Group #14561543 — subgroups

Subgroups — #14561543

Order 2432.

192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926508	C₂	1	2	yes	maximal
2	C₁₉×#381	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
4	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
5	C₂×#64520	—	2	2	no	—
6	C₁₉×#95	—	2	2	no	—
7	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
8	C₂²⋊(C₁₉⋊C₈)	C₄	1	4	yes	complemented
9	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₁₉	—	2	2	no	—
11	C₂²×C₄×C₁₉	—	4	2	no	—
12	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₉	D₄	1	2	yes	—
15	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
16	C₂²⋊C₄×C₁₉	—	4	2	no	—
17	#64520	—	4	4	no	—
18	C₂×C₁₉⋊C₈	—	2	4	no	—
19	C₂³×C₁₉	—	2	2	no	—
20	C₂³×C₁₉	—	4	2	no	—
21	C₂³×C₁₉	C₄²	1	1	yes	characteristic
22	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₉	—	2	4	no	—
25	C₂×C₄×C₁₉	—	4	2	no	—
26	C₂×C₄×C₁₉	—	4	1	no	—
27	C₂×C₄×C₁₉	—	4	1	no	—
28	C₂×C₄×C₁₉	—	4	4	no	—
29	C₂×C₄×C₁₉	—	4	2	no	—
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₁₉⋊C₈	—	4	4	no	—
33	#1306	—	19	1	no	maximal, Sylow
34	C₂²×C₁₉	—	2	2	no	—
35	C₂²×C₁₉	—	2	1	no	—
36	C₂²×C₁₉	—	2	1	no	—
37	C₂²×C₁₉	—	2	2	no	—
38	C₂²×C₁₉	—	2	2	no	—
39	C₂²×C₁₉	—	4	4	no	—
40	C₂²×C₁₉	#95	1	1	yes	characteristic
41	C₂²×C₁₉	#99	1	2	yes	—
42	C₄×C₁₉	—	2	2	no	—
43	C₄×C₁₉	—	2	2	no	—
44	C₄×C₁₉	—	8	2	no	—
45	#407	—	19	2	no	—
46	#381	D₁₉	1	1	yes	characteristic
47	C₂×C₁₉	—	2	2	no	—
48	C₂×C₁₉	—	4	1	no	—
49	C₂×C₁₉	—	4	1	no	—
50	C₂×C₁₉	#342	1	1	yes	characteristic
51	C₂×C₁₉	#344	1	2	yes	—
52	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
53	C₂×M₁₆	—	38	2	no	—
54	C₂×C₂²⋊C₄	Dic₁₉	1	2	yes	—
55	C₂²⋊C₈	—	19	4	no	—
56	C₂²⋊C₈	—	38	2	no	—
57	#95	—	2	2	no	—
58	C₁₉	#1306	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	C₂×Dic₁₉	1	1	yes	characteristic
60	C₂²×C₄	—	2	2	no	—
61	C₂²×C₄	—	4	2	no	—
62	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
63	C₂²×C₄	C₄×D₁₉	1	2	yes	—
64	C₂²×C₄	D₇₆	1	1	yes	characteristic
65	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
66	M₁₆	—	76	4	no	—
67	C₂×C₈	—	38	4	no	—
68	C₂²⋊C₄	—	4	2	no	—
69	C₂³	—	2	2	no	—
70	C₂³	—	4	2	no	—
71	C₂³	C₄×Dic₁₉	1	1	yes	characteristic
72	C₂³	C₄⋊Dic₁₉	1	1	yes	characteristic
73	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	4	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
81	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
82	C₈	—	76	4	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	2	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	4	4	no	—
89	C₂²	C₁₉⋊#95	1	1	yes	characteristic
90	C₂²	#10597291	1	2	yes	—
91	C₄	—	2	2	no	—
92	C₄	—	2	2	no	—
93	C₄	—	8	2	no	—
94	C₂	—	2	2	no	—
95	C₂	—	4	1	no	—
96	C₂	—	4	1	no	—
97	C₂	#11926311	1	1	yes	characteristic
98	C₂	#11926314	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926508

C₂

yes

maximal

C₁₉×#381

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₄

yes

—

C₂×#64520

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₄

yes

complemented

C₂⁴×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂²⋊C₄×C₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄²

yes

characteristic

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₁₉⋊C₈

—

#1306

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#95

yes

characteristic

C₂²×C₁₉

#99

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

#407

—

#381

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#342

yes

characteristic

C₂×C₁₉

#344

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×C₂²⋊C₄

Dic₁₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#95

—

C₁₉

#1306

yes

characteristic, complemented, Sylow

C₂⁴

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₃₈

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

—

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

—

M₁₆

—

C₂×C₈

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

C₄×Dic₁₉

yes

characteristic

C₂³

C₄⋊Dic₁₉

yes

characteristic

C₂³

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Dic₁₉⋊C₄

yes

—

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₁₉⋊#95

yes

characteristic

C₂²

#10597291

yes

—

C₄

—

C₄

—

C₄

—

C₂

—

C₂

—

C₂

—

C₂

#11926311

yes

characteristic

C₂

#11926314

yes

—

	subgroup	G/H
center	C₂²	C₁₉⋊#95
commutator	C₂³×C₁₉	C₄²
Frattini	C₂³×C₄	C₂×D₁₉
Fitting	C₁₉×#381	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂²
hypercenter	#381	D₁₉
hypocenter	C₁₉	#1306
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

subgroup

G/H

center

C₂²

C₁₉⋊#95

commutator

C₂³×C₁₉

C₄²

Frattini

C₂³×C₄

C₂×D₁₉

Fitting

C₁₉×#381

C₂

socle

C₂²×C₁₉

#95

prime radical

C₂⁴×C₁₉

C₂×C₄

cosocle

C₂³×C₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

N	H ≅ G/N	type
8. C₂²⋊(C₁₉⋊C₈)	C₄	semidirect
58. C₁₉	#1306	semidirect

H ≅ G/N

type

8. C₂²⋊(C₁₉⋊C₈)

C₄

semidirect

58. C₁₉

#1306

semidirect

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

subgroup	index
#11926508	2
C₁₉×#381	2
#1306	19

subgroup

index

#11926508

C₁₉×#381

#1306

Subgroups — #14561543

Conjugacy classes of subgroups

Complements

Maximal subgroups