Group #14565861 — subgroups

Subgroups — #14565861

Order 2432.

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

normal subgroups only

This group has 140 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	#11926948	C₂	1	1	yes	maximal, characteristic
2	#11926922	C₂	1	1	yes	maximal, characteristic
3	#11926349	C₂	1	1	yes	maximal, characteristic
4	#11926348	C₂	1	1	yes	maximal, characteristic
5	#11926347	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#358	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	#10597390	—	2	1	no	—
10	C₂×#64528	—	2	1	no	—
11	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
12	#10597334	—	2	1	no	—
13	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#107	C₂²	1	1	yes	characteristic
15	#10597275	C₂²	1	1	yes	characteristic
16	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
18	#10597264	—	2	1	no	—
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	C₂×Dic₃₈	—	2	1	no	—
21	C₂×Dic₃₈	—	4	1	no	—
22	Q₁₆×C₁₉	—	2	1	no	—
23	Q₁₆×C₁₉	—	2	1	no	—
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	#64528	—	4	2	no	—
27	C₄⋊Dic₁₉	—	2	1	no	—
28	Dic₁₉⋊C₄	—	4	1	no	—
29	Dic₁₉⋊C₄	—	4	1	no	—
30	Dic₁₉⋊C₄	—	4	1	no	—
31	C₄×Dic₁₉	D₄	1	1	yes	characteristic
32	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
33	Dic₇₆	—	2	1	no	—
34	Dic₇₆	—	2	1	no	—
35	C₁₆×C₁₉	—	2	1	no	—
36	C₁₉⋊C₁₆	—	2	1	no	—
37	Q₈×C₁₉	—	4	1	no	—
38	Q₈×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₁₉	—	4	1	no	—
43	C₂×Dic₁₉	—	4	1	no	—
44	C₂×Dic₁₉	D₈	1	1	yes	characteristic
45	C₂×Dic₁₉	D₈	1	1	yes	characteristic
46	Dic₃₈	—	4	1	no	—
47	Dic₃₈	—	4	1	no	—
48	Dic₃₈	—	8	2	no	—
49	C₈×C₁₉	#41	1	1	yes	characteristic
50	C₈×C₁₉	#41	1	1	yes	characteristic
51	C₁₉⋊C₈	SD₁₆	1	2	yes	—
52	#2241	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
54	C₄×C₁₉	—	8	1	no	—
55	C₄×C₁₉	—	8	1	no	—
56	C₄×C₁₉	#124	1	1	yes	characteristic
57	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
58	Dic₁₉	—	8	1	no	—
59	Dic₁₉	—	8	1	no	—
60	Dic₁₉	SD₃₂	1	2	yes	—
61	Dic₁₉	Q₃₂	1	2	yes	—
62	#500	—	19	1	no	—
63	#494	—	19	1	no	—
64	#358	—	19	1	no	—
65	#358	—	19	1	no	—
66	#358	—	19	1	no	—
67	#358	D₁₉	1	1	yes	characteristic
68	C₄×C₁₆	—	19	1	no	—
69	C₂×C₁₉	#486	1	1	yes	characteristic
70	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
71	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
72	C₂×Q₁₆	—	19	1	no	—
73	C₂×Q₁₆	—	38	1	no	—
74	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
75	C₄⋊Q₈	—	38	1	no	—
76	C₄⋊Q₈	—	38	1	no	—
77	C₂×C₁₆	—	19	1	no	—
78	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
79	#107	—	19	1	no	—
80	#107	—	38	1	no	—
81	#107	C₂×D₁₉	1	1	yes	characteristic
82	C₄×C₈	—	19	1	no	—
83	C₁₉	#2241	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₈	—	2	1	no	—
85	C₂×Q₈	—	38	1	no	—
86	C₂×Q₈	—	76	1	no	—
87	Q₁₆	—	2	1	no	—
88	Q₁₆	—	2	1	no	—
89	Q₁₆	—	38	1	no	—
90	Q₁₆	—	38	1	no	—
91	Q₁₆	—	76	2	no	—
92	C₂×C₈	—	19	1	no	—
93	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
94	C₄⋊C₄	—	2	1	no	—
95	C₄⋊C₄	—	38	1	no	—
96	C₄⋊C₄	—	76	1	no	—
97	C₄⋊C₄	—	76	1	no	—
98	C₄⋊C₄	—	76	1	no	—
99	C₄²	—	19	1	no	—
100	C₁₆	—	2	1	no	—
101	C₁₆	—	38	1	no	—
102	Q₈	—	4	1	no	—
103	Q₈	—	4	1	no	—
104	Q₈	—	76	1	no	—
105	Q₈	—	76	1	no	—
106	Q₈	—	152	2	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	—	19	1	no	—
110	C₂×C₄	—	19	1	no	—
111	C₂×C₄	—	76	1	no	—
112	C₂×C₄	—	76	1	no	—
113	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
114	C₈	—	19	2	no	—
115	C₈	#64541	1	1	yes	characteristic
116	C₈	#64543	1	1	yes	characteristic
117	C₂²	D₈×D₁₉	1	1	yes	characteristic
118	C₄	—	8	1	no	—
119	C₄	—	8	1	no	—
120	C₄	—	19	2	no	—
121	C₄	—	19	2	no	—
122	C₄	—	152	1	no	—
123	C₄	—	152	1	no	—
124	C₄	#10597331	1	1	yes	characteristic
125	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
126	C₂	#11926889	1	1	yes	characteristic
127	C₂	SD₃₂×D₁₉	1	1	yes	characteristic
128	C₂	Q₃₂×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926948

