Group #14564811 — subgroups

Subgroups — #14564811

Order 2432.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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×#10597263	C₂	1	3	yes	maximal
2	#11926310	C₂	1	3	yes	maximal, complemented
3	C₁₉×#543	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×C₂²⋊Q₈	—	2	6	no	—
6	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
7	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
8	#10597263	—	2	6	no	—
9	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
10	C₂³×D₁₉	Q₈	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₁₉	—	2	2	no	—
12	C₂²×C₄×C₁₉	—	2	3	no	—
13	C₂×C₂²⋊D₁₉	—	2	3	no	—
14	C₂×C₂²⋊D₁₉	—	2	3	no	—
15	C₂²×Dic₁₉	—	2	3	no	—
16	C₂²×Dic₁₉	Q₈	1	1	yes	characteristic, complemented
17	C₄⋊C₄×C₁₉	—	2	6	no	—
18	C₂²⋊C₄×C₁₉	—	2	3	no	—
19	C₂²⋊C₄×C₁₉	D₄	1	6	yes	—
20	C₂²⋊Dic₁₉	—	2	3	no	—
21	C₂²⋊Dic₁₉	—	2	3	no	—
22	C₂³×C₁₉	—	8	1	no	—
23	C₂³×C₁₉	C₂×D₄	1	3	yes	—
24	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
25	C₂³×C₁₉	#41	1	3	yes	—
26	C₂²×D₁₉	—	2	3	no	—
27	C₂²×D₁₉	—	8	1	no	—
28	Q₈×C₁₉	—	8	2	no	—
29	C₂×C₄×C₁₉	—	2	6	no	—
30	C₂×C₄×C₁₉	—	8	3	no	—
31	C₂²⋊D₁₉	—	4	1	no	—
32	C₂²⋊D₁₉	—	4	3	no	—
33	C₂×Dic₁₉	—	2	3	no	—
34	C₂×Dic₁₉	—	4	3	no	—
35	C₂×Dic₁₉	—	8	3	no	—
36	#2032	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	—	4	3	no	—
38	C₂²×C₁₉	—	4	3	no	—
39	C₂²×C₁₉	—	4	1	no	—
40	C₂²×C₁₉	#120	1	1	yes	characteristic
41	C₂²×C₁₉	C₂²⋊Q₈	1	3	yes	—
42	C₂²×C₁₉	#124	1	3	yes	—
43	C₂×D₁₉	—	4	1	no	—
44	C₂×D₁₉	—	8	3	no	—
45	C₄×C₁₉	—	4	6	no	—
46	Dic₁₉	—	4	1	no	—
47	Dic₁₉	—	8	3	no	—
48	#543	D₁₉	1	1	yes	characteristic, complemented
49	C₂×#99	—	19	3	no	—
50	#342	—	19	3	no	—
51	C₂×C₁₉	—	2	3	no	—
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	—	2	3	no	—
54	C₂×C₁₉	#393	1	1	yes	characteristic
55	D₁₉	—	8	1	no	—
56	C₂²×D₄	—	19	1	no	—
57	C₂²⋊Q₈	—	2	6	no	—
58	C₂×C₂²⋊C₄	—	19	3	no	—
59	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
60	#99	—	38	6	no	—
61	C₁₉	#2032	1	1	yes	characteristic, complemented, Sylow
62	C₂⁴	—	19	1	no	—
63	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
64	C₂×Q₈	—	2	2	no	—
65	C₂×D₄	—	38	3	no	—
66	C₂×D₄	—	38	3	no	—
67	C₂²×C₄	—	2	3	no	—
68	C₂²×C₄	—	19	1	no	—
69	C₂²×C₄	—	38	3	no	—
70	C₄⋊C₄	—	2	6	no	—
71	C₂²⋊C₄	—	2	3	no	—
72	C₂²⋊C₄	—	38	3	no	—
73	C₂²⋊C₄	—	38	3	no	—
74	C₂²⋊C₄	C₂²⋊D₁₉	1	6	yes	—
75	C₂³	—	8	1	no	—
76	C₂³	—	38	3	no	—
77	C₂³	—	152	1	no	—
78	C₂³	Q₈×D₁₉	1	1	yes	characteristic
79	C₂³	#64545	1	3	yes	—
80	C₂³	C₂×C₂²⋊D₁₉	1	3	yes	—
81	Q₈	—	8	2	no	—
82	D₄	—	76	3	no	—
83	D₄	—	76	1	no	—
84	C₂×C₄	—	2	6	no	—
85	C₂×C₄	—	8	3	no	—
86	C₂×C₄	—	38	3	no	—
87	C₂×C₄	—	76	3	no	—
88	C₂×C₄	—	152	3	no	—
89	C₂²	—	4	3	no	—
90	C₂²	—	4	3	no	—
91	C₂²	—	4	1	no	—
92	C₂²	—	76	1	no	—
93	C₂²	—	152	3	no	—
94	C₂²	#10597392	1	3	yes	—
95	C₂²	#10597393	1	3	yes	—
96	C₂²	#10597399	1	1	yes	characteristic
97	C₄	—	4	6	no	—
98	C₄	—	76	1	no	—
99	C₄	—	152	3	no	—
100	C₂	—	2	1	no	—
101	C₂	—	2	3	no	—
102	C₂	—	2	3	no	—
103	C₂	—	152	1	no	—
104	C₂	#11926455	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597263

