Group #14564601 — subgroups

Subgroups — #14564601

Order 2432.

252 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 113 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	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#11926410	C₂	1	1	yes	maximal, characteristic
3	#11926306	C₂	1	4	yes	maximal
4	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#125	—	2	2	no	—
6	C₁₉×#125	C₄	1	4	yes	complemented
7	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
12	C₁₉⋊#95	—	2	2	no	—
13	C₄×C₁₉⋊C₈	—	2	2	no	—
14	C₂²×C₄×C₁₉	—	2	2	no	—
15	C₂²×C₄×C₁₉	D₄	1	2	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₉	—	2	2	no	—
18	C₄⋊C₄×C₁₉	—	2	8	no	—
19	C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
21	C₄²×C₁₉	C₂×C₄	1	2	yes	—
22	C₄²×C₁₉	D₄	1	2	yes	—
23	C₄⋊Dic₁₉	—	2	4	no	—
24	C₂×C₁₉⋊C₈	—	2	2	no	—
25	C₂×C₁₉⋊C₈	—	2	2	no	—
26	C₂×C₁₉⋊C₈	Q₈	1	4	yes	—
27	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₁₉	—	2	4	no	—
29	C₂×C₄×C₁₉	—	2	4	no	—
30	C₂×C₄×C₁₉	—	4	4	no	—
31	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
32	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₁₉	#41	1	2	yes	—
36	C₂×Dic₁₉	—	4	2	no	—
37	C₂×Dic₁₉	—	4	4	no	—
38	C₁₉⋊C₈	—	2	4	no	—
39	#1991	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₁₉	#124	1	1	yes	characteristic
42	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
43	C₂²×C₁₉	#135	1	4	yes	—
44	C₄×C₁₉	—	2	4	no	—
45	C₄×C₁₉	—	4	4	no	—
46	C₄×C₁₉	C₄×Q₈	1	2	yes	—
47	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
48	Dic₁₉	—	8	2	no	—
49	C₂×#125	D₁₉	1	1	yes	characteristic
50	C₂×C₄×C₈	—	19	1	no	—
51	#382	—	19	1	no	—
52	#340	—	19	4	no	—
53	C₂×C₁₉	#391	1	1	yes	characteristic
54	C₂×C₁₉	#416	1	2	yes	—
55	C₂×C₁₉	#488	1	2	yes	—
56	C₂×C₁₉	#499	1	2	yes	—
57	C₂²×C₈	—	19	2	no	—
58	#125	—	2	2	no	—
59	#125	Dic₁₉	1	4	yes	complemented
60	C₂×C₄⋊C₄	—	2	2	no	—
61	C₂×C₄⋊C₄	—	19	2	no	—
62	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
63	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
64	C₄×C₈	—	38	2	no	—
65	#95	—	38	2	no	—
66	C₁₉	#1991	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	2	2	no	—
68	C₂²×C₄	—	38	2	no	—
69	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
70	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
71	C₂×C₈	—	19	4	no	—
72	C₂×C₈	—	38	2	no	—
73	C₂×C₈	—	38	2	no	—
74	C₄⋊C₄	—	2	8	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	38	4	no	—
77	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
78	C₄²	C₂×Dic₁₉	1	2	yes	—
79	C₄²	C₂²⋊D₁₉	1	2	yes	—
80	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	4	4	no	—
84	C₂×C₄	—	76	2	no	—
85	C₂×C₄	—	76	4	no	—
86	C₂×C₄	C₂²⋊Dic₁₉	1	4	yes	—
87	C₂×C₄	Q₈×D₁₉	1	2	yes	—
88	C₂×C₄	#64545	1	2	yes	—
89	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
90	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
91	C₈	—	38	4	no	—
92	C₂²	#10597390	1	1	yes	characteristic
93	C₂²	#10597393	1	1	yes	characteristic
94	C₂²	#10597396	1	4	yes	—
95	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
96	C₄	—	2	4	no	—
97	C₄	—	4	4	no	—
98	C₄	—	152	2	no	—
99	C₄	Q₈×Dic₁₉	1	2	yes	—
100	C₄	#10597392	1	2	yes	—
101	C₂	#11926451	1	1	yes	characteristic
102	C₂	#11926540	1	2	yes	—
103	C₂	#11926901	1	2	yes	—
104	C₂	#11926943	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#11926410

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₁₉×#125

—

C₁₉×#125

C₄

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉⋊#95

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1991

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#124

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₉

#135

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×Q₈

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

Dic₁₉

—

C₂×#125

D₁₉

yes

characteristic

C₂×C₄×C₈

—

#382

—

#340

—

C₂×C₁₉

#391

yes

characteristic

C₂×C₁₉

#416

yes

—

C₂×C₁₉

#488

yes

—

C₂×C₁₉

#499

yes

—

C₂²×C₈

—

#125

—

#125

Dic₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄×C₈

—

#95

—

C₁₉

#1991

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄²

C₂×Dic₁₉

yes

—

C₄²

C₂²⋊D₁₉

yes

—

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

Q₈×D₁₉

yes

—

C₂×C₄

#64545

yes

—

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

C₄

Q₈×Dic₁₉

yes

—

100

C₄

#10597392

yes

—

101

C₂

#11926451

yes

characteristic

102

C₂

#11926540

yes

—

103

C₂

#11926901

yes

—

104

C₂

#11926943

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#1991
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#125

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
6. C₁₉×#125	C₄	semidirect
59. #125	Dic₁₉	semidirect
66. C₁₉	#1991	semidirect

H ≅ G/N

type

6. C₁₉×#125

C₄

semidirect

59. #125

Dic₁₉

semidirect

66. C₁₉

#1991

semidirect

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

subgroup	index
C₂×C₄×C₁₉⋊C₈	2
#11926410	2
#11926306	2
C₂×C₁₉×#125	2
#1991	19

subgroup

index

C₂×C₄×C₁₉⋊C₈

#11926410

#11926306

C₂×C₁₉×#125

#1991

Subgroups — #14564601

Conjugacy classes of subgroups

Complements

Maximal subgroups