Group #18087048 — subgroups

Subgroups — #18087048

Order 4864.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14563768	C₂	1	3	yes	maximal
2	#14561516	C₂	1	3	yes	maximal
3	C₁₉×#2845	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597260	C₂²	1	3	yes	—
5	#11926414	C₂²	1	1	yes	characteristic
6	#11926306	—	2	6	no	—
7	C₁₉×#398	—	2	6	no	—
8	C₁₉×#382	C₂²	1	3	yes	—
9	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
10	C₂×C₄⋊C₄×C₁₉	D₄	1	6	yes	—
11	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	—	2	3	no	—
13	C₂²×C₁₉⋊C₈	—	2	3	no	—
14	C₁₉×#95	—	2	2	no	—
15	C₁₉×#95	—	2	6	no	—
16	#10597260	—	2	3	no	—
17	#10597260	Q₈	1	6	yes	—
18	C₂²×C₄×C₁₉	—	2	6	no	—
19	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
20	C₂²×Dic₁₉	—	4	1	no	—
21	C₄⋊C₄×C₁₉	—	4	6	no	—
22	C₄⋊C₄×C₁₉	—	8	6	no	—
23	C₄²×C₁₉	C₂×Q₈	1	3	yes	—
24	C₄²×C₁₉	#41	1	1	yes	characteristic
25	C₄⋊Dic₁₉	—	4	6	no	—
26	C₂×C₁₉⋊C₈	—	2	6	no	—
27	C₂×C₁₉⋊C₈	—	4	3	no	—
28	C₂×C₁₉⋊C₈	—	4	3	no	—
29	#10586	—	19	1	no	maximal, Sylow
30	C₂³×C₁₉	#120	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	3	no	—
32	C₂×C₄×C₁₉	—	2	3	no	—
33	C₂×C₄×C₁₉	—	4	6	no	—
34	C₂×C₄×C₁₉	—	4	6	no	—
35	C₂×C₄×C₁₉	—	4	6	no	—
36	C₂×C₄×C₁₉	C₂²⋊Q₈	1	3	yes	—
37	C₂×C₄×C₁₉	C₄⋊Q₈	1	3	yes	—
38	C₂×Dic₁₉	—	8	3	no	—
39	C₁₉⋊C₈	—	4	6	no	—
40	#2845	D₁₉	1	1	yes	characteristic
41	#1836	—	19	3	no	—
42	#1295	—	19	3	no	—
43	C₂²×C₁₉	#395	1	1	yes	characteristic
44	C₂²×C₁₉	#454	1	3	yes	—
45	C₂²×C₁₉	#455	1	3	yes	—
46	C₄×C₁₉	—	2	3	no	—
47	C₄×C₁₉	—	2	3	no	—
48	C₄×C₁₉	—	8	6	no	—
49	Dic₁₉	—	16	1	no	—
50	C₂×#97	—	19	3	no	—
51	#398	—	2	6	no	—
52	#384	—	19	1	no	—
53	#382	C₂×D₁₉	1	3	yes	—
54	#340	—	38	6	no	—
55	C₂×C₁₉	#1658	1	1	yes	characteristic
56	C₂×C₁₉	#1662	1	3	yes	—
57	C₂×C₁₉	#2061	1	3	yes	—
58	C₂²×C₈	—	38	3	no	—
59	C₂×C₄⋊C₄	—	2	6	no	—
60	C₂×C₄⋊C₄	—	38	3	no	—
61	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	6	yes	—
62	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
63	#97	—	19	6	no	—
64	#97	—	38	3	no	—
65	#95	—	2	2	no	—
66	#95	—	2	6	no	—
67	C₁₉	#10586	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	2	6	no	—
69	C₂²×C₄	—	76	1	no	—
70	C₂²×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
71	C₂×C₈	—	38	6	no	—
72	C₂×C₈	—	76	3	no	—
73	C₂×C₈	—	76	3	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	8	6	no	—
76	C₄⋊C₄	—	76	6	no	—
77	C₄²	Q₈×D₁₉	1	3	yes	—
78	C₄²	#64545	1	1	yes	characteristic
79	C₂³	#10597399	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	152	3	no	—
86	C₂×C₄	#10597390	1	3	yes	—
87	C₂×C₄	#10597392	1	3	yes	—
88	C₈	—	76	6	no	—
89	C₂²	#11926463	1	1	yes	characteristic
90	C₂²	#11926717	1	3	yes	—
91	C₂²	#11926722	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	304	1	no	—
96	C₂	#14562937	1	1	yes	characteristic
97	C₂	#14562958	1	3	yes	—
98	C₂	#14564982	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563768

C₂

yes

maximal

#14561516

C₂

yes

maximal

C₁₉×#2845

C₂

yes

maximal, characteristic

C₂×#10597260

C₂²

yes

—

#11926414

C₂²

yes

characteristic

#11926306

—

C₁₉×#398

—

C₁₉×#382

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

#10597260

—

#10597260

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2845

D₁₉

yes

characteristic

#1836

—

#1295

—

C₂²×C₁₉

#395

yes

characteristic

C₂²×C₁₉

#454

yes

—

C₂²×C₁₉

#455

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

C₂×#97

—

#398

—

#384

—

#382

C₂×D₁₉

yes

—

#340

—

C₂×C₁₉

#1658

yes

characteristic

C₂×C₁₉

#1662

yes

—

C₂×C₁₉

#2061

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

—

—

—

—

C₁₉

#10586

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Q₈×D₁₉

yes

—

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

152

—

C₂×C₄

#10597390

yes

—

C₂×C₄

#10597392

yes

—

C₈

—

C₂²

#11926463

yes

characteristic

C₂²

#11926717

yes

—

C₂²

#11926722

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

304

—

C₂

#14562937

yes

characteristic

C₂

#14562958

yes

—

C₂

#14564982

yes

—

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2845	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#2845	D₁₉
hypocenter	C₁₉	#10586
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2845

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
67. C₁₉	#10586	semidirect

H ≅ G/N

type

67. C₁₉

#10586

semidirect

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

subgroup	index
#14563768	2
#14561516	2
C₁₉×#2845	2
#10586	19

subgroup

index

#14563768

#14561516

C₁₉×#2845

#10586

Subgroups — #18087048

Conjugacy classes of subgroups

Complements

Maximal subgroups