Group #14658282 — subgroups

Subgroups — #14658282

Order 2816.

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	#13068749	C₂	1	3	yes	maximal
2	#13066497	C₂	1	3	yes	maximal
3	C₁₁×#2845	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#398	—	2	6	no	—
5	C₁₁×#382	C₂²	1	3	yes	—
6	#10622548	C₂²	1	1	yes	characteristic
7	C₂×#66867	C₂²	1	3	yes	—
8	#10622167	—	2	6	no	—
9	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
10	C₂×C₁₁×C₄⋊C₄	D₄	1	6	yes	—
11	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₁	—	2	3	no	—
13	C₂²×C₁₁⋊C₈	—	2	3	no	—
14	C₁₁×#95	—	2	2	no	—
15	C₁₁×#95	—	2	6	no	—
16	#66867	—	2	3	no	—
17	#66867	Q₈	1	6	yes	—
18	#10586	—	11	1	no	maximal, Sylow
19	C₂²×C₄×C₁₁	—	2	6	no	—
20	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
21	C₂²×Dic₁₁	—	4	1	no	—
22	C₁₁×C₄⋊C₄	—	4	6	no	—
23	C₁₁×C₄⋊C₄	—	8	6	no	—
24	C₄²×C₁₁	C₂×Q₈	1	3	yes	—
25	C₄²×C₁₁	#41	1	1	yes	characteristic
26	C₄⋊Dic₁₁	—	4	6	no	—
27	C₂×C₁₁⋊C₈	—	2	6	no	—
28	C₂×C₁₁⋊C₈	—	4	3	no	—
29	C₂×C₁₁⋊C₈	—	4	3	no	—
30	#2845	D₁₁	1	1	yes	characteristic
31	#1836	—	11	3	no	—
32	#1295	—	11	3	no	—
33	C₂³×C₁₁	#120	1	1	yes	characteristic
34	C₂×C₄×C₁₁	—	2	3	no	—
35	C₂×C₄×C₁₁	—	2	3	no	—
36	C₂×C₄×C₁₁	—	4	6	no	—
37	C₂×C₄×C₁₁	—	4	6	no	—
38	C₂×C₄×C₁₁	—	4	6	no	—
39	C₂×C₄×C₁₁	C₂²⋊Q₈	1	3	yes	—
40	C₂×C₄×C₁₁	C₄⋊Q₈	1	3	yes	—
41	C₂×Dic₁₁	—	8	3	no	—
42	C₁₁⋊C₈	—	4	6	no	—
43	C₂×#97	—	11	3	no	—
44	#398	—	2	6	no	—
45	#384	—	11	1	no	—
46	#382	C₂×D₁₁	1	3	yes	—
47	#340	—	22	6	no	—
48	C₂²×C₁₁	#395	1	1	yes	characteristic
49	C₂²×C₁₁	#454	1	3	yes	—
50	C₂²×C₁₁	#455	1	3	yes	—
51	C₄×C₁₁	—	2	3	no	—
52	C₄×C₁₁	—	2	3	no	—
53	C₄×C₁₁	—	8	6	no	—
54	Dic₁₁	—	16	1	no	—
55	C₂²×C₈	—	22	3	no	—
56	C₂×C₄⋊C₄	—	2	6	no	—
57	C₂×C₄⋊C₄	—	22	3	no	—
58	C₂×C₄⋊C₄	C₂²⋊D₁₁	1	6	yes	—
59	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
60	#97	—	11	6	no	—
61	#97	—	22	3	no	—
62	#95	—	2	2	no	—
63	#95	—	2	6	no	—
64	C₂×C₁₁	#1658	1	1	yes	characteristic
65	C₂×C₁₁	#1662	1	3	yes	—
66	C₂×C₁₁	#2061	1	3	yes	—
67	C₂²×C₄	—	2	6	no	—
68	C₂²×C₄	—	44	1	no	—
69	C₂²×C₄	C₂×C₂²⋊D₁₁	1	3	yes	—
70	C₂×C₈	—	22	6	no	—
71	C₂×C₈	—	44	3	no	—
72	C₂×C₈	—	44	3	no	—
73	C₄⋊C₄	—	4	6	no	—
74	C₄⋊C₄	—	8	6	no	—
75	C₄⋊C₄	—	44	6	no	—
76	C₄²	Q₈×D₁₁	1	3	yes	—
77	C₄²	#4343	1	1	yes	characteristic
78	C₁₁	#10586	1	1	yes	characteristic, complemented, Sylow
79	C₂³	#67006	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	—	88	3	no	—
86	C₂×C₄	#66997	1	3	yes	—
87	C₂×C₄	#66999	1	3	yes	—
88	C₈	—	44	6	no	—
89	C₂²	#10622842	1	1	yes	characteristic
90	C₂²	#10622855	1	3	yes	—
91	C₂²	#10622858	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	176	1	no	—
96	C₂	#13067918	1	1	yes	characteristic
97	C₂	#13067939	1	3	yes	—
98	C₂	#13069963	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068749

C₂

yes

maximal

#13066497

C₂

yes

maximal

C₁₁×#2845

C₂

yes

maximal, characteristic

C₁₁×#398

—

C₁₁×#382

C₂²

yes

—

#10622548

C₂²

yes

characteristic

C₂×#66867

C₂²

yes

—

#10622167

—

C₂×C₁₁×C₄⋊C₄

—

C₂×C₁₁×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂²×C₁₁⋊C₈

—

C₁₁×#95

—

C₁₁×#95

—

#66867

—

#66867

Q₈

yes

—

#10586

—

maximal, Sylow

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₂²×Dic₁₁

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

C₂×Q₈

yes

—

C₄²×C₁₁

#41

yes

characteristic

C₄⋊Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#2845

D₁₁

yes

characteristic

#1836

—

#1295

—

C₂³×C₁₁

#120

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×Dic₁₁

—

C₁₁⋊C₈

—

C₂×#97

—

#398

—

#384

—

#382

C₂×D₁₁

yes

—

#340

—

C₂²×C₁₁

#395

yes

characteristic

C₂²×C₁₁

#454

yes

—

C₂²×C₁₁

#455

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

Dic₁₁

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₁

yes

—

C₂×C₄²

C₂²×D₁₁

yes

—

—

—

—

C₂×C₁₁

#1658

yes

characteristic

C₂×C₁₁

#1662

yes

—

C₂×C₁₁

#2061

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Q₈×D₁₁

yes

—

C₄²

#4343

yes

characteristic

C₁₁

#10586

yes

characteristic, complemented, Sylow

C₂³

#67006

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#66997

yes

—

C₂×C₄

#66999

yes

—

C₈

—

C₂²

#10622842

yes

characteristic

C₂²

#10622855

yes

—

C₂²

#10622858

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

176

—

C₂

#13067918

yes

characteristic

C₂

#13067939

yes

—

C₂

#13069963

yes

—

	subgroup	G/H
center	C₂³	#67006
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2845	C₂
socle, prime radical	C₂³×C₁₁	#120
hypercenter	#2845	D₁₁
hypocenter	C₁₁	#10586
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#67006

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#2845

C₂

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
78. C₁₁	#10586	semidirect

H ≅ G/N

type

78. C₁₁

#10586

semidirect

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

subgroup	index
#13068749	2
#13066497	2
C₁₁×#2845	2
#10586	11

subgroup

index

#13068749

#13066497

C₁₁×#2845

#10586

Subgroups — #14658282

Conjugacy classes of subgroups

Complements

Maximal subgroups