Group #14565811 — subgroups

Subgroups — #14565811

Order 2432.

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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	#11926946	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926368	C₂	1	2	yes	maximal, complemented
3	#11926365	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926354	C₂	1	2	yes	maximal
5	C₁₉×#443	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#135	C₂²	1	1	yes	characteristic
7	C₁₉×#131	—	2	1	no	—
8	#10597316	—	2	1	no	—
9	C₁₉×#108	C₂²	1	1	yes	characteristic
10	C₁₉×#104	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597275	—	2	1	no	—
13	#10597274	C₂²	1	2	yes	—
14	#10597269	C₂²	1	2	yes	—
15	#41×C₁₉	—	2	1	no	—
16	Q₁₆×C₁₉	Q₈	1	1	yes	characteristic
17	SD₁₆×C₁₉	—	2	1	no	—
18	D₈×C₁₉	Q₈	1	1	yes	characteristic
19	M₁₆×C₁₉	—	2	1	no	—
20	M₁₆×C₁₉	—	4	1	no	—
21	C₂×C₈×C₁₉	—	4	1	no	—
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₄⋊Dic₁₉	—	2	2	no	—
26	Dic₁₉⋊C₄	—	4	2	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	Q₈×C₁₉	—	2	1	no	—
29	D₄×C₁₉	—	2	1	no	—
30	D₄×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	4	1	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₁₉	—	4	2	no	—
35	C₈×C₁₉	—	4	1	no	—
36	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
37	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
38	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2231	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	4	1	no	—
42	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₄×C₁₉	—	4	1	no	—
44	C₄×C₁₉	—	4	1	no	—
45	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
46	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
47	Dic₁₉	—	8	2	no	—
48	#499	—	19	1	no	—
49	#443	D₁₉	1	1	yes	characteristic
50	#365	—	19	2	no	—
51	#364	—	19	1	no	—
52	#360	—	19	2	no	—
53	C₂×C₁₉	—	2	1	no	—
54	C₂×C₁₉	—	8	1	no	—
55	C₂×C₁₉	#476	1	1	yes	characteristic
56	#135	C₂×D₁₉	1	1	yes	characteristic
57	#131	—	2	1	no	—
58	#125	—	38	1	no	—
59	M₃₂	—	19	2	no	—
60	#108	C₂×D₁₉	1	1	yes	characteristic
61	#107	—	38	1	no	—
62	#106	—	19	2	no	—
63	#104	—	2	1	no	—
64	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
65	C₁₉	#2231	1	1	yes	characteristic, complemented, Sylow
66	#41	—	2	1	no	—
67	Q₁₆	Dic₃₈	1	1	yes	characteristic
68	SD₁₆	—	2	1	no	—
69	D₈	Dic₃₈	1	1	yes	characteristic
70	M₁₆	—	2	1	no	—
71	M₁₆	—	4	1	no	—
72	C₂×C₈	—	4	1	no	—
73	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
75	C₄⋊C₄	—	38	2	no	—
76	C₄⋊C₄	—	76	2	no	—
77	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
78	C₁₆	—	38	2	no	—
79	Q₈	—	2	1	no	—
80	D₄	—	2	1	no	—
81	D₄	—	4	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	76	2	no	—
85	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
86	C₈	—	4	1	no	—
87	C₈	#64526	1	1	yes	characteristic
88	C₈	#64526	1	1	yes	characteristic
89	C₈	C₂×Dic₃₈	1	1	yes	characteristic
90	C₈	#64541	1	1	yes	characteristic
91	C₂²	—	4	1	no	—
92	C₂²	#10597395	1	1	yes	characteristic
93	C₄	—	4	1	no	—
94	C₄	—	4	1	no	—
95	C₄	—	152	2	no	—
96	C₄	#10597370	1	1	yes	characteristic
97	C₄	C₂×#64526	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	8	1	no	—
100	C₂	#11926834	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926946

C₂

yes

maximal, characteristic, complemented

#11926368

C₂

yes

maximal, complemented

#11926365

C₂

yes

maximal, characteristic, complemented

#11926354

C₂

yes

maximal

C₁₉×#443

C₂

yes

maximal, characteristic

C₁₉×#135

C₂²

yes

characteristic

C₁₉×#131

—

#10597316

—

C₁₉×#108

C₂²

yes

characteristic

C₁₉×#104

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

—

#10597274

C₂²

yes

—

#10597269

C₂²

yes

—

#41×C₁₉

—

Q₁₆×C₁₉

Q₈

yes

characteristic

SD₁₆×C₁₉

—

D₈×C₁₉

Q₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

SD₁₆

yes

characteristic

C₈×C₁₉

SD₁₆

yes

characteristic

C₈×C₁₉

C₂×Q₈

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

#499

—

#443

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#476

yes

characteristic

#135

C₂×D₁₉

yes

characteristic

#131

—

#125

—

M₃₂

—

#108

C₂×D₁₉

yes

—

—

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2231

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

Dic₃₈

yes

characteristic

SD₁₆

—

D₈

Dic₃₈

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

yes

C₈

yes

C₈

C₂×Dic₃₈

yes

characteristic

C₈

#64541

yes

characteristic

C₂²

—

C₂²

#10597395

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

C₄

yes

C₄

yes

C₂

—

C₂

—

100

C₂

#11926834

yes

characteristic

	subgroup	G/H
center	C₂	#11926834
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#443	C₂
socle	C₂×C₁₉	#476
prime radical	C₁₉×#135	C₂²
hypercenter	#443	D₁₉
hypocenter	C₁₉	#2231
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

subgroup

G/H

center

C₂

#11926834

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#443

C₂

socle

C₂×C₁₉

#476

prime radical

C₁₉×#135

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

N	H ≅ G/N	type
1. #11926946	C₂	semidirect
2. #11926368	C₂	semidirect
3. #11926365	C₂	semidirect
65. C₁₉	#2231	semidirect

H ≅ G/N

type

1. #11926946

C₂

semidirect

2. #11926368

C₂

semidirect

3. #11926365

C₂

semidirect

65. C₁₉

#2231

semidirect

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

subgroup	index
#11926946	2
#11926368	2
#11926365	2
#11926354	2
C₁₉×#443	2
#2231	19

subgroup

index

C₁₉×#443

Subgroups — #14565811

Conjugacy classes of subgroups

Complements

Maximal subgroups