C₂

yes

maximal

#11926310

C₂

yes

maximal, complemented

C₁₉×#543

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597263

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

Q₈

yes

characteristic, complemented

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

Q₈

yes

characteristic, complemented

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

D₄

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂³×C₁₉

#41

yes

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2032

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

#124

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#543

D₁₉

yes

characteristic, complemented

C₂×#99

—

#342

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#393

yes

characteristic

D₁₉

—

C₂²×D₄

—

C₂²⋊Q₈

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#99

—

C₁₉

#2032

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂²⋊D₁₉

yes

—

C₂³

—

C₂³

—

C₂³

—

152

—

C₂³

Q₈×D₁₉

yes

characteristic

C₂³

#64545

yes

—

C₂³

C₂×C₂²⋊D₁₉

yes

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

152

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

152

—

C₂²

#10597392

yes

—

C₂²

#10597393

yes

—

C₂²

#10597399

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

100

C₂

—

101

C₂

—

102

C₂

—

103

C₂

—

152

—

104

C₂

#11926455

yes

characteristic

	subgroup	G/H
center	C₂	#11926455
commutator, cosocle	C₂⁴×C₁₉	C₂³
Frattini	C₂⁴	C₂²×D₁₉
Fitting	C₁₉×#543	C₂
socle	C₂×C₁₉	#393
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	#543	D₁₉
hypocenter	C₁₉	#2032
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

subgroup

G/H

center

C₂

#11926455

commutator, cosocle

C₂⁴×C₁₉

C₂³

Frattini

C₂⁴

C₂²×D₁₉

Fitting

C₁₉×#543

C₂

socle

C₂×C₁₉

#393

prime radical

C₂²×C₂²⋊D₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

N	H ≅ G/N	type
2. #11926310	C₂	semidirect
3. C₁₉×#543	C₂	semidirect
10. C₂³×D₁₉	Q₈	semidirect
16. C₂²×Dic₁₉	Q₈	semidirect
48. #543	D₁₉	semidirect
61. C₁₉	#2032	semidirect

H ≅ G/N

type

2. #11926310

C₂

semidirect

3. C₁₉×#543

C₂

semidirect

10. C₂³×D₁₉

Q₈

semidirect

16. C₂²×Dic₁₉

Q₈

semidirect

48. #543

D₁₉

semidirect

61. C₁₉

#2032

semidirect

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

subgroup	index
C₂×#10597263	2
#11926310	2
C₁₉×#543	2
#2032	19

subgroup

index

C₂×#10597263

#11926310

C₁₉×#543

#2032

Subgroups — #14564811

Conjugacy classes of subgroups

Complements

Maximal subgroups