Group #14565053 — subgroups

Subgroups — #14565053

Order 2432.

222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 81 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×#10597292	C₂	1	2	yes	maximal
2	#11926410	C₂	1	1	yes	maximal, characteristic
3	#11926306	C₂	1	2	yes	maximal
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
11	C₁₉×#95	—	2	2	no	—
12	#10597292	—	2	4	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	C₂×Q₈×C₁₉	—	2	1	no	—
15	C₂×Q₈×C₁₉	—	2	2	no	—
16	C₂×Q₈×C₁₉	—	2	2	no	—
17	C₂×Q₈×C₁₉	D₄	1	2	yes	—
18	C₂²×C₄×C₁₉	—	2	1	no	—
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₁₉	—	2	2	no	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄²×C₁₉	—	2	2	no	—
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₁₉⋊C₈	—	2	2	no	—
28	C₂×C₁₉⋊C₈	—	2	2	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
31	Q₈×C₁₉	—	2	4	no	—
32	Q₈×C₁₉	—	4	2	no	—
33	C₂×C₄×C₁₉	—	2	2	no	—
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	—	2	2	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	2	yes	—
44	C₂×C₄×C₁₉	#41	1	2	yes	—
45	C₂×Dic₁₉	—	4	2	no	—
46	C₂×Dic₁₉	—	4	2	no	—
47	C₂×Dic₁₉	—	4	2	no	—
48	C₁₉⋊C₈	—	4	2	no	—
49	#2074	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	#121	1	1	yes	characteristic
51	C₂²×C₁₉	#123	1	1	yes	characteristic
52	C₂²×C₁₉	#124	1	1	yes	characteristic
53	C₂²×C₁₉	#135	1	2	yes	—
54	C₂²×C₁₉	#137	1	2	yes	—
55	C₄×C₁₉	—	4	2	no	—
56	C₄×C₁₉	—	4	2	no	—
57	C₄×C₁₉	—	8	1	no	—
58	C₄×C₁₉	#123	1	2	yes	—
59	C₄×C₁₉	#126	1	2	yes	—
60	Dic₁₉	—	8	2	no	—
61	C₂×#103	—	19	2	no	—
62	#391	D₁₉	1	1	yes	characteristic
63	#382	—	19	1	no	—
64	#340	—	19	2	no	—
65	#336	—	19	1	no	—
66	C₂×C₁₉	#397	1	1	yes	characteristic
67	C₂×C₁₉	#464	1	2	yes	—
68	C₂×C₁₉	#485	1	2	yes	—
69	C₂×C₁₉	#488	1	1	yes	characteristic
70	C₂×C₁₉	#491	1	1	yes	characteristic
71	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
72	C₂²×C₈	—	19	2	no	—
73	C₂×C₄⋊C₄	—	19	2	no	—
74	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
75	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
76	#103	—	38	4	no	—
77	#95	—	2	2	no	—
78	#95	—	38	2	no	—
79	C₁₉	#2074	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₈	—	2	1	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	D₇₆	1	2	yes	—
84	C₂²×C₄	—	2	1	no	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	—	38	2	no	—
87	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
88	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
89	C₂×C₈	—	38	2	no	—
90	C₂×C₈	—	38	2	no	—
91	C₂×C₈	—	38	2	no	—
92	C₄⋊C₄	—	2	2	no	—
93	C₄⋊C₄	—	38	2	no	—
94	C₄⋊C₄	—	38	2	no	—
95	C₄²	—	2	2	no	—
96	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
97	Q₈	—	2	4	no	—
98	Q₈	—	4	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	76	2	no	—
108	C₂×C₄	—	76	2	no	—
109	C₂×C₄	—	76	2	no	—
110	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
111	C₂×C₄	#64541	1	1	yes	characteristic
112	C₂×C₄	#64543	1	2	yes	—
113	C₂×C₄	#64543	1	2	yes	—
114	C₈	—	76	2	no	—
115	C₂²	#10597376	1	1	yes	characteristic
116	C₂²	#10597381	1	1	yes	characteristic
117	C₂²	#10597382	1	1	yes	characteristic
118	C₂²	#10597388	1	2	yes	—
119	C₂²	#10597396	1	2	yes	—
120	C₄	—	4	2	no	—
121	C₄	—	4	2	no	—
122	C₄	—	8	1	no	—
123	C₄	—	152	2	no	—
124	C₄	#10597325	1	2	yes	—
125	C₄	#10597332	1	2	yes	—
126	C₂	#11926469	1	1	yes	characteristic
127	C₂	#11926766	1	2	yes	—
128	C₂	#11926882	1	2	yes	—
129	C₂	#11926898	1	1	yes	characteristic
130	C₂	#11926912	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597292

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×#95

—

#10597292

—

C₁₉⋊#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#126

yes

—

Dic₁₉

—

C₂×#103

—

#391

D₁₉

yes

—

—

—

C₂×C₁₉

#397

yes

characteristic

C₂×C₁₉

#464

yes

—

C₂×C₁₉

#485

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2074

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₇₆

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₂×D₇₆

yes

characteristic

111

C₂×C₄

#64541

yes

characteristic

112

C₂×C₄

#64543

yes

—

113

C₂×C₄

#64543

yes

—

114

C₈

—

115

C₂²

#10597376

yes

characteristic

116

C₂²

#10597381

yes

characteristic

117

C₂²

#10597382

yes

characteristic

118

C₂²

#10597388

yes

—

119

C₂²

#10597396

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

152

—

124

C₄

#10597325

yes

—

125

C₄

#10597332

yes

—

126

C₂

#11926469

yes

characteristic

127

C₂

#11926766

yes

—

128

C₂

#11926882

yes

—

129

C₂

#11926898

yes

characteristic

130

C₂

#11926912

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2074
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
79. C₁₉	#2074	semidirect

H ≅ G/N

type

79. C₁₉

#2074

semidirect

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

subgroup	index
C₂×#10597292	2
#11926410	2
#11926306	2
#11926299	2
C₁₉×#391	2
#2074	19

subgroup

index

C₁₉×#391

Subgroups — #14565053

Conjugacy classes of subgroups

Complements

Maximal subgroups