Group #14565689 — subgroups

Subgroups — #14565689

Order 2432.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#10597257	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597283	C₂	1	1	yes	maximal, characteristic
3	#11926927	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926626	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926347	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597382	—	2	1	no	—
10	C₂×#64526	—	2	1	no	—
11	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
12	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
13	#10597339	—	2	1	no	—
14	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#107	C₂²	1	1	yes	characteristic
16	#10597283	—	2	2	no	—
17	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
19	#10597266	—	2	1	no	—
20	#10597257	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	1	no	—
22	C₂×D₇₆	—	2	1	no	—
23	C₂×C₄×D₁₉	—	4	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	D₈×C₁₉	—	2	1	no	—
26	D₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂²⋊Dic₁₉	—	4	1	no	—
30	C₂²⋊Dic₁₉	—	4	1	no	—
31	#64526	—	4	2	no	—
32	(C₂×D₁₉)⋊C₄	—	4	1	no	—
33	C₄×Dic₁₉	D₄	1	1	yes	characteristic
34	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
35	Dic₇₆	—	2	1	no	—
36	Dic₇₆	—	2	1	no	—
37	D₁₅₂	—	2	1	no	—
38	D₁₅₂	D₄	1	2	yes	—
39	C₁₆×C₁₉	—	2	1	no	—
40	C₁₉⋊C₁₆	—	2	1	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂²×D₁₉	—	4	1	no	—
43	D₄×C₁₉	—	4	1	no	—
44	D₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₁₉	—	4	1	no	—
48	C₂×Dic₁₉	D₈	1	1	yes	characteristic
49	C₂×Dic₁₉	D₈	1	1	yes	characteristic
50	D₇₆	—	2	2	no	—
51	D₇₆	—	4	1	no	—
52	C₄×D₁₉	—	8	2	no	—
53	Dic₃₈	—	4	1	no	—
54	Dic₃₈	—	4	1	no	—
55	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₁₉	#41	1	1	yes	characteristic
57	C₁₉⋊C₈	—	2	1	no	—
58	#2210	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	—	8	1	no	—
60	C₂²×C₁₉	—	8	1	no	—
61	C₂²×C₁₉	—	8	1	no	—
62	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
63	C₂×D₁₉	—	4	2	no	—
64	C₂×D₁₉	—	8	1	no	—
65	C₂×D₁₉	—	8	1	no	—
66	C₄×C₁₉	—	8	1	no	—
67	C₄×C₁₉	#121	1	1	yes	characteristic
68	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
69	Dic₁₉	—	2	1	no	—
70	Dic₁₉	—	2	1	no	—
71	Dic₁₉	—	8	1	no	—
72	C₂×SD₃₂	—	19	1	no	—
73	C₂×D₁₆	—	19	1	no	—
74	#495	—	19	1	no	—
75	C₄×D₈	—	19	1	no	—
76	C₄⋊C₁₆	—	19	1	no	—
77	#358	—	19	1	no	—
78	#357	D₁₉	1	1	yes	characteristic, complemented
79	C₂×C₁₉	—	16	1	no	—
80	C₂×C₁₉	#459	1	1	yes	characteristic
81	C₂×C₁₉	#508	1	1	yes	characteristic
82	C₂×C₁₉	#509	1	1	yes	characteristic
83	D₁₉	—	8	2	no	—
84	C₂×Q₁₆	—	19	1	no	—
85	C₂×SD₁₆	—	38	1	no	—
86	C₂×D₈	—	19	1	no	—
87	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
88	#124	—	38	1	no	—
89	C₄×D₄	—	38	1	no	—
90	SD₃₂	—	38	2	no	—
91	D₁₆	—	38	2	no	—
92	C₂×C₁₆	—	19	1	no	—
93	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
94	#107	C₂×D₁₉	1	1	yes	characteristic
95	#102	—	38	1	no	—
96	C₄×C₈	—	19	1	no	—
97	C₁₉	#2210	1	1	yes	characteristic, complemented, Sylow
98	C₂×Q₈	—	38	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	38	1	no	—
101	C₂²×C₄	—	76	1	no	—
102	Q₁₆	—	38	1	no	—
103	Q₁₆	—	38	1	no	—
104	SD₁₆	—	76	2	no	—
105	D₈	—	2	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	19	2	no	—
108	D₈	—	38	1	no	—
109	C₂×C₈	—	19	1	no	—
110	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
111	C₄⋊C₄	—	2	1	no	—
112	C₂²⋊C₄	—	76	1	no	—
113	C₂²⋊C₄	—	76	1	no	—
114	C₂²⋊C₄	—	76	1	no	—
115	C₄²	—	19	1	no	—
116	C₁₆	—	2	1	no	—
117	C₁₆	—	38	1	no	—
118	C₂³	—	4	1	no	—
119	C₂³	—	76	1	no	—
120	Q₈	—	76	1	no	—
121	Q₈	—	76	1	no	—
122	D₄	—	4	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	38	2	no	—
125	D₄	—	76	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	19	1	no	—
128	C₂×C₄	—	19	1	no	—
129	C₂×C₄	—	76	1	no	—
130	C₂×C₄	—	152	2	no	—
131	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
132	C₈	—	38	1	no	—
133	C₈	#64541	1	1	yes	characteristic
134	C₈	D₄×D₁₉	1	1	yes	characteristic
135	C₂²	—	8	1	no	—
136	C₂²	—	8	1	no	—
137	C₂²	—	8	1	no	—
138	C₂²	—	76	2	no	—
139	C₂²	—	152	1	no	—
140	C₂²	—	152	1	no	—
141	C₂²	D₈×D₁₉	1	1	yes	characteristic
142	C₄	—	8	1	no	—
143	C₄	—	38	1	no	—
144	C₄	—	38	1	no	—
145	C₄	—	152	1	no	—
146	C₄	#10597330	1	1	yes	characteristic
147	C₄	#10597360	1	1	yes	characteristic
148	C₂	—	16	1	no	—
149	C₂	—	152	2	no	—
150	C₂	#11926738	1	1	yes	characteristic
151	C₂	#11926975	1	1	yes	characteristic
152	C₂	#11926978	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597257

