Group #14565516 — subgroups

Subgroups — #14565516

Order 2432.

146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 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	#11926661	C₂	1	2	yes	maximal, complemented
2	#11926374	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926351	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#508	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#135	C₂²	1	2	yes	—
7	#10597394	—	2	2	no	—
8	C₁₉×Q₃₂	C₄	1	1	yes	characteristic, complemented
9	C₁₉×SD₃₂	C₄	1	2	yes	complemented
10	C₁₉×D₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	#10597294	—	2	2	no	—
13	#10597276	C₂²	1	2	yes	—
14	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	#41×C₁₉	—	2	2	no	—
17	Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
18	SD₁₆×C₁₉	—	2	2	no	—
19	D₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₄×Dic₁₉	D₄	1	1	yes	characteristic
22	#64520	—	2	2	no	—
23	#64520	—	4	2	no	—
24	C₂×C₁₉⋊C₈	—	4	2	no	—
25	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
26	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₉⋊C₁₆	—	2	1	no	—
29	Q₈×C₁₉	—	2	2	no	—
30	D₄×C₁₉	—	2	2	no	—
31	D₄×C₁₉	—	4	2	no	—
32	C₂×C₄×C₁₉	—	4	2	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₁₉	—	2	1	no	—
35	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₁₉	#41	1	1	yes	characteristic
37	C₁₉⋊C₈	—	4	2	no	—
38	C₁₉⋊C₈	D₈	1	1	yes	characteristic
39	C₁₉⋊C₈	D₈	1	1	yes	characteristic
40	#2178	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	4	2	no	—
42	C₂²×C₁₉	#135	1	1	yes	characteristic
43	C₄×C₁₉	—	4	2	no	—
44	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
45	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
46	Dic₁₉	—	2	2	no	—
47	#508	D₁₉	1	1	yes	characteristic
48	#443	—	19	2	no	—
49	#368	—	19	1	no	—
50	#359	—	19	2	no	—
51	C₄×C₁₆	—	19	1	no	—
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	—	8	2	no	—
54	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
55	#135	C₂×D₁₉	1	2	yes	—
56	#131	—	38	2	no	—
57	Q₃₂	Dic₁₉	1	1	yes	characteristic, complemented
58	SD₃₂	Dic₁₉	1	2	yes	complemented
59	D₁₆	Dic₁₉	1	1	yes	characteristic, complemented
60	C₂×C₁₆	—	19	1	no	—
61	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
62	#108	—	19	2	no	—
63	#104	—	38	2	no	—
64	C₄×C₈	—	19	1	no	—
65	C₁₉	#2178	1	1	yes	characteristic, complemented, Sylow
66	#41	—	2	2	no	—
67	Q₁₆	C₂×Dic₁₉	1	2	yes	—
68	SD₁₆	—	2	2	no	—
69	D₈	C₂×Dic₁₉	1	2	yes	—
70	M₁₆	—	38	2	no	—
71	M₁₆	—	76	2	no	—
72	C₂×C₈	—	19	1	no	—
73	C₂×C₈	—	76	2	no	—
74	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
75	C₄²	—	19	1	no	—
76	C₁₆	—	38	1	no	—
77	C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
78	C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
79	Q₈	—	2	2	no	—
80	D₄	—	2	2	no	—
81	D₄	—	4	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	38	1	no	—
84	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
85	C₈	—	19	1	no	—
86	C₈	—	19	1	no	—
87	C₈	—	76	2	no	—
88	C₈	#64543	1	1	yes	characteristic
89	C₈	C₂²×Dic₁₉	1	1	yes	characteristic
90	C₂²	—	4	2	no	—
91	C₂²	#10597358	1	1	yes	characteristic
92	C₄	—	4	2	no	—
93	C₄	—	38	2	no	—
94	C₄	D₈×D₁₉	1	1	yes	characteristic
95	C₄	D₄×Dic₁₉	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	8	2	no	—
98	C₂	D₈×Dic₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926661

