Group #14561626 — subgroups

Subgroups — #14561626

Order 2432.

110 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 33 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	#11926326	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#469	C₂	1	1	yes	maximal, characteristic
4	C₂×D₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×#121	—	2	1	no	—
7	C₂×#64520	—	2	1	no	—
8	C₁₉×#106	C₄	1	1	yes	characteristic
9	C₁₉×#102	—	2	1	no	—
10	#10597269	—	2	1	no	—
11	C₂×D₄×C₁₉	—	2	1	no	—
12	C₂×D₄×C₁₉	—	4	1	no	—
13	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
14	D₈×C₁₉	—	4	1	no	—
15	M₁₆×C₁₉	—	4	1	no	—
16	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₂²⋊C₄×C₁₉	—	4	1	no	—
20	#64520	—	4	1	no	—
21	#64520	—	4	1	no	—
22	C₂×C₁₉⋊C₈	—	2	2	no	—
23	C₁₉⋊C₁₆	—	4	1	no	—
24	C₂³×C₁₉	—	4	1	no	—
25	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
26	D₄×C₁₉	—	4	1	no	—
27	D₄×C₁₉	—	4	1	no	—
28	D₄×C₁₉	—	8	2	no	—
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
34	C₈×C₁₉	—	2	1	no	—
35	C₈×C₁₉	—	2	1	no	—
36	C₁₉⋊C₈	—	4	2	no	—
37	#1341	—	19	1	no	maximal, Sylow
38	C₂²×C₁₉	—	2	1	no	—
39	C₂²×C₁₉	—	4	1	no	—
40	C₂²×C₁₉	—	8	1	no	—
41	C₂²×C₁₉	—	8	1	no	—
42	C₂²×C₁₉	—	8	1	no	—
43	C₂²×C₁₉	#102	1	1	yes	characteristic
44	C₄×C₁₉	—	2	1	no	—
45	C₄×C₁₉	—	8	1	no	—
46	C₄×C₁₉	#99	1	1	yes	characteristic
47	C₄×C₁₉	#104	1	1	yes	characteristic
48	#469	D₁₉	1	1	yes	characteristic
49	#349	—	19	1	no	—
50	#338	—	19	1	no	—
51	C₂×C₁₉	—	2	1	no	—
52	C₂×C₁₉	—	4	1	no	—
53	C₂×C₁₉	—	16	1	no	—
54	C₂×C₁₉	#327	1	1	yes	characteristic
55	C₂×D₈	Dic₁₉	1	1	yes	characteristic
56	C₂×M₁₆	—	38	1	no	—
57	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
58	#121	—	2	1	no	—
59	M₃₂	—	38	1	no	—
60	#106	Dic₁₉	1	1	yes	characteristic
61	#102	—	2	1	no	—
62	C₁₉	#1341	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₄	—	2	1	no	—
64	C₂×D₄	—	4	1	no	—
65	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
66	D₈	—	4	1	no	—
67	M₁₆	—	4	1	no	—
68	M₁₆	—	76	1	no	—
69	M₁₆	—	76	1	no	—
70	C₂×C₈	—	38	2	no	—
71	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
72	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₁₆	—	76	1	no	—
76	C₂³	—	4	1	no	—
77	C₂³	#64526	1	1	yes	characteristic
78	D₄	—	4	1	no	—
79	D₄	—	4	1	no	—
80	D₄	—	8	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	#64525	1	1	yes	characteristic
85	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	—	76	2	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	4	1	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	8	1	no	—
94	C₂²	#10597289	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	8	1	no	—
97	C₄	#10597291	1	1	yes	characteristic
98	C₄	#10597294	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	4	1	no	—
101	C₂	—	16	1	no	—
102	C₂	#11926278	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926326

C₂

yes

maximal, characteristic, complemented

C₁₉⋊#338

C₂

yes

maximal, characteristic, complemented

C₁₉×#469

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#121

—

C₂×#64520

—

C₁₉×#106

C₄

yes

characteristic

C₁₉×#102

—

#10597269

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

D₈×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

C₂³×C₁₉

SD₁₆

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1341

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#102

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

D₁₉

yes

characteristic

#349

—

#338

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#327

yes

characteristic

C₂×D₈

Dic₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#121

—

M₃₂

—

#106

Dic₁₉

yes

characteristic

#102

—

C₁₉

#1341

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

—

C₂³

#64526

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64525

yes

characteristic

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#10597289

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

102

C₂

#11926278

yes

characteristic

	subgroup	G/H
center	C₂	#11926278
commutator	C₂×C₈×C₁₉	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₁₉
Fitting, prime radical	C₁₉×#469	C₂
socle	C₂×C₁₉	#327
cosocle	C₂×M₁₆×C₁₉	C₂²
hypercenter	#469	D₁₉
hypocenter	C₁₉	#1341
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

subgroup

G/H

center

C₂

#11926278

commutator

C₂×C₈×C₁₉

C₂×C₄

Frattini

C₂×M₁₆

C₂×D₁₉

Fitting, prime radical

C₁₉×#469

C₂

socle

C₂×C₁₉

#327

cosocle

C₂×M₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

N	H ≅ G/N	type
1. #11926326	C₂	semidirect
2. C₁₉⋊#338	C₂	semidirect
62. C₁₉	#1341	semidirect

H ≅ G/N

type

1. #11926326

C₂

semidirect

2. C₁₉⋊#338

C₂

semidirect

62. C₁₉

#1341

semidirect

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

subgroup	index
#11926326	2
C₁₉⋊#338	2
C₁₉×#469	2
#1341	19

subgroup

index

#11926326

C₁₉⋊#338

C₁₉×#469

#1341

Subgroups — #14561626

Conjugacy classes of subgroups

Complements

Maximal subgroups