Group #14563761 — subgroups

Subgroups — #14563761

Order 2432.

248 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 109 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×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926413	C₂	1	2	yes	maximal
3	#11926307	C₂	1	1	yes	maximal, characteristic
4	#11926306	C₂	1	2	yes	maximal
5	C₁₉×#340	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
9	C₂×Dic₁₉⋊C₄	—	2	2	no	—
10	C₂×Dic₁₉⋊C₄	—	2	2	no	—
11	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₉	C₄	1	4	yes	complemented
14	C₂²×C₄×C₁₉	—	2	2	no	—
15	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₉	—	2	2	no	—
17	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
18	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄⋊Dic₁₉	—	2	2	no	—
24	C₄⋊Dic₁₉	—	2	2	no	—
25	Dic₁₉⋊C₄	—	4	4	no	—
26	Dic₁₉⋊C₄	—	4	4	no	—
27	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
28	C₄×Dic₁₉	Q₈	1	2	yes	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
31	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	4	2	no	—
33	C₂×C₄×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₁₉	#41	1	2	yes	—
38	C₂×C₄×C₁₉	#41	1	2	yes	—
39	C₂×Dic₁₉	—	4	2	no	—
40	C₂×Dic₁₉	—	4	2	no	—
41	C₂×Dic₁₉	—	4	2	no	—
42	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
43	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
44	C₂×Dic₁₉	D₈	1	2	yes	—
45	C₂×Dic₁₉	SD₁₆	1	4	yes	—
46	C₂×Dic₁₉	Q₁₆	1	2	yes	—
47	C₈×C₁₉	—	2	2	no	—
48	C₁₉⋊C₈	—	2	2	no	—
49	#1834	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₁₉	#124	1	2	yes	—
52	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
53	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
54	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
55	C₄×C₁₉	—	8	2	no	—
56	C₄×C₁₉	#117	1	1	yes	characteristic
57	C₄×C₁₉	#117	1	1	yes	characteristic
58	C₄×C₁₉	#125	1	2	yes	—
59	Dic₁₉	—	8	2	no	—
60	Dic₁₉	#106	1	4	yes	—
61	Dic₁₉	#107	1	4	yes	—
62	C₂×C₄×C₈	—	19	1	no	—
63	#384	—	19	2	no	—
64	#340	—	19	1	no	—
65	#340	—	19	2	no	—
66	#340	D₁₉	1	1	yes	characteristic
67	C₂×C₁₉	#382	1	1	yes	characteristic
68	C₂×C₁₉	C₂×#106	1	1	yes	characteristic
69	C₂×C₁₉	C₂×#107	1	1	yes	characteristic
70	C₂×C₁₉	#486	1	2	yes	—
71	C₂×C₁₉	#487	1	2	yes	—
72	C₂²×C₈	—	19	1	no	—
73	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
74	C₂×C₄⋊C₄	—	19	2	no	—
75	C₂×C₄⋊C₄	—	38	2	no	—
76	C₂×C₄⋊C₄	—	38	2	no	—
77	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
78	C₂×C₄²	—	19	1	no	—
79	C₄×C₈	—	19	4	no	—
80	C₁₉	#1834	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	—	19	1	no	—
83	C₂²×C₄	—	19	1	no	—
84	C₂²×C₄	—	38	2	no	—
85	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	19	2	no	—
88	C₂×C₈	—	38	2	no	—
89	C₂×C₈	C₄×D₁₉	1	2	yes	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	38	2	no	—
93	C₄⋊C₄	—	38	2	no	—
94	C₄⋊C₄	—	76	4	no	—
95	C₄⋊C₄	—	76	4	no	—
96	C₄²	—	19	2	no	—
97	C₄²	—	19	2	no	—
98	C₂³	D₄×D₁₉	1	1	yes	characteristic
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	19	2	no	—
103	C₂×C₄	—	19	2	no	—
104	C₂×C₄	—	19	2	no	—
105	C₂×C₄	—	19	4	no	—
106	C₂×C₄	—	19	2	no	—
107	C₂×C₄	—	76	2	no	—
108	C₂×C₄	—	76	2	no	—
109	C₂×C₄	—	76	2	no	—
110	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
111	C₂×C₄	#64541	1	2	yes	—
112	C₂×C₄	#64543	1	2	yes	—
113	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	38	2	no	—
116	C₂²	#10597331	1	2	yes	—
117	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
118	C₂²	D₈×D₁₉	1	1	yes	characteristic
119	C₂²	SD₁₆×D₁₉	1	2	yes	—
120	C₂²	Q₁₆×D₁₉	1	1	yes	characteristic
121	C₄	—	8	2	no	—
122	C₄	—	19	4	no	—
123	C₄	—	19	4	no	—
124	C₄	—	152	2	no	—
125	C₄	#10597318	1	1	yes	characteristic
126	C₄	#10597323	1	1	yes	characteristic
127	C₄	#10597335	1	2	yes	—
128	C₂	#11926408	1	1	yes	characteristic
129	C₂	#106×D₁₉	1	1	yes	characteristic
130	C₂	#107×D₁₉	1	1	yes	characteristic
131	C₂	#11926889	1	2	yes	—
132	C₂	#11926893	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₉

C₂

yes

maximal, characteristic

#11926413

C₂

yes

maximal

#11926307

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

C₁₉×#340

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₈×Dic₁₉

C₄

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₁₉

D₈

yes

—

C₂×Dic₁₉

SD₁₆

yes

—

C₂×Dic₁₉

Q₁₆

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1834

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

C₂×Q₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

Dic₁₉

#106

yes

—

Dic₁₉

#107

yes

—

C₂×C₄×C₈

—

—

—

—

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#487

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₄×C₈

—

C₁₉

#1834

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂³

D₄×D₁₉

yes

characteristic

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×C₄×D₁₉

yes

characteristic

111

C₂×C₄

#64541

yes

—

112

C₂×C₄

#64543

yes

—

113

C₂×C₄

Q₈×D₁₉

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#10597331

yes

—

117

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

118

C₂²

D₈×D₁₉

yes

characteristic

119

C₂²

SD₁₆×D₁₉

yes

—

120

C₂²

Q₁₆×D₁₉

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

152

—

125

C₄

#10597318

yes

characteristic

126

C₄

#10597323

yes

characteristic

127

C₄

#10597335

yes

—

128

C₂

#11926408

yes

characteristic

129

C₂

#106×D₁₉

yes

characteristic

130

C₂

#107×D₁₉

yes

characteristic

131

C₂

#11926889

yes

—

132

C₂

#11926893

yes

—

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#340	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#340	D₁₉
hypocenter	C₁₉	#1834
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#340

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
13. C₈×Dic₁₉	C₄	semidirect
80. C₁₉	#1834	semidirect

H ≅ G/N

type

13. C₈×Dic₁₉

C₄

semidirect

80. C₁₉

#1834

semidirect

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

subgroup	index
C₂×C₈×Dic₁₉	2
#11926413	2
#11926307	2
#11926306	2
C₁₉×#340	2
#1834	19

subgroup

index

C₂×C₈×Dic₁₉

C₁₉×#340

Subgroups — #14563761

Conjugacy classes of subgroups

Complements

Maximal subgroups