Group #14571709 — subgroups

Subgroups — #14571709

Order 2432.

456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597322	C₂	1	2	yes	maximal, complemented
2	#11926474	C₂	1	3	yes	maximal, complemented
3	#11926466	C₂	1	6	yes	maximal, complemented
4	#11926461	C₂	1	3	yes	maximal
5	C₁₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
11	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
14	#10597322	—	2	8	no	—
15	C₁₉⋊#95	C₂²	1	3	yes	—
16	C₁₉⋊#95	C₂²	1	3	yes	—
17	C₂³×D₁₉	C₂³	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
21	C₂²×Dic₁₉	C₂³	1	6	yes	—
22	C₂×D₇₆	—	4	3	no	—
23	C₄⋊C₄×C₁₉	—	4	3	no	—
24	C₄⋊C₄×C₁₉	—	4	3	no	—
25	C₄²×C₁₉	D₄	1	4	yes	complemented
26	(C₂×D₁₉)⋊C₄	—	2	12	no	—
27	(C₂×D₁₉)⋊C₄	—	4	6	no	—
28	C₄⋊Dic₁₉	—	4	3	no	—
29	Dic₁₉⋊C₄	—	2	12	no	—
30	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
31	C₂²×D₁₉	—	2	2	no	—
32	C₂²×D₁₉	—	2	6	no	—
33	C₂²×D₁₉	—	2	6	no	—
34	C₂×C₄×C₁₉	—	2	3	no	—
35	C₂×C₄×C₁₉	—	2	3	no	—
36	C₂×C₄×C₁₉	—	2	3	no	—
37	C₂×C₄×C₁₉	—	2	6	no	—
38	C₂×C₄×C₁₉	—	2	3	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
40	C₂×Dic₁₉	—	2	6	no	—
41	C₂×Dic₁₉	—	2	6	no	—
42	C₂×Dic₁₉	—	2	6	no	—
43	D₇₆	—	4	4	no	—
44	#2823	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
46	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
47	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
48	C₂×D₁₉	—	4	6	no	—
49	C₂×D₁₉	—	4	2	no	—
50	C₂×D₁₉	—	4	6	no	—
51	C₄×C₁₉	—	2	6	no	—
52	C₄×C₁₉	—	4	1	no	—
53	C₄×C₁₉	—	4	3	no	—
54	Dic₁₉	—	4	6	no	—
55	C₂×#126	—	19	2	no	—
56	#398	—	19	3	no	—
57	#396	—	19	6	no	—
58	#394	—	19	3	no	—
59	#384	D₁₉	1	1	yes	characteristic, complemented
60	C₂×C₁₉	#537	1	3	yes	—
61	C₂×C₁₉	#560	1	1	yes	characteristic
62	C₂×C₁₉	#563	1	3	yes	—
63	D₁₉	—	8	2	no	—
64	C₂²×D₄	—	19	1	no	—
65	#126	—	38	8	no	—
66	C₂×C₄⋊C₄	—	19	6	no	—
67	C₂×C₄⋊C₄	—	19	3	no	—
68	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
69	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
70	C₂×C₂²⋊C₄	—	19	6	no	—
71	C₂×C₂²⋊C₄	—	19	6	no	—
72	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
73	#95	—	19	3	no	—
74	#95	—	19	3	no	—
75	C₁₉	#2823	1	1	yes	characteristic, complemented, Sylow
76	C₂⁴	—	19	2	no	—
77	C₂×D₄	—	76	3	no	—
78	C₂²×C₄	—	19	6	no	—
79	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
80	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
81	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
82	C₄⋊C₄	—	4	3	no	—
83	C₄⋊C₄	—	4	3	no	—
84	C₄⋊C₄	—	38	12	no	—
85	C₄⋊C₄	—	76	3	no	—
86	C₂²⋊C₄	—	38	12	no	—
87	C₂²⋊C₄	—	76	6	no	—
88	C₄²	D₇₆	1	4	yes	complemented
89	C₂³	—	38	2	no	—
90	C₂³	—	38	6	no	—
91	C₂³	—	38	6	no	—
92	C₂³	C₂³×D₁₉	1	1	yes	characteristic
93	D₄	—	76	4	no	—
94	C₂×C₄	—	2	3	no	—
95	C₂×C₄	—	2	3	no	—
96	C₂×C₄	—	2	6	no	—
97	C₂×C₄	—	2	3	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	38	6	no	—
100	C₂×C₄	—	38	6	no	—
101	C₂×C₄	—	38	6	no	—
102	C₂×C₄	C₂×D₇₆	1	6	yes	—
103	C₂²	—	76	6	no	—
104	C₂²	—	76	2	no	—
105	C₂²	—	76	6	no	—
106	C₂²	C₂²×D₇₆	1	1	yes	characteristic
107	C₂²	#10597430	1	3	yes	—
108	C₂²	#10597433	1	3	yes	—
109	C₄	—	2	6	no	—
110	C₄	—	4	1	no	—
111	C₄	—	4	3	no	—
112	C₄	—	76	6	no	—
113	C₂	—	152	2	no	—
114	C₂	#11927125	1	3	yes	—
115	C₂	#11927281	1	1	yes	characteristic
116	C₂	#11927293	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597322

C₂

yes

maximal, complemented

#11926474

C₂

yes

maximal, complemented

#11926466

C₂

yes

maximal, complemented

#11926461

C₂

yes

maximal

C₁₉×#384

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597322

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

complemented

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2823

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#537

yes

—

C₂×C₁₉

#560

yes

characteristic

C₂×C₁₉

#563

yes

—

D₁₉

—

C₂²×D₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

#95

—

C₁₉

#2823

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

D₇₆

yes

complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₁₉

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂×D₇₆

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂²×D₇₆

yes

characteristic

107

C₂²

#10597430

yes

—

108

C₂²

#10597433

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₂

—

152

—

114

C₂

#11927125

yes

—

115

C₂

#11927281

yes

characteristic

116

C₂

#11927293

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#384	C₂
prime radical	C₂²×D₇₆	C₂²
hypercenter	#384	D₁₉
hypocenter	C₁₉	#2823
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#384

C₂

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
1. C₂×#10597322	C₂	semidirect
2. #11926474	C₂	semidirect
3. #11926466	C₂	semidirect
5. C₁₉×#384	C₂	semidirect
25. C₄²×C₁₉	D₄	semidirect
59. #384	D₁₉	semidirect
75. C₁₉	#2823	semidirect
88. C₄²	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597322

C₂

semidirect

2. #11926474

C₂

semidirect

3. #11926466

C₂

semidirect

5. C₁₉×#384

C₂

semidirect

25. C₄²×C₁₉

D₄

semidirect

59. #384

D₁₉

semidirect

75. C₁₉

#2823

semidirect

88. C₄²

D₇₆

semidirect

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

subgroup	index
C₂×#10597322	2
#11926474	2
#11926466	2
#11926461	2
C₁₉×#384	2
#2823	19

subgroup

index

C₁₉×#384

Subgroups — #14571709

Conjugacy classes of subgroups

Complements

Maximal subgroups