Group #14647584 — subgroups

Subgroups — #14647584

Order 2816.

338 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 187 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	#13068788	C₂	1	2	yes	maximal
2	#13067372	C₂	1	4	yes	maximal
3	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66883	—	2	4	no	—
7	#10622537	C₂²	1	4	yes	—
8	C₁₁×#322	C₄	1	4	yes	—
9	#10622095	—	2	8	no	—
10	C₂²×C₈×C₁₁	D₄	1	2	yes	—
11	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
12	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×#4318	—	2	4	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	4	yes	—
17	C₄×C₈×C₁₁	Q₈	1	2	yes	—
18	#66883	—	4	8	no	—
19	C₄⋊(C₁₁⋊C₈)	—	2	8	no	—
20	#8825	—	11	1	no	maximal, Sylow
21	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
23	C₂×C₈×C₁₁	—	4	4	no	—
24	C₂×C₈×C₁₁	C₄⋊C₄	1	8	yes	—
25	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
26	C₂×C₈×C₁₁	SD₁₆	1	8	yes	—
27	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
28	C₄²×C₁₁	C₂×D₄	1	2	yes	—
29	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
30	#4318	—	4	8	no	—
31	C₂×C₁₁⋊C₈	—	4	4	no	—
32	#1848	—	11	2	no	—
33	#1566	—	11	4	no	—
34	C₂×#322	D₁₁	1	1	yes	characteristic
35	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
36	C₂×C₄×C₁₁	—	2	4	no	—
37	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
39	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
40	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
41	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
42	C₈×C₁₁	—	2	8	no	—
43	C₈×C₁₁	#106	1	8	yes	—
44	C₁₁⋊C₈	—	8	4	no	—
45	C₂×#108	—	22	4	no	—
46	#423	—	11	4	no	—
47	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
48	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
49	#334	—	22	8	no	—
50	#322	Dic₁₁	1	4	yes	—
51	C₂²×C₁₁	—	2	2	no	—
52	C₂²×C₁₁	#384	1	1	yes	characteristic
53	C₂²×C₁₁	#498	1	2	yes	—
54	C₄×C₁₁	—	2	2	no	—
55	C₄×C₁₁	C₂×#106	1	2	yes	—
56	C₄×C₁₁	#430	1	4	yes	—
57	C₄×C₁₁	#492	1	2	yes	—
58	C₂×M₁₆	—	22	4	no	—
59	C₂²×C₈	Dic₂₂	1	4	yes	—
60	C₂²×C₈	D₄₄	1	2	yes	—
61	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
62	#108	—	44	8	no	—
63	C₄⋊C₈	—	22	8	no	—
64	C₄×C₈	Dic₂₂	1	2	yes	—
65	C₄×C₈	D₄₄	1	4	yes	—
66	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
67	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
68	C₂×C₁₁	—	2	2	no	—
69	C₂×C₁₁	#1844	1	1	yes	characteristic
70	C₂×C₁₁	#1849	1	2	yes	—
71	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
72	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
73	M₁₆	—	44	8	no	—
74	C₂×C₈	—	4	4	no	—
75	C₂×C₈	—	44	4	no	—
76	C₂×C₈	#4314	1	8	yes	—
77	C₂×C₈	C₄⋊Dic₁₁	1	8	yes	—
78	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
79	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
80	C₄²	C₂×D₄₄	1	2	yes	—
81	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
82	C₁₁	#8825	1	1	yes	characteristic, complemented, Sylow
83	C₂³	#66922	1	1	yes	characteristic
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	#66922	1	2	yes	—
86	C₂×C₄	#66927	1	1	yes	characteristic
87	C₂×C₄	C₂×#4314	1	4	yes	—
88	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
89	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
90	C₈	—	2	8	no	—
91	C₈	—	88	4	no	—
92	C₈	#66881	1	8	yes	—
93	C₂²	—	2	2	no	—
94	C₂²	#10622293	1	2	yes	—
95	C₂²	#10622548	1	1	yes	characteristic
96	C₄	—	2	2	no	—
97	C₄	#10622306	1	2	yes	—
98	C₄	C₂×#66881	1	2	yes	—
99	C₄	#10622738	1	4	yes	—
100	C₂	—	2	2	no	—
101	C₂	#13068773	1	1	yes	characteristic
102	C₂	#13068791	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068788

C₂

yes

maximal

#13067372

C₂

yes

maximal

C₂×C₁₁×#322

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

#10622537

C₂²

yes

—

C₁₁×#322

C₄

yes

—

#10622095

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

#8825

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#4318

—

C₂×C₁₁⋊C₈

—

#1848

—

#1566

—

C₂×#322

D₁₁

yes

characteristic

C₂³×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

#106

yes

—

C₁₁⋊C₈

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₂×C₄×C₈

C₂×D₁₁

yes

—

#334

—

#322

Dic₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#498

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#106

yes

—

C₄×C₁₁

#430

yes

—

C₄×C₁₁

#492

yes

—

C₂×M₁₆

—

C₂²×C₈

Dic₂₂

yes

—

C₂²×C₈

D₄₄

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

D₄₄

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

#1844

yes

characteristic

C₂×C₁₁

#1849

yes

—

C₂²×C₄

C₂×Dic₂₂

yes

—

C₂²×C₄

C₂×D₄₄

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#4314

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₄²

C₂×Dic₂₂

yes

characteristic

C₄²

C₂×D₄₄

yes

—

C₄²

C₂²×Dic₁₁

yes

characteristic

C₁₁

#8825

yes

characteristic, complemented, Sylow

C₂³

#66922

yes

characteristic

C₂×C₄

—

C₂×C₄

#66922

yes

—

C₂×C₄

#66927

yes

characteristic

C₂×C₄

C₂×#4314

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

C₈

—

C₈

—

C₈

#66881

yes

—

C₂²

—

C₂²

#10622293

yes

—

C₂²

#10622548

yes

characteristic

C₄

—

C₄

#10622306

yes

—

C₄

C₂×#66881

yes

—

C₄

#10622738

yes

—

100

C₂

—

101

C₂

#13068773

yes

characteristic

102

C₂

#13068791

yes

—

	subgroup	G/H
center	C₂×C₄	#66927
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#322	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#322	D₁₁
hypocenter	C₁₁	#8825
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#66927

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₂×C₁₁×#322

C₂

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
82. C₁₁	#8825	semidirect

H ≅ G/N

type

82. C₁₁

#8825

semidirect

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

subgroup	index
#13068788	2
#13067372	2
C₂×C₁₁×#322	2
#8825	11

subgroup

index

#13068788

#13067372

C₂×C₁₁×#322

#8825

Subgroups — #14647584

Conjugacy classes of subgroups

Complements

Maximal subgroups