Group #14565440 — subgroups

Subgroups — #14565440

Order 2432.

138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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	#11926498	C₂	1	1	yes	maximal, characteristic
2	Dic₁₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	(C₂×D₁₉)⋊C₁₆	C₂	1	2	yes	maximal
4	#11926320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64515	C₄	1	1	yes	characteristic
7	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
8	#10597318	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597272	C₄	1	1	yes	characteristic
12	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
14	#10597260	C₄	1	1	yes	characteristic
15	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
18	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	(C₂×D₁₉)⋊C₄	C₈	1	2	yes	—
20	Dic₁₉⋊C₄	C₈	1	2	yes	—
21	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#64515	—	2	2	no	—
25	C₈×D₁₉	—	2	2	no	—
26	C₁₆×C₁₉	—	2	2	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	C₂²×D₁₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₁₉	C₂×C₈	1	2	yes	—
32	C₂×Dic₁₉	C₂×C₈	1	1	yes	characteristic
33	C₄×D₁₉	—	2	1	no	—
34	C₄×D₁₉	—	2	1	no	—
35	C₈×C₁₉	M₁₆	1	2	yes	—
36	C₈×C₁₉	#41	1	2	yes	—
37	C₁₉⋊C₈	—	2	1	no	—
38	C₁₉⋊C₈	—	2	1	no	—
39	#2164	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₁₉	—	2	1	no	—
42	C₂×D₁₉	—	2	2	no	—
43	C₄×C₁₉	—	2	2	no	—
44	C₄×C₁₉	#117	1	1	yes	characteristic
45	C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
46	Dic₁₉	—	2	1	no	—
47	Dic₁₉	—	2	2	no	—
48	#405	—	19	1	no	—
49	C₄⋊C₁₆	—	19	2	no	—
50	C₂²⋊C₁₆	—	19	2	no	—
51	#346	—	19	1	no	—
52	C₄×C₁₆	D₁₉	1	1	yes	characteristic, complemented
53	C₂×C₁₉	#431	1	1	yes	characteristic
54	C₂×C₁₉	#504	1	2	yes	—
55	D₁₉	—	4	1	no	—
56	C₂×M₁₆	—	19	1	no	—
57	C₂²×C₈	—	19	1	no	—
58	#117	—	19	1	no	—
59	C₂×C₁₆	—	19	2	no	—
60	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
61	#97	—	19	1	no	—
62	#97	—	19	1	no	—
63	C₄×C₈	—	19	1	no	—
64	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
65	C₁₉	#2164	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	19	1	no	—
67	M₁₆	—	38	2	no	—
68	C₂×C₈	—	19	1	no	—
69	C₂×C₈	—	19	1	no	—
70	C₂×C₈	—	38	2	no	—
71	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
73	C₄⋊C₄	—	19	2	no	—
74	C₂²⋊C₄	—	19	2	no	—
75	C₄²	—	19	1	no	—
76	C₄²	C₄×D₁₉	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	38	2	no	—
79	C₂³	—	19	1	no	—
80	C₂×C₄	—	19	2	no	—
81	C₂×C₄	—	19	1	no	—
82	C₂×C₄	—	38	1	no	—
83	C₂×C₄	—	38	1	no	—
84	C₂×C₄	C₈×D₁₉	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
86	C₈	—	38	1	no	—
87	C₈	—	38	1	no	—
88	C₈	#64515	1	2	yes	—
89	C₈	#64541	1	2	yes	—
90	C₂²	—	38	1	no	—
91	C₂²	—	38	2	no	—
92	C₂²	C₂×C₈×D₁₉	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	38	1	no	—
95	C₄	—	38	2	no	—
96	C₄	#10597318	1	1	yes	characteristic
97	C₄	C₂×#64515	1	1	yes	characteristic
98	C₂	—	76	1	no	—
99	C₂	#11926595	1	1	yes	characteristic
100	C₂	#11926960	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926498

C₂

yes

maximal, characteristic

Dic₁₉⋊C₁₆

C₂

yes

maximal, complemented

(C₂×D₁₉)⋊C₁₆

C₂

yes

maximal

#11926320

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×#64515

C₄

yes

characteristic

C₂×C₈×D₁₉

C₂²

yes

characteristic

#10597318

C₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597272

C₄

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

—

#10597260

C₄

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

(C₂×D₁₉)⋊C₄

C₈

yes

—

Dic₁₉⋊C₄

C₈

yes

—

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

#64515

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂²×D₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×Dic₁₉

C₂×C₈

yes

—

C₂×Dic₁₉

C₂×C₈

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

M₁₆

yes

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2164

—

maximal, Sylow

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₂×M₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#431

yes

characteristic

C₂×C₁₉

#504

yes

—

D₁₉

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2164

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₁₉

yes

—

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

#64515

yes

—

C₈

#64541

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#11926595

yes

characteristic

100

C₂

#11926960

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂²×C₈
Fitting	C₄×C₁₆×C₁₉	C₂
prime radical	C₂²×D₁₉	C₂×C₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#2164
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₉

commutator, socle

C₂²×C₁₉

C₂²×C₈

Fitting

C₄×C₁₆×C₁₉

C₂

prime radical

C₂²×D₁₉

C₂×C₈

cosocle

C₂×C₈×C₁₉

C₂³

hypercenter

C₄×C₁₆

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. Dic₁₉⋊C₁₆	C₂	semidirect
4. #11926320	C₂	semidirect
5. C₄×C₁₆×C₁₉	C₂	semidirect
52. C₄×C₁₆	D₁₉	semidirect
65. C₁₉	#2164	semidirect

H ≅ G/N

type

2. Dic₁₉⋊C₁₆

C₂

semidirect

4. #11926320

C₂

semidirect

5. C₄×C₁₆×C₁₉

C₂

semidirect

52. C₄×C₁₆

D₁₉

semidirect

65. C₁₉

#2164

semidirect

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

subgroup	index
#11926498	2
Dic₁₉⋊C₁₆	2
(C₂×D₁₉)⋊C₁₆	2
#11926320	2
C₄×C₁₆×C₁₉	2
#2164	19

subgroup

index

#11926498

Dic₁₉⋊C₁₆

(C₂×D₁₉)⋊C₁₆

#11926320

C₄×C₁₆×C₁₉

#2164

Subgroups — #14565440

Conjugacy classes of subgroups

Complements

Maximal subgroups