Group #14565151 — subgroups

Subgroups — #14565151

Order 2432.

222 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 65 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	#11926593	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926592	C₂	1	2	yes	maximal, complemented
3	#11926508	C₂	1	2	yes	maximal
4	C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#407	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	2	yes	—
11	C₁₉×C₂²⋊C₈	—	2	2	no	—
12	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
13	#10597279	—	2	4	no	—
14	#10597276	—	2	2	no	—
15	C₂⁴×C₁₉	Q₈	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	—	2	1	no	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₁₉	—	2	2	no	—
23	M₁₆×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	D₄	1	2	yes	—
26	#64520	—	2	2	no	—
27	#64520	—	2	2	no	—
28	#64520	—	2	2	no	—
29	#64520	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
32	C₂³×C₁₉	—	2	2	no	—
33	C₂³×C₁₉	—	2	1	no	—
34	C₂³×C₁₉	—	4	2	no	—
35	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	—	2	2	no	—
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#41	1	2	yes	—
45	C₈×C₁₉	—	2	2	no	—
46	C₈×C₁₉	—	4	1	no	—
47	C₁₉⋊C₈	—	2	4	no	—
48	C₁₉⋊C₈	—	4	2	no	—
49	#2091	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	2	4	no	—
51	C₂²×C₁₉	—	2	2	no	—
52	C₂²×C₁₉	—	4	1	no	—
53	C₂²×C₁₉	—	4	2	no	—
54	C₂²×C₁₉	—	4	1	no	—
55	C₂²×C₁₉	—	4	1	no	—
56	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
57	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
58	C₄×C₁₉	—	4	1	no	—
59	C₄×C₁₉	#123	1	1	yes	characteristic
60	C₄×C₁₉	#123	1	2	yes	—
61	C₄×C₁₉	#127	1	1	yes	characteristic
62	#430	—	19	2	no	—
63	#430	—	19	1	no	—
64	#407	—	19	2	no	—
65	#407	D₁₉	1	1	yes	characteristic
66	#338	—	19	1	no	—
67	C₂×C₁₉	—	2	2	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	—	4	2	no	—
70	C₂×C₁₉	#399	1	1	yes	characteristic
71	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
72	C₂×M₁₆	—	19	2	no	—
73	C₂×M₁₆	—	19	2	no	—
74	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
75	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
76	#108	—	38	4	no	—
77	#108	—	38	2	no	—
78	C₂²⋊C₈	—	2	2	no	—
79	C₂²⋊C₈	—	38	4	no	—
80	C₁₉	#2091	1	1	yes	characteristic, complemented, Sylow
81	C₂⁴	Dic₃₈	1	1	yes	characteristic
82	C₂²×C₄	—	2	1	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
87	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
88	M₁₆	—	2	2	no	—
89	M₁₆	—	2	2	no	—
90	M₁₆	—	38	2	no	—
91	M₁₆	—	38	2	no	—
92	M₁₆	—	38	2	no	—
93	M₁₆	—	38	2	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	19	4	no	—
96	C₂×C₈	—	38	2	no	—
97	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
98	C₂³	—	2	2	no	—
99	C₂³	—	2	1	no	—
100	C₂³	—	4	2	no	—
101	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	#64541	1	1	yes	characteristic
108	C₂×C₄	D₄×D₁₉	1	2	yes	—
109	C₂×C₄	#64543	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	4	1	no	—
113	C₈	—	38	4	no	—
114	C₈	—	76	2	no	—
115	C₂²	—	2	4	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	4	1	no	—
118	C₂²	—	4	2	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#10597324	1	2	yes	—
122	C₂²	#10597370	1	1	yes	characteristic
123	C₄	—	4	1	no	—
124	C₄	#10597329	1	2	yes	—
125	C₄	#10597381	1	1	yes	characteristic
126	C₄	#10597386	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	1	no	—
129	C₂	—	4	2	no	—
130	C₂	#11926480	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926593

C₂

yes

maximal, characteristic, complemented

#11926592

C₂

yes

maximal, complemented

#11926508

C₂

yes

maximal

C₁₉⋊#338

C₂

yes

maximal, characteristic, complemented

C₁₉×#407

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

#10597276

—

C₂⁴×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2091

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#123

yes

characteristic

C₄×C₁₉

#123

yes

—

C₄×C₁₉

yes

—

—

—

D₁₉

yes

characteristic

#338

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#399

yes

characteristic

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#108

—

#108

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₁₉

#2091

yes

characteristic, complemented, Sylow

C₂⁴

Dic₃₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₃₈

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×Dic₃₈

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

#64541

yes

characteristic

108

C₂×C₄

D₄×D₁₉

yes

—

109

C₂×C₄

#64543

yes

—

110

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#10597324

yes

—

122

C₂²

#10597370

yes

characteristic

123

C₄

—

124

C₄

#10597329

yes

—

125

C₄

#10597381

yes

characteristic

126

C₄

#10597386

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#11926480

yes

characteristic

	subgroup	G/H
center	C₄	#10597386
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#407	C₂
socle	C₂×C₁₉	#399
prime radical	C₂⁴×C₁₉	Q₈
hypercenter	#407	D₁₉
hypocenter	C₁₉	#2091
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #407

subgroup

G/H

center

C₄

#10597386

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#407

C₂

socle

C₂×C₁₉

#399

prime radical

C₂⁴×C₁₉

Q₈

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #407

N	H ≅ G/N	type
1. #11926593	C₂	semidirect
2. #11926592	C₂	semidirect
4. C₁₉⋊#338	C₂	semidirect
80. C₁₉	#2091	semidirect

H ≅ G/N

type

1. #11926593

C₂

semidirect

2. #11926592

C₂

semidirect

4. C₁₉⋊#338

C₂

semidirect

80. C₁₉

#2091

semidirect

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

subgroup	index
#11926593	2
#11926592	2
#11926508	2
C₁₉⋊#338	2
C₁₉×#407	2
#2091	19

subgroup

index

#11926593

#11926592

#11926508

C₁₉⋊#338

C₁₉×#407

#2091

Subgroups — #14565151

Conjugacy classes of subgroups

Complements

Maximal subgroups