Group #14569737 — subgroups

Subgroups — #14569737

Order 2432.

804 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597376	C₂	1	6	yes	maximal, complemented
2	#11926481	C₂	1	4	yes	maximal, complemented
3	#11926454	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
6	C₂²×C₂²⋊D₁₉	C₂²	1	4	yes	—
7	C₂²×D₇₆	C₂²	1	6	yes	—
8	#10597376	—	2	24	no	—
9	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	12	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	6	yes	—
11	C₁₉×#95	C₂²	1	4	yes	—
12	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
13	C₂³×D₁₉	C₂³	1	4	yes	—
14	C₂²×C₄×C₁₉	—	4	6	no	—
15	C₂²×C₄×C₁₉	D₄	1	12	yes	complemented
16	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
17	C₂×C₂²⋊D₁₉	—	2	24	no	—
18	C₂²×Dic₁₉	C₂³	1	4	yes	—
19	C₂×D₇₆	—	2	12	no	—
20	C₂×D₇₆	—	4	12	no	—
21	(C₂×D₁₉)⋊C₄	—	2	24	no	—
22	C₄⋊Dic₁₉	—	2	12	no	—
23	C₂³×C₁₉	—	2	3	no	—
24	C₂³×C₁₉	—	2	1	no	—
25	C₂³×C₁₉	C₂×D₄	1	6	yes	—
26	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
27	C₂²×D₁₉	—	2	12	no	—
28	C₂²×D₁₉	—	2	12	no	—
29	C₂²×D₁₉	—	2	4	no	—
30	C₂×C₄×C₁₉	—	2	12	no	—
31	C₂×C₄×C₁₉	—	4	12	no	—
32	C₂×C₄×C₁₉	C₂×D₄	1	12	yes	—
33	C₂²⋊D₁₉	—	4	16	no	—
34	C₂×Dic₁₉	—	2	12	no	—
35	D₇₆	—	4	24	no	—
36	#2656	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	—	2	6	no	—
38	C₂²×C₁₉	—	2	6	no	—
39	C₂²×C₁₉	#127	1	4	yes	—
40	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
41	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
42	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
43	C₂×D₁₉	—	4	4	no	—
44	C₂×D₁₉	—	4	12	no	—
45	C₂×D₁₉	—	4	12	no	—
46	C₄×C₁₉	—	2	12	no	—
47	Dic₁₉	—	4	4	no	—
48	C₂×#121	—	19	6	no	—
49	#399	—	19	4	no	—
50	#392	—	19	4	no	—
51	C₂×#95	D₁₉	1	1	yes	characteristic, complemented
52	C₂×C₁₉	—	2	4	no	—
53	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
54	C₂×C₁₉	#534	1	3	yes	—
55	C₂×C₁₉	#537	1	3	yes	—
56	D₁₉	—	8	4	no	—
57	C₂²×D₄	—	19	4	no	—
58	C₂²×D₄	—	19	6	no	—
59	C₂³×C₄	C₂×D₁₉	1	3	yes	—
60	#121	—	38	24	no	—
61	C₂×C₄⋊C₄	—	19	6	no	—
62	C₂×C₂²⋊C₄	—	19	12	no	—
63	#95	C₂×D₁₉	1	4	yes	—
64	C₁₉	#2656	1	1	yes	characteristic, complemented, Sylow
65	C₂⁴	—	19	4	no	—
66	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
67	C₂×D₄	—	38	24	no	—
68	C₂×D₄	—	38	12	no	—
69	C₂×D₄	—	76	12	no	—
70	C₂²×C₄	—	4	6	no	—
71	C₂²×C₄	—	19	4	no	—
72	C₂²×C₄	D₇₆	1	12	yes	complemented
73	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
74	C₄⋊C₄	—	38	12	no	—
75	C₂²⋊C₄	—	38	24	no	—
76	C₂³	—	2	3	no	—
77	C₂³	—	2	1	no	—
78	C₂³	—	38	12	no	—
79	C₂³	—	38	12	no	—
80	C₂³	—	38	4	no	—
81	C₂³	C₂×D₇₆	1	6	yes	—
82	C₂³	C₂³×D₁₉	1	1	yes	characteristic
83	D₄	—	76	24	no	—
84	D₄	—	76	16	no	—
85	C₂×C₄	—	2	12	no	—
86	C₂×C₄	—	4	12	no	—
87	C₂×C₄	—	38	12	no	—
88	C₂×C₄	C₂×D₇₆	1	12	yes	—
89	C₂²	—	2	6	no	—
90	C₂²	—	2	6	no	—
91	C₂²	—	76	4	no	—
92	C₂²	—	76	12	no	—
93	C₂²	—	76	12	no	—
94	C₂²	#10597320	1	4	yes	—
95	C₂²	C₂²×D₇₆	1	3	yes	—
96	C₂²	#10597430	1	3	yes	—
97	C₂²	#10597433	1	1	yes	characteristic
98	C₄	—	2	12	no	—
99	C₄	—	76	4	no	—
100	C₂	—	2	4	no	—
101	C₂	—	152	4	no	—
102	C₂	C₂×#10597320	1	1	yes	characteristic
103	C₂	#11927106	1	3	yes	—
104	C₂	#11927125	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597376

C₂

yes

maximal, complemented

#11926481

C₂

yes

maximal, complemented

#11926454

C₂

yes

maximal, complemented

C₂×C₁₉×#95

C₂

yes

maximal, characteristic, complemented

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊D₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

#10597376

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2656

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

Dic₁₉

—

C₂×#121

—

#399

—

#392

—

C₂×#95

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

#534

yes

—

C₂×C₁₉

#537

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

C₂×D₁₉

yes

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

#95

C₂×D₁₉

yes

—

C₁₉

#2656

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

complemented

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×D₇₆

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#10597320

yes

—

C₂²

C₂²×D₇₆

yes

—

C₂²

#10597430

yes

—

C₂²

#10597433

yes

characteristic

C₄

—

C₄

—

100

C₂

—

101

C₂

—

152

—

102

C₂

C₂×#10597320

yes

characteristic

103

C₂

#11927106

yes

—

104

C₂

#11927125

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#95	C₂
hypercenter	C₂×#95	D₁₉
hypocenter	C₁₉	#2656
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#95

C₂

hypercenter

C₂×#95

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
1. C₂×#10597376	C₂	semidirect
2. #11926481	C₂	semidirect
3. #11926454	C₂	semidirect
4. C₂×C₁₉×#95	C₂	semidirect
15. C₂²×C₄×C₁₉	D₄	semidirect
51. C₂×#95	D₁₉	semidirect
64. C₁₉	#2656	semidirect
72. C₂²×C₄	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597376

C₂

semidirect

2. #11926481

C₂

semidirect

3. #11926454

C₂

semidirect

4. C₂×C₁₉×#95

C₂

semidirect

15. C₂²×C₄×C₁₉

D₄

semidirect

51. C₂×#95

D₁₉

semidirect

64. C₁₉

#2656

semidirect

72. C₂²×C₄

D₇₆

semidirect

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

subgroup	index
C₂×#10597376	2
#11926481	2
#11926454	2
C₂×C₁₉×#95	2
#2656	19

subgroup

index

C₂×C₁₉×#95

Subgroups — #14569737

Conjugacy classes of subgroups

Complements

Maximal subgroups