C₂

yes

maximal, characteristic

#11926922

C₂

yes

maximal, characteristic

#11926349

C₂

yes

maximal, characteristic

#11926348

C₂

yes

maximal, characteristic

#11926347

C₂

yes

maximal, characteristic

C₁₆×Dic₁₉

C₂

yes

maximal, characteristic

C₁₉×#358

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

#10597390

—

C₂×#64528

—

C₂×Dic₇₆

C₂²

yes

characteristic

#10597334

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597264

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

#64528

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₂×Dic₁₉

D₈

yes

characteristic

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

SD₁₆

yes

—

#2241

—

maximal, Sylow

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

SD₃₂

yes

—

Dic₁₉

Q₃₂

yes

—

—

—

—

—

—

D₁₉

yes

characteristic

C₄×C₁₆

—

C₂×C₁₉

#486

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

characteristic

C₄×C₈

—

C₁₉

#2241

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

100

C₁₆

—

101

C₁₆

—

102

Q₈

—

103

Q₈

—

104

Q₈

—

105

Q₈

—

106

Q₈

—

152

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

D₄×D₁₉

yes

characteristic

114

C₈

—

115

C₈

#64541

yes

characteristic

116

C₈

#64543

yes

characteristic

117

C₂²

D₈×D₁₉

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

152

—

123

C₄

—

152

—

124

C₄

#10597331

yes

characteristic

125

C₄

SD₁₆×D₁₉

yes

characteristic

126

C₂

#11926889

yes

characteristic

127

C₂

SD₃₂×D₁₉

yes

characteristic

128

C₂

Q₃₂×D₁₉

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#358	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	#358	D₁₉
hypocenter	C₁₉	#2241
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#358

C₂

socle, prime radical

C₂²×C₁₉

C₂×D₈

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
83. C₁₉	#2241	semidirect

H ≅ G/N

type

83. C₁₉

#2241

semidirect

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

subgroup	index
#11926948	2
#11926922	2
#11926349	2
#11926348	2
#11926347	2
C₁₆×Dic₁₉	2
C₁₉×#358	2
#2241	19

subgroup

index

C₁₆×Dic₁₉

C₁₉×#358

#2241

Subgroups — #14565861

Conjugacy classes of subgroups

Complements

Maximal subgroups