Group #14576848 — subgroups

Subgroups — 2₋¹⁺⁴×Dic₁₉ #14576848

Order 2432.

1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 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	#11927027	C₂	1	10	yes	maximal, complemented
2	#11927022	C₂	1	5	yes	maximal, complemented
3	#41×Dic₁₉	C₂	1	10	yes	maximal, complemented
4	C₂×Q₈×Dic₁₉	C₂	1	5	yes	maximal, complemented
5	C₂×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
6	C₁₉×2₋¹⁺⁴	C₄	1	16	yes	complemented
7	C₂×#41×C₁₉	C₂²	1	10	yes	—
8	C₂²×Q₈×C₁₉	C₂²	1	5	yes	—
9	Q₈×Dic₁₉	C₂²	1	10	yes	—
10	Q₈×Dic₁₉	C₂²	1	20	yes	—
11	Q₈×Dic₁₉	C₂²	1	10	yes	—
12	D₄×Dic₁₉	C₂²	1	10	yes	—
13	D₄×Dic₁₉	C₂²	1	30	yes	—
14	#10597372	C₂²	1	30	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	15	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	15	yes	—
17	#41×C₁₉	C₂×C₄	1	80	yes	complemented
18	C₂×Q₈×C₁₉	C₂×C₄	1	40	yes	complemented
19	C₂×Q₈×C₁₉	C₂³	1	10	yes	—
20	C₂×D₄×C₁₉	C₂³	1	10	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	15	yes	—
22	C₂²×Dic₁₉	C₂³	1	5	yes	—
23	C₂²×Dic₁₉	C₂³	1	15	yes	—
24	C₂²⋊Dic₁₉	C₂³	1	20	yes	—
25	C₄⋊Dic₁₉	C₂³	1	30	yes	—
26	C₄⋊Dic₁₉	C₂³	1	10	yes	—
27	C₄×Dic₁₉	C₂³	1	10	yes	—
28	C₄×Dic₁₉	C₂³	1	30	yes	—
29	C₂³×C₁₉	C₂⁴	1	5	yes	—
30	Q₈×C₁₉	C₂²×C₄	1	40	yes	—
31	D₄×C₁₉	C₂²×C₄	1	40	yes	—
32	C₂×C₄×C₁₉	C₂²×C₄	1	60	yes	—
33	C₂×C₄×C₁₉	C₂⁴	1	10	yes	—
34	C₂×Dic₁₉	—	2	10	no	—
35	C₂×Dic₁₉	—	4	15	no	—
36	C₂×Dic₁₉	C₂⁴	1	5	yes	—
37	C₂×Dic₁₉	C₂⁴	1	10	yes	—
38	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
39	C₄×2₋¹⁺⁴	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	—	2	5	no	—
41	C₂²×C₁₉	—	2	5	no	—
42	C₂²×C₁₉	C₂³×C₄	1	10	yes	—
43	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
44	C₄×C₁₉	C₂³×C₄	1	20	yes	—
45	Dic₁₉	—	2	5	no	—
46	Dic₁₉	—	2	10	no	—
47	Dic₁₉	2₋¹⁺⁴	1	2	yes	direct product factor
48	C₂×2₋¹⁺⁴	D₁₉	1	1	yes	characteristic
49	#520	—	19	10	no	—
50	#519	—	19	5	no	—
51	C₄×#41	—	19	10	no	—
52	C₂×C₄×Q₈	—	19	5	no	—
53	C₂×C₁₉	—	2	10	no	—
54	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
55	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
56	C₂×C₁₉	#585	1	1	yes	characteristic
57	2₋¹⁺⁴	Dic₁₉	1	16	yes	direct product factor
58	C₂×#41	C₂×D₁₉	1	10	yes	—
59	C₂²×Q₈	C₂×D₁₉	1	5	yes	—
60	C₄×Q₈	—	19	10	no	—
61	C₄×Q₈	—	19	20	no	—
62	C₄×Q₈	—	19	10	no	—
63	C₄×D₄	—	19	10	no	—
64	C₄×D₄	—	19	30	no	—
65	#117	—	19	30	no	—
66	C₂×C₄⋊C₄	—	19	15	no	—
67	C₂×C₄²	—	19	15	no	—
68	C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
69	#41	C₂×Dic₁₉	1	80	yes	complemented
70	C₂×Q₈	C₂×Dic₁₉	1	40	yes	complemented
71	C₂×Q₈	C₂²×D₁₉	1	10	yes	—
72	C₂×D₄	C₂²×D₁₉	1	10	yes	—
73	C₂²×C₄	—	19	5	no	—
74	C₂²×C₄	—	19	15	no	—
75	C₂²×C₄	C₂²×D₁₉	1	15	yes	—
76	C₄⋊C₄	—	19	30	no	—
77	C₄⋊C₄	—	19	10	no	—
78	C₂²⋊C₄	—	19	20	no	—
79	C₄²	—	19	10	no	—
80	C₄²	—	19	30	no	—
81	C₂³	C₂³×D₁₉	1	5	yes	—
82	Q₈	C₂²×Dic₁₉	1	40	yes	—
83	D₄	C₂²×Dic₁₉	1	40	yes	—
84	C₂×C₄	—	19	1	no	—
85	C₂×C₄	—	19	5	no	—
86	C₂×C₄	—	19	10	no	—
87	C₂×C₄	—	38	10	no	—
88	C₂×C₄	—	76	15	no	—
89	C₂×C₄	C₂²×Dic₁₉	1	60	yes	—
90	C₂×C₄	C₂³×D₁₉	1	10	yes	—
91	C₂²	—	2	5	no	—
92	C₂²	—	2	5	no	—
93	C₂²	C₂³×Dic₁₉	1	10	yes	—
94	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
95	C₄	—	19	2	no	—
96	C₄	—	38	5	no	—
97	C₄	—	38	10	no	—
98	C₄	C₂³×Dic₁₉	1	20	yes	—
99	C₂	—	2	10	no	—
100	C₂	C₂⁴×Dic₁₉	1	1	yes	characteristic
101	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
102	C₂	#11927381	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927027

