Group #14647489 — subgroups

Subgroups — #14647489

Order 2816.

220 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 99 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	#13067379	C₂	1	2	yes	maximal
2	#13066478	C₂	1	4	yes	maximal
3	C₁₁×#1452	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#431	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	#10622539	C₂²	1	4	yes	—
7	C₁₁×#322	C₄	1	4	yes	—
8	#10622096	—	2	2	no	—
9	#10622095	—	2	2	no	—
10	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
11	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
12	C₁₁×C₄⋊C₈	—	2	2	no	—
13	C₁₁×C₂²⋊C₈	—	2	2	no	—
14	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
15	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₁	D₄	1	2	yes	—
17	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
18	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
19	#66867	—	2	4	no	—
20	#8799	—	11	1	no	maximal, Sylow
21	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	#41	1	2	yes	—
23	C₂×C₈×C₁₁	—	2	4	no	—
24	C₂×C₈×C₁₁	—	4	2	no	—
25	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
26	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
27	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₄²×C₁₁	#41	1	2	yes	—
29	C₂×C₁₁⋊C₈	—	4	4	no	—
30	#1568	—	11	2	no	—
31	#1452	D₁₁	1	1	yes	characteristic
32	#1287	—	11	4	no	—
33	C₂³×C₁₁	#125	1	1	yes	characteristic
34	C₂×C₄×C₁₁	—	2	2	no	—
35	C₂×C₄×C₁₁	—	4	2	no	—
36	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₁	#117	1	2	yes	—
38	C₂×C₄×C₁₁	#124	1	2	yes	—
39	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
40	C₈×C₁₁	—	2	4	no	—
41	C₈×C₁₁	—	4	4	no	—
42	C₁₁⋊C₈	—	8	4	no	—
43	#432	—	11	4	no	—
44	#431	C₂×D₁₁	1	2	yes	—
45	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
46	#335	—	22	2	no	—
47	#334	—	22	2	no	—
48	#322	Dic₁₁	1	4	yes	—
49	C₂²×C₁₁	—	2	2	no	—
50	C₂²×C₁₁	—	2	1	no	—
51	C₂²×C₁₁	#382	1	1	yes	characteristic
52	C₄×C₁₁	—	2	2	no	—
53	C₄×C₁₁	—	2	2	no	—
54	C₄×C₁₁	—	2	1	no	—
55	C₄×C₁₁	#430	1	2	yes	—
56	C₂²×C₈	Dic₂₂	1	2	yes	—
57	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
58	C₄⋊C₈	—	2	2	no	—
59	C₄⋊C₈	—	22	4	no	—
60	C₂²⋊C₈	—	2	2	no	—
61	C₂²⋊C₈	—	22	4	no	—
62	#97	—	22	4	no	—
63	C₄×C₈	D₄₄	1	2	yes	—
64	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
65	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
66	C₂×C₁₁	—	4	1	no	—
67	C₂×C₁₁	#1833	1	2	yes	—
68	C₂×C₁₁	#1838	1	1	yes	characteristic
69	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
70	C₂²×C₄	#4339	1	2	yes	—
71	C₂×C₈	—	2	4	no	—
72	C₂×C₈	—	4	2	no	—
73	C₂×C₈	—	44	4	no	—
74	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
75	C₄²	C₂×D₄₄	1	1	yes	characteristic
76	C₄²	#4339	1	2	yes	—
77	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
78	C₁₁	#8799	1	1	yes	characteristic, complemented, Sylow
79	C₂³	#66923	1	1	yes	characteristic
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	#66923	1	1	yes	characteristic
83	C₂×C₄	#66928	1	2	yes	—
84	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
85	C₂×C₄	#66979	1	2	yes	—
86	C₈	—	2	4	no	—
87	C₈	—	4	4	no	—
88	C₈	—	88	4	no	—
89	C₂²	—	2	2	no	—
90	C₂²	—	2	1	no	—
91	C₂²	#10622549	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	2	2	no	—
94	C₄	—	2	1	no	—
95	C₄	#10622738	1	2	yes	—
96	C₂	—	4	1	no	—
97	C₂	#13068740	1	2	yes	—
98	C₂	#13068757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13067379

C₂

yes

maximal

#13066478

C₂

yes

maximal

C₁₁×#1452

C₂

yes

maximal, characteristic

C₁₁×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622539

C₂²

yes

—

C₁₁×#322

C₄

yes

—

#10622096

—

#10622095

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#66867

—

#8799

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

#41

yes

—

C₂×C₁₁⋊C₈

—

#1568

—

#1452

D₁₁

yes

characteristic

#1287

—

C₂³×C₁₁

#125

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#117

yes

—

C₂×C₄×C₁₁

#124

yes

—

C₂×C₄×C₁₁

#125

yes

characteristic

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

#432

—

#431

C₂×D₁₁

yes

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

Dic₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#382

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#430

yes

—

C₂²×C₈

Dic₂₂

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

D₄₄

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

#1833

yes

—

C₂×C₁₁

#1838

yes

characteristic

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

C₂²×C₄

#4339

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₄²

C₂×D₄₄

yes

characteristic

C₄²

#4339

yes

—

C₄²

C₂²×Dic₁₁

yes

characteristic

C₁₁

#8799

yes

characteristic, complemented, Sylow

C₂³

#66923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#66923

yes

characteristic

C₂×C₄

#66928

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

C₂×C₄

#66979

yes

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

#10622549

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#10622738

yes

—

C₂

—

C₂

#13068740

yes

—

C₂

#13068757

yes

characteristic

	subgroup	G/H
center	C₂²	#10622549
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1452	C₂
socle	C₂²×C₁₁	#382
prime radical	C₂³×C₁₁	#125
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1452	D₁₁
hypocenter	C₁₁	#8799
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#10622549

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1452

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
78. C₁₁	#8799	semidirect

H ≅ G/N

type

78. C₁₁

#8799

semidirect

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

subgroup	index
#13067379	2
#13066478	2
C₁₁×#1452	2
#8799	11

subgroup

index

#13067379

#13066478

C₁₁×#1452

#8799

Subgroups — #14647489

Conjugacy classes of subgroups

Complements

Maximal subgroups