Group #14647447 — subgroups

Subgroups — #14647447

Order 2816.

322 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 147 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	#13068733	C₂	1	2	yes	maximal
2	#13066451	C₂	1	4	yes	maximal
3	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
5	C₄³×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
7	C₁₁×#336	C₄	1	4	yes	—
8	#10622162	—	2	4	no	—
9	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
10	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₁	D₄	1	2	yes	—
12	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
13	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
14	C₂²×C₁₁⋊C₈	—	2	4	no	—
15	C₄×C₈×C₁₁	—	2	4	no	—
16	C₄⋊(C₁₁⋊C₈)	—	2	8	no	—
17	#8788	—	11	1	no	maximal, Sylow
18	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
19	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₈×C₁₁	—	2	4	no	—
23	C₂×C₈×C₁₁	—	2	8	no	—
24	C₄²×C₁₁	—	2	4	no	—
25	C₄²×C₁₁	—	2	4	no	—
26	C₄²×C₁₁	—	4	2	no	—
27	C₄²×C₁₁	#41	1	4	yes	—
28	C₂×C₁₁⋊C₈	—	4	4	no	—
29	C₂×C₁₁⋊C₈	—	4	8	no	—
30	#1831	—	11	2	no	—
31	#1744	D₁₁	1	1	yes	characteristic
32	#1277	—	11	4	no	—
33	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₁	—	2	2	no	—
35	C₂×C₄×C₁₁	—	2	4	no	—
36	C₂×C₄×C₁₁	—	2	4	no	—
37	C₂×C₄×C₁₁	—	2	4	no	—
38	C₂×C₄×C₁₁	#117	1	2	yes	—
39	C₂×C₄×C₁₁	#124	1	2	yes	—
40	C₂×C₄×C₁₁	#125	1	2	yes	—
41	C₂×C₄×C₁₁	#131	1	4	yes	—
42	C₂×C₄×C₁₁	#135	1	4	yes	—
43	C₈×C₁₁	—	4	4	no	—
44	C₁₁⋊C₈	—	8	4	no	—
45	C₂×C₄⋊C₈	—	11	4	no	—
46	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
47	C₄³	C₂×D₁₁	1	1	yes	characteristic
48	#336	—	22	4	no	—
49	#336	Dic₁₁	1	4	yes	—
50	C₂²×C₁₁	#382	1	1	yes	characteristic
51	C₂²×C₁₁	#424	1	2	yes	—
52	C₂²×C₁₁	#427	1	2	yes	—
53	C₂²×C₁₁	#430	1	2	yes	—
54	C₄×C₁₁	—	2	2	no	—
55	C₄×C₁₁	—	4	4	no	—
56	C₄×C₁₁	#433	1	4	yes	—
57	C₄×C₁₁	#488	1	4	yes	—
58	C₂²×C₈	—	22	4	no	—
59	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
60	C₂×C₄²	Dic₂₂	1	2	yes	—
61	C₂×C₄²	D₄₄	1	2	yes	—
62	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
63	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
64	C₄⋊C₈	—	22	8	no	—
65	C₄×C₈	—	2	4	no	—
66	C₂×C₁₁	#1572	1	4	yes	—
67	C₂×C₁₁	#1832	1	1	yes	characteristic
68	C₂×C₁₁	#1835	1	1	yes	characteristic
69	C₂×C₁₁	#1838	1	1	yes	characteristic
70	C₂²×C₄	C₄⋊Dic₁₁	1	4	yes	—
71	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
72	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
73	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
74	C₂×C₈	—	2	4	no	—
75	C₂×C₈	—	2	8	no	—
76	C₂×C₈	—	44	4	no	—
77	C₂×C₈	—	44	8	no	—
78	C₄²	—	2	4	no	—
79	C₄²	—	2	4	no	—
80	C₄²	—	4	2	no	—
81	C₄²	#4339	1	4	yes	—
82	C₁₁	#8788	1	1	yes	characteristic, complemented, Sylow
83	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	#66923	1	2	yes	—
89	C₂×C₄	#66928	1	2	yes	—
90	C₂×C₄	#66957	1	4	yes	—
91	C₂×C₄	#66979	1	2	yes	—
92	C₂×C₄	#67001	1	4	yes	—
93	C₈	—	4	4	no	—
94	C₈	—	88	4	no	—
95	C₂²	#10622549	1	1	yes	characteristic
96	C₂²	#10622612	1	2	yes	—
97	C₂²	#10622719	1	2	yes	—
98	C₂²	#10622738	1	2	yes	—
99	C₄	—	2	2	no	—
100	C₄	—	4	4	no	—
101	C₄	#10622310	1	4	yes	—
102	C₄	#10622613	1	4	yes	—
103	C₂	#13067396	1	4	yes	—
104	C₂	#13068736	1	1	yes	characteristic
105	C₂	#13068747	1	1	yes	characteristic
106	C₂	#13068757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068733

C₂

yes

maximal

#13066451

C₂

yes

maximal

C₁₁×#1744

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₄³×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₁₁×#336

C₄

yes

—

#10622162

—

C₂²×C₈×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂²×C₁₁⋊C₈

—

C₄×C₈×C₁₁

—

C₄⋊(C₁₁⋊C₈)

—

#8788

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

#41

yes

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#1831

—

#1744

D₁₁

yes

characteristic

#1277

—

C₂³×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#117

yes

—

C₂×C₄×C₁₁

#124

yes

—

C₂×C₄×C₁₁

#125

yes

—

C₂×C₄×C₁₁

#131

yes

—

C₂×C₄×C₁₁

#135

yes

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

C₄³

C₂×D₁₁

yes

characteristic

#336

—

#336

Dic₁₁

yes

—

C₂²×C₁₁

#382

yes

characteristic

C₂²×C₁₁

#424

yes

—

C₂²×C₁₁

#427

yes

—

C₂²×C₁₁

#430

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#433

yes

—

C₄×C₁₁

#488

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₁

yes

—

C₂×C₄²

Dic₂₂

yes

—

C₂×C₄²

D₄₄

yes

—

C₂×C₄²

C₂×Dic₁₁

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

C₂×C₁₁

#1572

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂²×C₄

C₄⋊Dic₁₁

yes

—

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

C₂²×C₄

C₂×D₄₄

yes

characteristic

C₂²×C₄

C₂²×Dic₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

#4339

yes

—

C₁₁

#8788

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄⋊Dic₁₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#66923

yes

—

C₂×C₄

#66928

yes

—

C₂×C₄

#66957

yes

—

C₂×C₄

#66979

yes

—

C₂×C₄

#67001

yes

—

C₈

—

C₈

—

C₂²

#10622549

yes

characteristic

C₂²

#10622612

yes

—

C₂²

#10622719

yes

—

C₂²

#10622738

yes

—

C₄

—

100

C₄

—

101

C₄

#10622310

yes

—

102

C₄

#10622613

yes

—

103

C₂

#13067396

yes

—

104

C₂

#13068736

yes

characteristic

105

C₂

#13068747

yes

characteristic

106

C₂

#13068757

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₄
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1744	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1744	D₁₁
hypocenter	C₁₁	#8788
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₄₄

commutator

C₂²×C₄×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1744

C₂

socle, prime radical

C₂³×C₁₁

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
82. C₁₁	#8788	semidirect

H ≅ G/N

type

82. C₁₁

#8788

semidirect

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

subgroup	index
#13068733	2
#13066451	2
C₁₁×#1744	2
#8788	11

subgroup

index

#13068733

#13066451

C₁₁×#1744

#8788

Subgroups — #14647447

Conjugacy classes of subgroups

Complements

Maximal subgroups