Group #14565189 — subgroups

Subgroups — #14565189

Order 2432.

210 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 67 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	#11926571	C₂	1	2	yes	maximal, complemented
3	#11926562	C₂	1	2	yes	maximal
4	#11926512	C₂	1	1	yes	maximal, characteristic
5	C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#117	C₂²	1	2	yes	—
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	(C₂×D₁₉)⋊C₈	—	2	2	no	—
12	#10597276	—	2	2	no	—
13	#10597262	—	2	4	no	—
14	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
15	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₂×C₂²⋊D₁₉	—	2	1	no	—
17	#64541	—	2	2	no	—
18	#64541	—	2	2	no	—
19	C₂×D₇₆	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₁₉	—	2	1	no	—
21	C₂×Dic₃₈	Q₈	1	1	yes	characteristic
22	M₁₆×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	D₄	1	2	yes	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂²⋊C₄×C₁₉	—	2	2	no	—
26	C₄²×C₁₉	D₄	1	4	yes	—
27	#64520	—	2	2	no	—
28	#64520	—	2	2	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	1	no	—
32	C₂³×C₁₉	#41	1	1	yes	characteristic
33	C₂²×D₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#41	1	2	yes	—
39	C₂²⋊D₁₉	—	4	2	no	—
40	C₂×Dic₁₉	—	2	1	no	—
41	D₇₆	—	2	2	no	—
42	C₄×D₁₉	—	4	1	no	—
43	C₄×D₁₉	—	4	1	no	—
44	Dic₃₈	—	2	2	no	—
45	C₈×C₁₉	—	2	2	no	—
46	C₁₉⋊C₈	—	4	1	no	—
47	C₁₉⋊C₈	—	4	2	no	—
48	#2098	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	—	4	1	no	—
50	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₁₉	#123	1	2	yes	—
52	C₂×D₁₉	—	4	2	no	—
53	C₂×D₁₉	—	4	1	no	—
54	C₄×C₁₉	—	4	4	no	—
55	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
56	C₄×C₁₉	#123	1	1	yes	characteristic
57	C₄×C₁₉	#127	1	1	yes	characteristic
58	Dic₁₉	—	4	1	no	—
59	#430	—	19	1	no	—
60	#424	—	19	2	no	—
61	#421	—	19	2	no	—
62	#408	—	19	1	no	—
63	H(3,ℤ/4)	D₁₉	1	1	yes	characteristic, complemented
64	C₂×C₁₉	—	2	2	no	—
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	#399	1	1	yes	characteristic
67	D₁₉	—	8	1	no	—
68	C₂×#41	—	19	1	no	—
69	C₂×M₁₆	—	19	2	no	—
70	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
71	C₂²×C₈	—	19	1	no	—
72	#117	C₂×D₁₉	1	2	yes	—
73	#108	—	38	2	no	—
74	C₄⋊C₈	—	38	4	no	—
75	#104	—	38	4	no	—
76	C₂²⋊C₈	—	38	2	no	—
77	C₁₉	#2098	1	1	yes	characteristic, complemented, Sylow
78	#41	—	38	2	no	—
79	#41	—	38	2	no	—
80	C₂×Q₈	—	19	1	no	—
81	C₂×D₄	—	19	1	no	—
82	C₂×D₄	—	38	1	no	—
83	C₂²×C₄	—	38	1	no	—
84	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	38	2	no	—
87	M₁₆	—	38	2	no	—
88	C₂×C₈	—	38	1	no	—
89	C₂×C₈	—	38	2	no	—
90	C₂×C₈	—	38	2	no	—
91	C₂×C₈	D₇₆	1	2	yes	—
92	C₄⋊C₄	—	2	2	no	—
93	C₂²⋊C₄	—	2	2	no	—
94	C₄²	D₇₆	1	4	yes	—
95	C₂³	—	38	1	no	—
96	C₂³	#64543	1	1	yes	characteristic
97	Q₈	—	38	2	no	—
98	D₄	—	38	2	no	—
99	D₄	—	76	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	38	1	no	—
102	C₂×C₄	—	76	1	no	—
103	C₂×C₄	—	76	1	no	—
104	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
105	C₂×C₄	C₂×D₇₆	1	2	yes	—
106	C₂×C₄	#64543	1	2	yes	—
107	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	76	1	no	—
110	C₈	—	76	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	76	2	no	—
113	C₂²	—	76	1	no	—
114	C₂²	#10597332	1	2	yes	—
115	C₂²	#10597343	1	1	yes	characteristic
116	C₄	—	4	4	no	—
117	C₄	—	76	1	no	—
118	C₄	#10597320	1	1	yes	characteristic
119	C₄	#10597332	1	1	yes	characteristic
120	C₄	#10597343	1	2	yes	—
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	152	1	no	—
124	C₂	#11926481	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926593

C₂

yes

maximal, characteristic, complemented

#11926571

C₂

yes

maximal, complemented

#11926562

C₂

yes

maximal

#11926512

C₂

yes

maximal, characteristic

C₁₉×H(3,ℤ/4)

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

(C₂×D₁₉)⋊C₈

—

#10597276

—

#10597262

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

Q₈

yes

characteristic

C₂×C₄×D₁₉

—

C₂×Dic₃₈

Q₈

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2098

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#123

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#399

yes

characteristic

D₁₉

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

#117

C₂×D₁₉

yes

—

#108

—

C₄⋊C₈

—

#104

—

C₂²⋊C₈

—

C₁₉

#2098

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₇₆

yes

—

C₂³

—

C₂³

#64543

yes

characteristic

Q₈

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×D₇₆

yes

characteristic

105

C₂×C₄

C₂×D₇₆

yes

—

106

C₂×C₄

#64543

yes

—

107

C₂×C₄

Q₈×D₁₉

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

#10597332

yes

—

115

C₂²

#10597343

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

#10597320

yes

characteristic

119

C₄

#10597332

yes

characteristic

120

C₄

#10597343

yes

—

121

C₂

—

122

C₂

—

123

C₂

—

152

—

124

C₂

#11926481

yes

characteristic

	subgroup	G/H
center	C₄	#10597320
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×H(3,ℤ/4)	C₂
socle	C₂×C₁₉	#399
prime radical	C₂×#64541	C₂²
hypercenter	H(3,ℤ/4)	D₁₉
hypocenter	C₁₉	#2098
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#10597320

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×H(3,ℤ/4)

C₂

C₂×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
1. #11926593	C₂	semidirect
2. #11926571	C₂	semidirect
5. C₁₉×H(3,ℤ/4)	C₂	semidirect
63. H(3,ℤ/4)	D₁₉	semidirect
77. C₁₉	#2098	semidirect

H ≅ G/N

type

1. #11926593

C₂

semidirect

2. #11926571

C₂

semidirect

5. C₁₉×H(3,ℤ/4)

C₂

semidirect

63. H(3,ℤ/4)

D₁₉

semidirect

77. C₁₉

#2098

semidirect

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

subgroup	index
#11926593	2
#11926571	2
#11926562	2
#11926512	2
C₁₉×H(3,ℤ/4)	2
#2098	19

subgroup

index

C₁₉×H(3,ℤ/4)

Subgroups — #14565189

Conjugacy classes of subgroups

Complements

Maximal subgroups