	—	76	2	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	—	38	2	no	—
135	C₂²	—	38	2	no	—
136	C₂²	—	38	2	no	—
137	C₂²	—	76	2	no	—
138	C₂²	—	76	2	no	—
139	C₂²	#10597318	1	1	yes	characteristic
140	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
141	C₂²	#10597338	1	1	yes	characteristic
142	C₄	—	4	2	no	—
143	C₄	—	38	2	no	—
144	C₄	—	76	2	no	—
145	C₄	#10597329	1	2	yes	—
146	C₄	#10597340	1	2	yes	—
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	—	76	2	no	—
150	C₂	#11926406	1	1	yes	characteristic
151	C₂	#11926525	1	1	yes	characteristic
152	C₂	#11926527	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597338

C₂

yes

maximal, characteristic

#11926507

C₂

yes

maximal

#11926313

C₂

yes

maximal, characteristic, complemented

#11926312

C₂

yes

maximal, complemented

C₁₉×#343

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₄

yes

—

C₂×#64520

C₂²

yes

—

#10597338

—

(C₂×D₁₉)⋊C₈

—

C₂³×D₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²⋊C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1822

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#123

yes

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

C₁₉

#1822

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

—

100

C₂²×C₄

C₂²×D₁₉

yes

characteristic

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

C₂×C₄×D₁₉

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#64541

yes

—

127

C₂×C₄

D₄×D₁₉

yes

—

128

C₂×C₄

#64543

yes

characteristic

129

C₂×C₄

#64545

yes

characteristic

130

C₈

—

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

#10597318

yes

characteristic

140

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

141

C₂²

#10597338

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

#10597329

yes

—

146

C₄

#10597340

yes

—

147

C₂

—

148

C₂

—

149

C₂

—

150

C₂

#11926406

yes

characteristic

151

C₂

#11926525

yes

characteristic

152

C₂

#11926527

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₁₉
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#343	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#343	D₁₉
hypocenter	C₁₉	#1822
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₁₉

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#343

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×D₁₉

C₂×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

N	H ≅ G/N	type
3. #11926313	C₂	semidirect
4. #11926312	C₂	semidirect
5. C₁₉×#343	C₂	semidirect
75. #343	D₁₉	semidirect
91. C₁₉	#1822	semidirect

H ≅ G/N

type

3. #11926313

C₂

semidirect

4. #11926312

C₂

semidirect

5. C₁₉×#343

C₂

semidirect

75. #343

D₁₉

semidirect

91. C₁₉

#1822

semidirect

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

subgroup	index
C₂×#10597338	2
#11926507	2
#11926313	2
#11926312	2
C₁₉×#343	2
#1822	19

subgroup

index

C₁₉×#343

Subgroups — #14563717

Conjugacy classes of subgroups

Complements

Maximal subgroups