Group #14565741 — subgroups

Subgroups — #14565741

Order 2432.

150 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 51 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×#10597286	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597269	C₂	1	1	yes	maximal, characteristic
3	#11926785	C₂	1	1	yes	maximal, characteristic
4	#11926371	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926348	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926347	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#467	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×C₂²⋊Q₈	—	2	1	no	—
11	#10597370	—	2	1	no	—
12	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
13	C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₁₉×#103	—	2	1	no	—
15	#10597286	—	2	2	no	—
16	#10597275	C₂²	1	1	yes	characteristic
17	#10597273	—	2	1	no	—
18	#10597269	—	2	2	no	—
19	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×Dic₃₈	—	2	1	no	—
24	Q₁₆×C₁₉	—	2	1	no	—
25	Q₁₆×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	4	1	no	—
32	C₂²⋊C₄×C₁₉	—	4	1	no	—
33	C₂²⋊Dic₁₉	—	4	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	Dic₁₉⋊C₄	—	4	1	no	—
36	Dic₇₆	—	2	1	no	—
37	Dic₇₆	—	2	1	no	—
38	C₁₉⋊C₁₆	—	2	1	no	—
39	C₁₉⋊C₁₆	D₄	1	2	yes	—
40	C₂³×C₁₉	D₈	1	1	yes	characteristic
41	Q₈×C₁₉	—	4	1	no	—
42	Q₈×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₁₉	—	4	1	no	—
50	C₂×Dic₁₉	—	4	1	no	—
51	Dic₃₈	—	4	1	no	—
52	Dic₃₈	—	4	1	no	—
53	C₈×C₁₉	—	2	1	no	—
54	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₁₉	#41	1	1	yes	characteristic
56	#2219	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	8	1	no	—
63	C₄×C₁₉	—	8	1	no	—
64	C₄×C₁₉	#121	1	1	yes	characteristic
65	C₄×C₁₉	#135	1	1	yes	characteristic
66	Dic₁₉	—	8	1	no	—
67	Dic₁₉	—	8	1	no	—
68	C₂×Q₃₂	—	19	1	no	—
69	C₂×M₃₂	—	19	1	no	—
70	#467	—	19	1	no	—
71	#467	D₁₉	1	1	yes	characteristic
72	#367	—	19	1	no	—
73	#358	—	19	1	no	—
74	#358	—	19	1	no	—
75	C₂×C₁₉	—	4	1	no	—
76	C₂×C₁₉	#466	1	1	yes	characteristic
77	C₂×C₁₉	#510	1	1	yes	characteristic
78	C₂×C₁₉	#510	1	1	yes	characteristic
79	C₂×Q₁₆	—	19	1	no	—
80	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
81	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
82	C₂²⋊Q₈	—	2	1	no	—
83	C₂²⋊Q₈	—	38	1	no	—
84	Q₃₂	—	38	2	no	—
85	M₃₂	—	38	2	no	—
86	C₂×C₁₆	—	19	1	no	—
87	C₂×C₁₆	—	19	1	no	—
88	#107	—	19	1	no	—
89	#107	C₂×D₁₉	1	1	yes	characteristic
90	#103	—	2	1	no	—
91	#103	—	38	1	no	—
92	C₁₉	#2219	1	1	yes	characteristic, complemented, Sylow
93	C₂×Q₈	—	2	1	no	—
94	C₂×Q₈	—	38	1	no	—
95	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
96	Q₁₆	—	2	1	no	—
97	Q₁₆	—	2	1	no	—
98	Q₁₆	—	38	1	no	—
99	Q₁₆	—	38	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
103	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	4	1	no	—
106	C₄⋊C₄	—	38	1	no	—
107	C₄⋊C₄	—	76	1	no	—
108	C₂²⋊C₄	—	4	1	no	—
109	C₂²⋊C₄	—	76	1	no	—
110	C₁₆	—	19	2	no	—
111	C₁₆	—	38	1	no	—
112	C₂³	#64525	1	1	yes	characteristic
113	Q₈	—	4	1	no	—
114	Q₈	—	4	1	no	—
115	Q₈	—	76	1	no	—
116	Q₈	—	76	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	76	1	no	—
122	C₂×C₄	—	76	1	no	—
123	C₂×C₄	#64525	1	1	yes	characteristic
124	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	D₄×D₁₉	1	1	yes	characteristic
127	C₈	#64543	1	1	yes	characteristic
128	C₂²	—	2	1	no	—
129	C₂²	—	2	1	no	—
130	C₂²	—	2	1	no	—
131	C₂²	C₂×#64525	1	1	yes	characteristic
132	C₄	—	2	1	no	—
133	C₄	—	8	1	no	—
134	C₄	—	8	1	no	—
135	C₄	—	152	1	no	—
136	C₄	—	152	1	no	—
137	C₄	#10597385	1	1	yes	characteristic
138	C₄	#10597396	1	1	yes	characteristic
139	C₂	—	4	1	no	—
140	C₂	#11926778	1	1	yes	characteristic
141	C₂	#11926984	1	1	yes	characteristic
142	C₂	#11926985	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597286

C₂

yes

maximal, characteristic, complemented

C₂×#10597269

C₂

yes

maximal, characteristic

#11926785

C₂

yes

maximal, characteristic

#11926371

C₂

yes

maximal, characteristic, complemented

#11926348

C₂

yes

maximal, characteristic, complemented

#11926347

C₂

yes

maximal, characteristic, complemented

C₁₉×#467

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

#10597370

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

#10597286

—

#10597275

C₂²

yes

characteristic

#10597273

—

#10597269

—

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₇₆

—

Dic₇₆

—

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

D₄

yes

—

C₂³×C₁₉

D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

—

C₂×M₃₂

—

#467

—

#467

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₁₉

yes

characteristic

#103

—

#103

—

C₁₉

#2219

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

103

C₂×C₈

C₂²×D₁₉

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₁₆

—

111

C₁₆

—

112

C₂³

#64525

yes

characteristic

113

Q₈

—

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

#64525

yes

characteristic

124

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

125

C₈

—

126

C₈

D₄×D₁₉

yes

characteristic

127

C₈

#64543

yes

characteristic

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

C₂×#64525

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

152

—

136

C₄

—

152

—

137

C₄

#10597385

yes

characteristic

138

C₄

#10597396

yes

characteristic

139

C₂

—

140

C₂

#11926778

yes

characteristic

141

C₂

#11926984

yes

characteristic

142

C₂

#11926985

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#467	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂³×C₁₉	D₈
hypercenter	#467	D₁₉
hypocenter	C₁₉	#2219
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #467

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#467

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂³×C₁₉

D₈

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #467

N	H ≅ G/N	type
1. C₂×#10597286	C₂	semidirect
4. #11926371	C₂	semidirect
5. #11926348	C₂	semidirect
6. #11926347	C₂	semidirect
92. C₁₉	#2219	semidirect

H ≅ G/N

type

1. C₂×#10597286

C₂

semidirect

4. #11926371

C₂

semidirect

5. #11926348

C₂

semidirect

6. #11926347

C₂

semidirect

92. C₁₉

#2219

semidirect

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

subgroup	index
C₂×#10597286	2
C₂×#10597269	2
#11926785	2
#11926371	2
#11926348	2
#11926347	2
C₁₉×#467	2
#2219	19

subgroup

index

C₁₉×#467

Subgroups — #14565741

Conjugacy classes of subgroups

Complements

Maximal subgroups