Group #14586019 — subgroups

Subgroups — C₁₁×#8826 #14586019

Order 2816.

338 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 198 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	C₁₁×#1848	C₂	1	2	yes	maximal
2	C₁₁×#1567	C₂	1	4	yes	maximal
3	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#108	—	2	4	no	—
5	C₁₁×#423	C₂²	1	4	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×#335	—	2	8	no	—
9	C₁₁×#322	C₄	1	4	yes	—
10	C₂×C₁₁×M₁₆	—	2	4	no	—
11	C₂²×C₈×C₁₁	D₄	1	2	yes	—
12	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
13	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
14	C₁₁×#108	—	4	8	no	—
15	C₁₁×C₄⋊C₈	—	2	8	no	—
16	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₁	D₄	1	4	yes	—
19	C₄×C₈×C₁₁	Q₈	1	2	yes	—
20	#8826	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
23	C₁₁×M₁₆	—	4	8	no	—
24	C₂×C₈×C₁₁	—	4	4	no	—
25	C₂×C₈×C₁₁	—	4	4	no	—
26	C₂×C₈×C₁₁	C₄⋊C₄	1	8	yes	—
27	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
28	C₂×C₈×C₁₁	D₈	1	4	yes	—
29	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
30	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
31	C₄²×C₁₁	C₂×D₄	1	2	yes	—
32	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
33	#1848	C₂×C₁₁	1	2	yes	—
34	#1567	C₂×C₁₁	1	4	yes	—
35	C₂×#322	C₂×C₁₁	1	1	yes	characteristic
36	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
37	C₂×C₄×C₁₁	—	2	4	no	—
38	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
41	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
42	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
43	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
44	C₈×C₁₁	—	2	8	no	—
45	C₈×C₁₁	—	8	4	no	—
46	C₈×C₁₁	#107	1	8	yes	—
47	C₂×#108	—	2	4	no	—
48	#423	C₂²×C₁₁	1	4	yes	—
49	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
50	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
51	#335	—	2	8	no	—
52	#322	C₄×C₁₁	1	4	yes	—
53	C₂²×C₁₁	—	2	2	no	—
54	C₂²×C₁₁	#384	1	1	yes	characteristic
55	C₂²×C₁₁	#500	1	2	yes	—
56	C₄×C₁₁	—	2	2	no	—
57	C₄×C₁₁	C₂×#107	1	2	yes	—
58	C₄×C₁₁	#430	1	4	yes	—
59	C₄×C₁₁	#493	1	1	yes	characteristic
60	C₄×C₁₁	#494	1	1	yes	characteristic
61	C₂×M₁₆	—	2	4	no	—
62	C₂²×C₈	D₄×C₁₁	1	2	yes	—
63	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
64	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
65	#108	—	4	8	no	—
66	C₄⋊C₈	—	2	8	no	—
67	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
68	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
69	C₄×C₈	D₄×C₁₁	1	4	yes	—
70	C₄×C₈	Q₈×C₁₁	1	2	yes	—
71	C₂×C₁₁	—	2	2	no	—
72	C₂×C₁₁	#1845	1	1	yes	characteristic
73	C₂×C₁₁	#1849	1	2	yes	—
74	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
75	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
76	M₁₆	—	4	8	no	—
77	C₂×C₈	—	4	4	no	—
78	C₂×C₈	—	4	4	no	—
79	C₂×C₈	C₁₁×C₄⋊C₄	1	8	yes	—
80	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
81	C₂×C₈	C₁₁×D₈	1	4	yes	—
82	C₂×C₈	C₁₁×Q₁₆	1	4	yes	—
83	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
84	C₄²	C₂×D₄×C₁₁	1	2	yes	—
85	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
86	C₁₁	#8826	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
91	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
92	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
93	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
94	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
95	C₈	—	2	8	no	—
96	C₈	—	8	4	no	—
97	C₈	C₁₁×#107	1	8	yes	—
98	C₂²	—	2	2	no	—
99	C₂²	C₁₁×#384	1	1	yes	characteristic
100	C₂²	C₁₁×#500	1	2	yes	—
101	C₄	—	2	2	no	—
102	C₄	C₂×C₁₁×#107	1	2	yes	—
103	C₄	C₁₁×#430	1	4	yes	—
104	C₄	C₁₁×#493	1	1	yes	characteristic
105	C₄	C₁₁×#494	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	C₁₁×#1845	1	1	yes	characteristic
108	C₂	C₁₁×#1849	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#1848

