Group #14569354 — subgroups

Subgroups — #14569354

Order 2432.

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

normal subgroups only

This group has 782 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×#10597375	C₂	1	3	yes	maximal
2	#11926463	C₂	1	4	yes	maximal, complemented
3	#11926455	C₂	1	4	yes	maximal, complemented
4	#11926407	C₂	1	3	yes	maximal, complemented
5	C₂³×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Q₈×C₁₉	—	2	12	no	—
7	C₂²×Q₈×C₁₉	C₂²	1	4	yes	—
8	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
11	#10597375	—	2	12	no	—
12	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
14	C₁₉⋊#95	C₂²	1	12	yes	—
15	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
16	C₂³×D₁₉	C₂³	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	2	32	no	—
18	C₂×Q₈×C₁₉	—	2	24	no	—
19	C₂²×C₄×C₁₉	—	2	12	no	—
20	C₂²×C₄×C₁₉	D₄	1	12	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
22	C₂×C₂²⋊D₁₉	—	2	6	no	—
23	C₂²×Dic₁₉	C₂³	1	6	yes	—
24	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
25	C₂²⋊Dic₁₉	—	2	6	no	—
26	(C₂×D₁₉)⋊C₄	—	2	12	no	—
27	Dic₁₉⋊C₄	—	2	12	no	—
28	C₂³×C₁₉	—	2	4	no	—
29	C₂³×C₁₉	C₂×D₄	1	6	yes	—
30	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
31	C₂²×D₁₉	—	2	3	no	—
32	C₂²×D₁₉	—	2	4	no	—
33	Q₈×C₁₉	—	2	32	no	—
34	C₂×C₄×C₁₉	—	2	24	no	—
35	C₂×C₄×C₁₉	—	2	12	no	—
36	C₂×C₄×C₁₉	C₂×D₄	1	12	yes	—
37	C₂²⋊D₁₉	—	4	4	no	—
38	C₂×Dic₁₉	—	2	3	no	—
39	C₂×Dic₁₉	—	2	6	no	—
40	C₂×Dic₁₉	—	2	12	no	—
41	#2614	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	2	12	no	—
43	C₂²×C₁₉	#120	1	4	yes	—
44	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
45	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
46	C₂×D₁₉	—	4	1	no	—
47	C₂×D₁₉	—	4	6	no	—
48	C₄×C₁₉	—	2	12	no	—
49	Dic₁₉	—	4	1	no	—
50	Dic₁₉	—	4	6	no	—
51	C₂³×Q₈	D₁₉	1	1	yes	characteristic, complemented
52	C₂×#123	—	19	3	no	—
53	#395	—	19	4	no	—
54	#393	—	19	4	no	—
55	#381	—	19	3	no	—
56	C₂×C₁₉	—	2	4	no	—
57	C₂×C₁₉	C₂×#120	1	1	yes	characteristic
58	C₂×C₁₉	#536	1	6	yes	—
59	D₁₉	—	8	1	no	—
60	C₂²×Q₈	—	2	12	no	—
61	C₂²×Q₈	C₂×D₁₉	1	4	yes	—
62	C₂²×D₄	—	19	1	no	—
63	C₂³×C₄	C₂×D₁₉	1	3	yes	—
64	#123	—	38	12	no	—
65	C₂×C₄⋊C₄	—	19	6	no	—
66	C₂×C₂²⋊C₄	—	19	3	no	—
67	C₂×C₂²⋊C₄	—	19	6	no	—
68	#95	—	19	12	no	—
69	C₁₉	#2614	1	1	yes	characteristic, complemented, Sylow
70	C₂⁴	—	19	1	no	—
71	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
72	C₂×Q₈	—	2	32	no	—
73	C₂×Q₈	—	2	24	no	—
74	C₂×D₄	—	38	6	no	—
75	C₂²×C₄	—	2	12	no	—
76	C₂²×C₄	—	19	6	no	—
77	C₂²×C₄	—	19	1	no	—
78	C₂²×C₄	C₂²⋊D₁₉	1	12	yes	—
79	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
80	C₄⋊C₄	—	38	12	no	—
81	C₂²⋊C₄	—	38	6	no	—
82	C₂²⋊C₄	—	38	12	no	—
83	C₂³	—	2	4	no	—
84	C₂³	—	38	4	no	—
85	C₂³	—	38	3	no	—
86	C₂³	C₂×C₂²⋊D₁₉	1	6	yes	—
87	C₂³	C₂³×D₁₉	1	1	yes	characteristic
88	Q₈	—	2	32	no	—
89	D₄	—	76	4	no	—
90	C₂×C₄	—	2	24	no	—
91	C₂×C₄	—	2	12	no	—
92	C₂×C₄	—	38	12	no	—
93	C₂×C₄	—	38	6	no	—
94	C₂×C₄	—	38	3	no	—
95	C₂×C₄	C₂×C₂²⋊D₁₉	1	12	yes	—
96	C₂²	—	2	12	no	—
97	C₂²	—	76	6	no	—
98	C₂²	—	76	1	no	—
99	C₂²	#10597399	1	4	yes	—
100	C₂²	#10597433	1	4	yes	—
101	C₂²	C₂²×C₂²⋊D₁₉	1	3	yes	—
102	C₄	—	2	12	no	—
103	C₄	—	76	6	no	—
104	C₄	—	76	1	no	—
105	C₂	—	2	4	no	—
106	C₂	—	152	1	no	—
107	C₂	C₂×#10597399	1	1	yes	characteristic
108	C₂	#11927118	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597375

C₂

yes

maximal

#11926463

C₂

yes

maximal, complemented

#11926455

C₂

yes

maximal, complemented

#11926407

C₂

yes

maximal, complemented

C₂³×Q₈×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊D₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597375

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2614

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂³×Q₈

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#120

yes

characteristic

C₂×C₁₉

#536

yes

—

D₁₉

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₂²×D₄

—

C₂³×C₄

C₂×D₁₉

yes

—

#123

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₁₉

#2614

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×C₂²⋊D₁₉

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#10597399

yes

—

100

C₂²

#10597433

yes

—

101

C₂²

C₂²×C₂²⋊D₁₉

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₂

—

106

C₂

—

152

—

107

C₂

C₂×#10597399

yes

characteristic

108

C₂

#11927118

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂³×Q₈×C₁₉	C₂
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	C₂³×Q₈	D₁₉
hypocenter	C₁₉	#2614
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂³×Q₈×C₁₉

C₂

prime radical

C₂²×C₂²⋊D₁₉

C₂²

hypercenter

C₂³×Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂³×Q₈

N	H ≅ G/N	type
2. #11926463	C₂	semidirect
3. #11926455	C₂	semidirect
4. #11926407	C₂	semidirect
5. C₂³×Q₈×C₁₉	C₂	semidirect
51. C₂³×Q₈	D₁₉	semidirect
69. C₁₉	#2614	semidirect

H ≅ G/N

type

2. #11926463

C₂

semidirect

3. #11926455

C₂

semidirect

4. #11926407

C₂

semidirect

5. C₂³×Q₈×C₁₉

C₂

semidirect

51. C₂³×Q₈

D₁₉

semidirect

69. C₁₉

#2614

semidirect

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

subgroup	index
C₂×#10597375	2
#11926463	2
#11926455	2
#11926407	2
C₂³×Q₈×C₁₉	2
#2614	19

subgroup

index

C₂³×Q₈×C₁₉

Subgroups — #14569354

Conjugacy classes of subgroups

Complements

Maximal subgroups