Group #14563149 — subgroups

Subgroups — #14563149

Order 2432.

166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11926949	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926750	C₂	1	2	yes	maximal
3	#11926623	C₂	1	1	yes	maximal, characteristic
4	#11926291	C₂	1	2	yes	maximal, complemented
5	C₁₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64516	—	2	2	no	—
7	C₂×#64515	—	2	1	no	—
8	C₄×D₇₆	C₂²	1	1	yes	characteristic
9	#10597315	C₂²	1	2	yes	—
10	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	(C₂×D₁₉)⋊C₈	—	2	1	no	—
13	#10597275	—	2	1	no	—
14	#10597275	—	2	1	no	—
15	#10597273	—	2	2	no	—
16	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×D₇₆	D₄	1	1	yes	characteristic
18	C₂×C₄×D₁₉	—	2	1	no	—
19	C₂×Dic₃₈	—	2	2	no	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	(C₂×D₁₉)⋊C₄	—	2	1	no	—
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
28	C₂×C₁₉⋊C₈	—	2	1	no	—
29	#64516	—	4	4	no	—
30	#64515	—	4	2	no	—
31	C₂²×D₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
35	C₂×Dic₁₉	—	2	1	no	—
36	C₂×Dic₁₉	—	4	2	no	—
37	D₇₆	—	2	2	no	—
38	C₄×D₁₉	—	4	1	no	—
39	C₄×D₁₉	—	4	1	no	—
40	Dic₃₈	—	4	2	no	—
41	Dic₃₈	—	4	2	no	—
42	C₈×C₁₉	—	2	1	no	—
43	C₈×C₁₉	—	4	2	no	—
44	C₈×C₁₉	SD₁₆	1	2	yes	complemented
45	C₁₉⋊C₈	—	4	1	no	—
46	#1693	—	19	1	no	maximal, Sylow
47	C₂²×C₁₉	#121	1	1	yes	characteristic
48	C₂×D₁₉	—	4	1	no	—
49	C₂×D₁₉	—	4	1	no	—
50	C₂×D₁₉	—	4	1	no	—
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
53	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
54	C₄×C₁₉	#137	1	1	yes	characteristic
55	Dic₁₉	—	4	1	no	—
56	Dic₁₉	—	8	2	no	—
57	#500	—	19	1	no	—
58	#461	—	19	2	no	—
59	#436	—	19	1	no	—
60	#334	D₁₉	1	1	yes	characteristic, complemented
61	#332	—	19	2	no	—
62	C₂×C₁₉	#461	1	1	yes	characteristic
63	C₂×C₁₉	#469	1	1	yes	characteristic
64	C₂×C₁₉	#473	1	1	yes	characteristic
65	D₁₉	—	8	1	no	—
66	C₂×SD₁₆	—	38	2	no	—
67	C₂×M₁₆	—	38	1	no	—
68	C₄⋊Q₈	—	19	2	no	—
69	C₄×D₄	—	19	1	no	—
70	#107	—	38	1	no	—
71	#107	—	38	1	no	—
72	C₄⋊C₈	—	19	1	no	—
73	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
74	#103	—	38	2	no	—
75	C₂²⋊C₈	—	38	1	no	—
76	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
77	C₁₉	#1693	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₈	—	38	2	no	—
79	C₂×D₄	—	19	1	no	—
80	C₂²×C₄	—	38	1	no	—
81	SD₁₆	—	76	4	no	—
82	M₁₆	—	76	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	38	1	no	—
85	C₂×C₈	D₇₆	1	1	yes	characteristic
86	C₂×C₈	D₇₆	1	1	yes	characteristic
87	C₄⋊C₄	—	19	1	no	—
88	C₄⋊C₄	—	38	2	no	—
89	C₄⋊C₄	—	38	2	no	—
90	C₂²⋊C₄	—	38	1	no	—
91	C₄²	C₂²×D₁₉	1	1	yes	characteristic
92	C₂³	—	38	1	no	—
93	Q₈	—	76	2	no	—
94	Q₈	—	76	2	no	—
95	D₄	—	38	2	no	—
96	C₂×C₄	—	38	1	no	—
97	C₂×C₄	—	76	1	no	—
98	C₂×C₄	—	76	1	no	—
99	C₂×C₄	—	76	2	no	—
100	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
101	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
102	C₂×C₄	#64545	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	4	2	no	—
105	C₈	—	76	1	no	—
106	C₈	#64516	1	2	yes	complemented
107	C₂²	—	76	1	no	—
108	C₂²	—	76	1	no	—
109	C₂²	—	76	1	no	—
110	C₂²	#10597341	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	76	1	no	—
113	C₄	—	152	2	no	—
114	C₄	C₂×#64516	1	1	yes	characteristic
115	C₄	#10597355	1	1	yes	characteristic
116	C₄	#10597360	1	2	yes	—
117	C₂	—	152	1	no	—
118	C₂	#11926750	1	1	yes	characteristic
119	C₂	#11926798	1	1	yes	characteristic
120	C₂	#11926820	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926949

C₂

yes

maximal, characteristic, complemented

#11926750

C₂

yes

maximal

#11926623

C₂

yes

maximal, characteristic

#11926291

C₂

yes

maximal, complemented

C₁₉×#334

C₂

yes

maximal, characteristic, complemented

C₂×#64516

—

C₂×#64515

—

C₄×D₇₆

C₂²

yes

characteristic

#10597315

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

(C₂×D₁₉)⋊C₈

—

#10597275

—

#10597275

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

—

#64516

—

#64515

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

SD₁₆

yes

complemented

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×SD₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

#103

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1693

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

SD₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×D₇₆

yes

characteristic

101

C₂×C₄

D₄×D₁₉

yes

characteristic

102

C₂×C₄

#64545

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

#64516

yes

complemented

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

#10597341

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

152

—

114

C₄

C₂×#64516

yes

characteristic

115

C₄

#10597355

yes

characteristic

116

C₄

#10597360

yes

—

117

C₂

—

152

—

118

C₂

#11926750

yes

characteristic

119

C₂

#11926798

yes

characteristic

120

C₂

#11926820

yes

characteristic

	subgroup	G/H
center	C₂²	#10597341
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#334	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂×D₇₆	D₄
hypercenter	#334	D₁₉
hypocenter	C₁₉	#1693
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#10597341

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#334

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #11926949	C₂	semidirect
4. #11926291	C₂	semidirect
5. C₁₉×#334	C₂	semidirect
44. C₈×C₁₉	SD₁₆	semidirect
60. #334	D₁₉	semidirect
77. C₁₉	#1693	semidirect
106. C₈	#64516	semidirect

H ≅ G/N

type

1. #11926949

C₂

semidirect

4. #11926291

C₂

semidirect

5. C₁₉×#334

C₂

semidirect

44. C₈×C₁₉

SD₁₆

semidirect

60. #334

D₁₉

semidirect

77. C₁₉

#1693

semidirect

106. C₈

#64516

semidirect

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

subgroup	index
#11926949	2
#11926750	2
#11926623	2
#11926291	2
C₁₉×#334	2
#1693	19

subgroup

index

C₁₉×#334

Subgroups — #14563149

Conjugacy classes of subgroups

Complements

Maximal subgroups