C₂

yes

maximal, complemented

#11927022

C₂

yes

maximal, complemented

#41×Dic₁₉

C₂

yes

maximal, complemented

C₂×Q₈×Dic₁₉

C₂

yes

maximal, complemented

C₂×C₁₉×2₋¹⁺⁴

C₂

yes

maximal, characteristic

C₁₉×2₋¹⁺⁴

C₄

yes

complemented

C₂×#41×C₁₉

C₂²

yes

—

C₂²×Q₈×C₁₉

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

D₄×Dic₁₉

C₂²

yes

—

D₄×Dic₁₉

C₂²

yes

—

#10597372

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#41×C₁₉

C₂×C₄

yes

complemented

C₂×Q₈×C₁₉

C₂×C₄

yes

complemented

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂³×C₁₉

C₂⁴

yes

—

Q₈×C₁₉

C₂²×C₄

yes

—

D₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

characteristic

C₄×2₋¹⁺⁴

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

—

C₂²×C₁₉

C₂⁵

yes

characteristic

C₄×C₁₉

C₂³×C₄

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

2₋¹⁺⁴

yes

direct product factor

C₂×2₋¹⁺⁴

D₁₉

yes

characteristic

#520

—

#519

—

C₄×#41

—

C₂×C₄×Q₈

—

C₂×C₁₉

—

C₂×C₁₉

C₂⁴×C₄

yes

characteristic

C₂×C₁₉

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₁₉

#585

yes

characteristic

2₋¹⁺⁴

Dic₁₉

yes

direct product factor

C₂×#41

C₂×D₁₉

yes

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₁₉

C₄×2₋¹⁺⁴

yes

characteristic, complemented, Sylow

#41

C₂×Dic₁₉

yes

complemented

C₂×Q₈

C₂×Dic₁₉

yes

complemented

C₂×Q₈

C₂²×D₁₉

yes

—

C₂×D₄

C₂²×D₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₂³

C₂³×D₁₉

yes

—

Q₈

C₂²×Dic₁₉

yes

—

D₄

C₂²×Dic₁₉

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₁₉

yes

—

C₂×C₄

C₂³×D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

C₂³×Dic₁₉

yes

—

C₂²

C₂⁴×D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂³×Dic₁₉

yes

—

C₂

—

100

C₂

C₂⁴×Dic₁₉

yes

characteristic

101

C₂

2₋¹⁺⁴×D₁₉

yes

characteristic

102

C₂

#11927381

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Fitting, prime radical	C₂×C₁₉×2₋¹⁺⁴	C₂
socle, cosocle	C₂²×C₁₉	C₂⁵
hypercenter	C₂×2₋¹⁺⁴	D₁₉
hypocenter	C₁₉	C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×2₋¹⁺⁴

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₁₉

commutator

C₂×C₁₉

C₂⁴×C₄

Fitting, prime radical

C₂×C₁₉×2₋¹⁺⁴

C₂

socle, cosocle

C₂²×C₁₉

C₂⁵

hypercenter

C₂×2₋¹⁺⁴

D₁₉

hypocenter

C₁₉

C₄×2₋¹⁺⁴

LCS

G ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×2₋¹⁺⁴

N	H ≅ G/N	type
1. #11927027	C₂	semidirect
2. #11927022	C₂	semidirect
3. #41×Dic₁₉	C₂	semidirect
4. C₂×Q₈×Dic₁₉	C₂	semidirect
6. C₁₉×2₋¹⁺⁴	C₄	semidirect
17. #41×C₁₉	C₂×C₄	semidirect
18. C₂×Q₈×C₁₉	C₂×C₄	semidirect
47. Dic₁₉	2₋¹⁺⁴	direct (N × H)
57. 2₋¹⁺⁴	Dic₁₉	direct (N × H)
68. C₁₉	C₄×2₋¹⁺⁴	semidirect
69. #41	C₂×Dic₁₉	semidirect
70. C₂×Q₈	C₂×Dic₁₉	semidirect

H ≅ G/N

type

1. #11927027

C₂

semidirect

2. #11927022

C₂

semidirect

3. #41×Dic₁₉

C₂

semidirect

4. C₂×Q₈×Dic₁₉

C₂

semidirect

6. C₁₉×2₋¹⁺⁴

C₄

semidirect

17. #41×C₁₉

C₂×C₄

semidirect

18. C₂×Q₈×C₁₉

C₂×C₄

semidirect

47. Dic₁₉

2₋¹⁺⁴

direct (N × H)

57. 2₋¹⁺⁴

Dic₁₉

direct (N × H)

68. C₁₉

C₄×2₋¹⁺⁴

semidirect

69. #41

C₂×Dic₁₉

semidirect

70. C₂×Q₈

C₂×Dic₁₉

semidirect

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

subgroup	index
#11927027	2
#11927022	2
#41×Dic₁₉	2
C₂×Q₈×Dic₁₉	2
C₂×C₁₉×2₋¹⁺⁴	2
C₄×2₋¹⁺⁴	19

subgroup

index

#11927027

#11927022

#41×Dic₁₉

C₂×Q₈×Dic₁₉

C₂×C₁₉×2₋¹⁺⁴

C₄×2₋¹⁺⁴

Subgroups — 2₋¹⁺⁴×Dic₁₉ #14576848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 2−1+4×Dic19 #14576848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 2₋¹⁺⁴×Dic₁₉ #14576848