Group #14572737 — subgroups

Subgroups — #14572737

Order 2432.

330 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 205 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	#11926675	C₂	1	4	yes	maximal, complemented
2	Q₈×C₁₉⋊C₈	C₂	1	4	yes	maximal, complemented
3	#11926605	C₂	1	4	yes	maximal
4	#11926597	C₂	1	2	yes	maximal
5	C₁₉×#533	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	C₄	1	2	yes	—
7	C₁₉×#125	C₄	1	2	yes	—
8	C₁₉×C₂²⋊Q₈	C₄	1	4	yes	—
9	C₄×Q₈×C₁₉	C₂²	1	4	yes	—
10	C₁₉×#117	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
13	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
15	C₄⋊(C₁₉⋊C₈)	C₂²	1	8	yes	—
16	#10597260	C₂²	1	4	yes	—
17	C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
18	C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
19	C₂×Q₈×C₁₉	C₂×C₄	1	4	yes	—
20	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
23	C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
24	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
26	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₁₉	C₂³	1	2	yes	—
29	C₄²×C₁₉	C₂³	1	4	yes	—
30	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
31	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
32	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	Q₈×C₁₉	—	2	8	no	—
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₁₉	C₂²×C₄	1	8	yes	—
39	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
40	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
41	C₁₉⋊C₈	—	2	4	no	—
42	C₁₉⋊C₈	—	2	4	no	—
43	#2986	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	—	2	2	no	—
46	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	—	2	8	no	—
50	C₄×C₁₉	#131	1	4	yes	—
51	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
52	#533	D₁₉	1	1	yes	characteristic
53	#446	—	19	4	no	—
54	C₈×Q₈	—	19	4	no	—
55	#433	—	19	4	no	—
56	#431	—	19	2	no	—
57	C₂×C₁₉	—	4	1	no	—
58	C₂×C₁₉	#519	1	1	yes	characteristic
59	C₂×C₁₉	C₂×#131	1	2	yes	—
60	C₄⋊Q₈	Dic₁₉	1	2	yes	—
61	#125	Dic₁₉	1	2	yes	—
62	C₂²⋊Q₈	Dic₁₉	1	4	yes	—
63	C₄×Q₈	C₂×D₁₉	1	4	yes	—
64	#117	C₂×D₁₉	1	2	yes	—
65	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
66	C₄⋊C₈	—	19	2	no	—
67	C₄⋊C₈	—	19	2	no	—
68	C₄⋊C₈	—	19	8	no	—
69	C₂²⋊C₈	—	19	4	no	—
70	#97	—	19	4	no	—
71	C₄×C₈	—	19	4	no	—
72	C₄×C₈	—	19	4	no	—
73	C₁₉	#2986	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	C₂×Dic₁₉	1	4	yes	—
75	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
76	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
77	C₂×C₈	—	19	4	no	—
78	C₂×C₈	—	19	4	no	—
79	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
80	C₄⋊C₄	C₂×Dic₁₉	1	8	yes	—
81	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
82	C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
83	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
84	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
85	C₄²	C₂²×D₁₉	1	2	yes	—
86	C₄²	C₂²×D₁₉	1	4	yes	—
87	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
88	Q₈	—	2	8	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
92	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
93	C₂×C₄	C₂²×Dic₁₉	1	8	yes	—
94	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
95	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
96	C₈	—	38	4	no	—
97	C₈	—	38	4	no	—
98	C₂²	—	2	2	no	—
99	C₂²	—	2	1	no	—
100	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	2	8	no	—
103	C₄	—	2	1	no	—
104	C₄	#10597394	1	4	yes	—
105	C₄	#10597433	1	2	yes	—
106	C₂	—	4	1	no	—
107	C₂	#11927022	1	1	yes	characteristic
108	C₂	C₂×#10597394	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926675

C₂

yes

maximal, complemented

Q₈×C₁₉⋊C₈

C₂

yes

maximal, complemented

#11926605

C₂

yes

maximal

#11926597

C₂

yes

maximal

C₁₉×#533

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₄

yes

—

C₁₉×#125

C₄

yes

—

C₁₉×C₂²⋊Q₈

C₄

yes

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₁₉×#117

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2986

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

2₋¹⁺⁴

yes

—

#533

D₁₉

yes

characteristic

#446

—

C₈×Q₈

—

#433

—

#431

—

C₂×C₁₉

—

C₂×C₁₉

#519

yes

characteristic

C₂×C₁₉

C₂×#131

yes

—

C₄⋊Q₈

Dic₁₉

yes

—

#125

Dic₁₉

yes

—

C₂²⋊Q₈

Dic₁₉

yes

—

C₄×Q₈

C₂×D₁₉

yes

—

#117

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#2986

yes

characteristic, complemented, Sylow

C₂×Q₈

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₂²⋊C₄

C₂×Dic₁₉

yes

—

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂²×D₁₉

yes

—

C₄²

C₂²×D₁₉

yes

—

C₂³

C₂²×Dic₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂×C₄

C₂³×D₁₉

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

100

C₂²

C₂³×Dic₁₉

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

#10597394

yes

—

105

C₄

#10597433

yes

—

106

C₂

—

107

C₂

#11927022

yes

characteristic

108

C₂

C₂×#10597394

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#533	C₂
prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#533	D₁₉
hypocenter	C₁₉	#2986
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #533

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₉

commutator, socle

C₂²×C₁₉

C₂³×C₄

Fitting

C₁₉×#533

C₂

prime radical

C₂³×C₁₉

C₂²×C₄

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #533

N	H ≅ G/N	type
1. #11926675	C₂	semidirect
2. Q₈×C₁₉⋊C₈	C₂	semidirect
73. C₁₉	#2986	semidirect

H ≅ G/N

type

1. #11926675

C₂

semidirect

2. Q₈×C₁₉⋊C₈

C₂

semidirect

73. C₁₉

#2986

semidirect

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

subgroup	index
#11926675	2
Q₈×C₁₉⋊C₈	2
#11926605	2
#11926597	2
C₁₉×#533	2
#2986	19

subgroup

index

Q₈×C₁₉⋊C₈

C₁₉×#533

Subgroups — #14572737

Conjugacy classes of subgroups

Complements

Maximal subgroups