C₂

yes

maximal

C₁₁×#1567

C₂

yes

maximal

C₂×C₁₁×#322

C₂

yes

maximal, characteristic

C₂×C₁₁×#108

—

C₁₁×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₁₁×#335

—

C₁₁×#322

C₄

yes

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₁₁×#108

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#8826

C₁₁

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#1848

C₂×C₁₁

yes

—

#1567

C₂×C₁₁

yes

—

C₂×#322

C₂×C₁₁

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×D₈

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#107

yes

—

C₂×#108

—

#423

C₂²×C₁₁

yes

—

C₂×C₄×C₈

C₂²×C₁₁

yes

—

C₂×C₄×C₈

C₂²×C₁₁

yes

characteristic

#335

—

#322

C₄×C₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#500

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#107

yes

—

C₄×C₁₁

#430

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂²×C₈

D₄×C₁₁

yes

—

C₂²×C₈

Q₈×C₁₁

yes

—

C₂×C₄²

C₂³×C₁₁

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₁₁

yes

—

C₄×C₈

C₂×C₄×C₁₁

yes

—

C₄×C₈

D₄×C₁₁

yes

—

C₄×C₈

Q₈×C₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

#1845

yes

characteristic

C₂×C₁₁

#1849

yes

—

C₂²×C₄

C₂×D₄×C₁₁

yes

characteristic

C₂²×C₄

C₂×Q₈×C₁₁

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₁₁×C₄⋊C₄

yes

—

C₂×C₈

C₁₁×C₄⋊C₄

yes

—

C₂×C₈

C₁₁×D₈

yes

—

C₂×C₈

C₁₁×Q₁₆

yes

—

C₄²

C₂²×C₄×C₁₁

yes

characteristic

C₄²

C₂×D₄×C₁₁

yes

—

C₄²

C₂×Q₈×C₁₁

yes

characteristic

C₁₁

#8826

yes

characteristic, direct product factor, Sylow

C₂³

C₁₁×C₄⋊Q₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₁₁×C₄⋊C₄

yes

characteristic

C₂×C₄

C₂×C₁₁×C₄⋊C₄

yes

—

C₂×C₄

C₁₁×#127

yes

characteristic

C₂×C₄

C₁₁×C₄⋊Q₈

yes

—

C₂×C₄

C₂×C₁₁×D₈

yes

—

C₂×C₄

C₂×C₁₁×Q₁₆

yes

—

C₈

—

C₈

—

C₈

C₁₁×#107

yes

—

C₂²

—

C₂²

C₁₁×#384

yes

characteristic

100

C₂²

C₁₁×#500

yes

—

101

C₄

—

102

C₄

C₂×C₁₁×#107

yes

—

103

C₄

C₁₁×#430

yes

—

104

C₄

C₁₁×#493

yes

characteristic

105

C₄

C₁₁×#494

yes

characteristic

106

C₂

—

107

C₂

C₁₁×#1845

yes

characteristic

108

C₂

C₁₁×#1849

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₁	#127
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₁

#127

commutator

C₄²

C₂²×C₄×C₁₁

Frattini, cosocle

C₂×C₄²

C₂³×C₁₁

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

N	H ≅ G/N	type
20. #8826	C₁₁	direct (N × H)
86. C₁₁	#8826	direct (N × H)

H ≅ G/N

type

20. #8826

C₁₁

direct (N × H)

86. C₁₁

#8826

direct (N × H)

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

subgroup	index
C₁₁×#1848	2
C₁₁×#1567	2
C₂×C₁₁×#322	2
#8826	11

subgroup

index

C₁₁×#1848

C₁₁×#1567

C₂×C₁₁×#322

#8826

Subgroups — C₁₁×#8826 #14586019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C11×#8826 #14586019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#8826 #14586019