C₂

yes

maximal, characteristic, complemented

C₂×#10597283

C₂

yes

maximal, characteristic

#11926927

C₂

yes

maximal, characteristic, complemented

#11926626

C₂

yes

maximal, characteristic, complemented

Dic₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#11926347

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₉

C₂²

yes

characteristic

#10597382

—

C₂×#64526

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₂×D₁₅₂

C₂²

yes

characteristic

#10597339

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

#10597283

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597266

—

#10597257

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64526

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

—

D₁₅₂

—

D₁₅₂

D₄

yes

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₂×Dic₁₉

D₈

yes

characteristic

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

#2210

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×D₈

—

C₄⋊C₁₆

—

#358

—

#357

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

characteristic

#124

—

C₄×D₄

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#107

C₂×D₁₉

yes

characteristic

#102

—

C₄×C₈

—

C₁₉

#2210

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂²×C₄

—

102

Q₁₆

—

103

Q₁₆

—

104

SD₁₆

—

105

D₈

—

106

D₈

—

107

D₈

—

108

D₈

—

109

C₂×C₈

—

110

C₂×C₈

C₂²×D₁₉

yes

characteristic

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

—

116

C₁₆

—

117

C₁₆

—

118

C₂³

—

119

C₂³

—

120

Q₈

—

121

Q₈

—

122

D₄

—

123

D₄

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

152

—

131

C₂×C₄

D₄×D₁₉

yes

characteristic

132

C₈

—

133

C₈

#64541

yes

characteristic

134

C₈

D₄×D₁₉

yes

characteristic

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

152

—

140

C₂²

—

152

—

141

C₂²

D₈×D₁₉

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

152

—

146

C₄

#10597330

yes

characteristic

147

C₄

#10597360

yes

characteristic

148

C₂

—

149

C₂

—

152

—

150

C₂

#11926738

yes

characteristic

151

C₂

#11926975

yes

characteristic

152

C₂

#11926978

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#357	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×#10597283	C₂
hypercenter	#357	D₁₉
hypocenter	C₁₉	#2210
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#357

C₂

socle

C₂²×C₁₉

C₂×D₈

C₂

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#10597257	C₂	semidirect
3. #11926927	C₂	semidirect
4. #11926626	C₂	semidirect
5. Dic₁₉⋊C₁₆	C₂	semidirect
6. #11926347	C₂	semidirect
7. C₁₉×#357	C₂	semidirect
78. #357	D₁₉	semidirect
97. C₁₉	#2210	semidirect

H ≅ G/N

type

1. C₂×#10597257

C₂

semidirect

3. #11926927

C₂

semidirect

4. #11926626

C₂

semidirect

5. Dic₁₉⋊C₁₆

C₂

semidirect

6. #11926347

C₂

semidirect

7. C₁₉×#357

C₂

semidirect

78. #357

D₁₉

semidirect

97. C₁₉

#2210

semidirect

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

subgroup	index
C₂×#10597257	2
C₂×#10597283	2
#11926927	2
#11926626	2
Dic₁₉⋊C₁₆	2
#11926347	2
C₁₉×#357	2
#2210	19

subgroup

index

Dic₁₉⋊C₁₆

C₁₉×#357

Subgroups — #14565689

Conjugacy classes of subgroups

Complements

Maximal subgroups