C₂

yes

maximal, complemented

#11926374

C₂

yes

maximal, characteristic, complemented

#11926351

C₂

yes

maximal, complemented

C₁₆×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×#508

C₂

yes

maximal, characteristic

C₁₉×#135

C₂²

yes

—

#10597394

—

C₁₉×Q₃₂

C₄

yes

characteristic, complemented

C₁₉×SD₃₂

C₄

yes

complemented

C₁₉×D₁₆

C₄

yes

characteristic, complemented

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597294

—

#10597276

C₂²

yes

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#41×C₁₉

—

Q₁₆×C₁₉

C₂×C₄

yes

—

SD₁₆×C₁₉

—

D₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

D₈

yes

characteristic

C₁₉⋊C₈

D₈

yes

characteristic

#2178

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#135

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

#508

D₁₉

yes

—

—

—

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₄×D₈

yes

characteristic

#135

C₂×D₁₉

yes

—

#131

—

Q₃₂

Dic₁₉

yes

characteristic, complemented

SD₃₂

Dic₁₉

yes

complemented

D₁₆

Dic₁₉

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#108

—

#104

—

C₄×C₈

—

C₁₉

#2178

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

C₂×Dic₁₉

yes

—

SD₁₆

—

D₈

C₂×Dic₁₉

yes

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₁₉

yes

characteristic

C₁₆

C₂×Dic₁₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#64543

yes

characteristic

C₈

C₂²×Dic₁₉

yes

characteristic

C₂²

—

C₂²

#10597358

yes

characteristic

C₄

—

C₄

—

C₄

D₈×D₁₉

yes

characteristic

C₄

D₄×Dic₁₉

yes

characteristic

C₂

—

C₂

—

C₂

D₈×Dic₁₉

yes

characteristic

	subgroup	G/H
center	C₄	D₈×D₁₉
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting, prime radical	C₁₉×#508	C₂
socle	C₂×C₁₉	C₄×D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#508	D₁₉
hypocenter	C₁₉	#2178
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

subgroup

G/H

center

C₄

D₈×D₁₉

commutator

C₈×C₁₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₁₉

Fitting, prime radical

C₁₉×#508

C₂

socle

C₂×C₁₉

C₄×D₈

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

N	H ≅ G/N	type
1. #11926661	C₂	semidirect
2. #11926374	C₂	semidirect
3. #11926351	C₂	semidirect
4. C₁₆×Dic₁₉	C₂	semidirect
8. C₁₉×Q₃₂	C₄	semidirect
9. C₁₉×SD₃₂	C₄	semidirect
10. C₁₉×D₁₆	C₄	semidirect
57. Q₃₂	Dic₁₉	semidirect
58. SD₃₂	Dic₁₉	semidirect
59. D₁₆	Dic₁₉	semidirect
65. C₁₉	#2178	semidirect

H ≅ G/N

type

1. #11926661

C₂

semidirect

2. #11926374

C₂

semidirect

3. #11926351

C₂

semidirect

4. C₁₆×Dic₁₉

C₂

semidirect

8. C₁₉×Q₃₂

C₄

semidirect

9. C₁₉×SD₃₂

C₄

semidirect

10. C₁₉×D₁₆

C₄

semidirect

57. Q₃₂

Dic₁₉

semidirect

58. SD₃₂

Dic₁₉

semidirect

59. D₁₆

Dic₁₉

semidirect

65. C₁₉

#2178

semidirect

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

subgroup	index
#11926661	2
#11926374	2
#11926351	2
C₁₆×Dic₁₉	2
C₁₉×#508	2
#2178	19

subgroup

index

#11926661

#11926374

#11926351

C₁₆×Dic₁₉

C₁₉×#508

#2178

Subgroups — #14565516

Conjugacy classes of subgroups

Complements

Maximal subgroups