Group #14565806 — subgroups

Subgroups — #14565806

Order 2432.

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

normal subgroups only

This group has 126 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	#11926942	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	#10597315	—	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	#10597274	—	2	1	no	—
13	#10597274	C₂²	1	2	yes	—
14	#10597269	C₂²	1	2	yes	—
15	#41×C₁₉	—	2	1	no	—
16	C₂×Dic₃₈	—	4	1	no	—
17	Q₁₆×C₁₉	Q₈	1	1	yes	characteristic, complemented
18	SD₁₆×C₁₉	—	2	1	no	—
19	D₈×C₁₉	Q₈	1	1	yes	characteristic, complemented
20	M₁₆×C₁₉	—	2	1	no	—
21	M₁₆×C₁₉	—	4	1	no	—
22	C₂×C₈×C₁₉	—	4	1	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	—	4	1	no	—
28	C₁₉⋊C₁₆	—	2	2	no	—
29	Q₈×C₁₉	—	2	1	no	—
30	D₄×C₁₉	—	2	1	no	—
31	D₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₁₉	—	4	2	no	—
36	Dic₃₈	—	8	2	no	—
37	C₈×C₁₉	—	4	1	no	—
38	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
39	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
40	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₁₉	#41	1	1	yes	characteristic
42	#2230	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	—	4	1	no	—
44	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
45	C₄×C₁₉	—	2	2	no	—
46	C₄×C₁₉	—	4	1	no	—
47	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
48	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
49	Dic₁₉	—	8	2	no	—
50	#498	—	19	1	no	—
51	#443	D₁₉	1	1	yes	characteristic
52	#365	—	19	2	no	—
53	#364	—	19	1	no	—
54	#360	—	19	2	no	—
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	8	1	no	—
57	C₂×C₁₉	#476	1	1	yes	characteristic
58	#135	C₂×D₁₉	1	1	yes	characteristic
59	#131	—	2	1	no	—
60	C₄⋊Q₈	—	38	1	no	—
61	M₃₂	—	19	2	no	—
62	#108	C₂×D₁₉	1	1	yes	characteristic
63	#106	—	19	2	no	—
64	#106	—	38	1	no	—
65	#104	—	2	1	no	—
66	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
67	C₁₉	#2230	1	1	yes	characteristic, complemented, Sylow
68	#41	—	2	1	no	—
69	C₂×Q₈	—	76	1	no	—
70	Q₁₆	Dic₃₈	1	1	yes	characteristic, complemented
71	SD₁₆	—	2	1	no	—
72	D₈	Dic₃₈	1	1	yes	characteristic, complemented
73	M₁₆	—	2	1	no	—
74	M₁₆	—	4	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
77	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	38	2	no	—
79	C₄⋊C₄	—	76	1	no	—
80	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
81	C₁₆	—	38	2	no	—
82	Q₈	—	2	1	no	—
83	Q₈	—	152	2	no	—
84	D₄	—	2	1	no	—
85	D₄	—	4	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	76	2	no	—
89	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
90	C₈	—	4	1	no	—
91	C₈	#64526	1	1	yes	characteristic
92	C₈	#64526	1	1	yes	characteristic
93	C₈	C₂×Dic₃₈	1	1	yes	characteristic
94	C₈	#64541	1	1	yes	characteristic
95	C₂²	—	4	1	no	—
96	C₂²	#10597395	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	4	1	no	—
99	C₄	—	152	2	no	—
100	C₄	#10597370	1	1	yes	characteristic
101	C₄	C₂×#64526	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	8	1	no	—
104	C₂	#11926834	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926942

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

—

#10597315

—

C₁₉×#108

C₂²

yes

characteristic

C₁₉×#104

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597274

—

#10597274

C₂²

yes

—

#10597269

C₂²

yes

—

#41×C₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

Q₈

yes

characteristic, complemented

SD₁₆×C₁₉

—

D₈×C₁₉

Q₈

yes

characteristic, complemented

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

—

C₄⋊Dic₁₉

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

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

—

#498

—

#443

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#476

yes

characteristic

#135

C₂×D₁₉

yes

characteristic

#131

—

C₄⋊Q₈

—

M₃₂

—

#108

C₂×D₁₉

yes

—

—

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2230

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

Q₁₆

Dic₃₈

yes

characteristic, complemented

SD₁₆

—

D₈

Dic₃₈

yes

characteristic, complemented

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

—

Q₈

—

152

—

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

—

100

C₄

#10597370

yes

characteristic

101

C₄

C₂×#64526

yes

characteristic

102

C₂

—

103

C₂

—

104

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	#2230
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. #11926942	C₂	semidirect
2. #11926368	C₂	semidirect
3. #11926365	C₂	semidirect
17. Q₁₆×C₁₉	Q₈	semidirect
19. D₈×C₁₉	Q₈	semidirect
67. C₁₉	#2230	semidirect
70. Q₁₆	Dic₃₈	semidirect
72. D₈	Dic₃₈	semidirect

H ≅ G/N

type

1. #11926942

C₂

semidirect

2. #11926368

C₂

semidirect

3. #11926365

C₂

semidirect

17. Q₁₆×C₁₉

Q₈

semidirect

19. D₈×C₁₉

Q₈

semidirect

67. C₁₉

#2230

semidirect

70. Q₁₆

Dic₃₈

semidirect

72. D₈

Dic₃₈

semidirect

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

subgroup	index
#11926942	2
#11926368	2
#11926365	2
#11926354	2
C₁₉×#443	2
#2230	19

subgroup

index

C₁₉×#443

Subgroups — #14565806

Conjugacy classes of subgroups

Complements

Maximal subgroups