Group #14586018 — subgroups

Subgroups — C₁₁×#8825 #14586018

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×#1566	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×#334	—	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	#8825	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	SD₁₆	1	8	yes	—
29	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
30	C₄²×C₁₁	C₂×D₄	1	2	yes	—
31	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
32	#1848	C₂×C₁₁	1	2	yes	—
33	#1566	C₂×C₁₁	1	4	yes	—
34	C₂×#322	C₂×C₁₁	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	—	8	4	no	—
44	C₈×C₁₁	#106	1	8	yes	—
45	C₂×#108	—	2	4	no	—
46	#423	C₂²×C₁₁	1	4	yes	—
47	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
48	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
49	#334	—	2	8	no	—
50	#322	C₄×C₁₁	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	—	2	4	no	—
59	C₂²×C₈	D₄×C₁₁	1	2	yes	—
60	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
61	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
62	#108	—	4	8	no	—
63	C₄⋊C₈	—	2	8	no	—
64	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
65	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
66	C₄×C₈	D₄×C₁₁	1	4	yes	—
67	C₄×C₈	Q₈×C₁₁	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×D₄×C₁₁	1	1	yes	characteristic
72	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
73	M₁₆	—	4	8	no	—
74	C₂×C₈	—	4	4	no	—
75	C₂×C₈	—	4	4	no	—
76	C₂×C₈	C₁₁×C₄⋊C₄	1	8	yes	—
77	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
78	C₂×C₈	C₁₁×SD₁₆	1	8	yes	—
79	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
80	C₄²	C₂×D₄×C₁₁	1	2	yes	—
81	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
82	C₁₁	#8825	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
87	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
88	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
89	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
90	C₈	—	2	8	no	—
91	C₈	—	8	4	no	—
92	C₈	C₁₁×#106	1	8	yes	—
93	C₂²	—	2	2	no	—
94	C₂²	C₁₁×#384	1	1	yes	characteristic
95	C₂²	C₁₁×#498	1	2	yes	—
96	C₄	—	2	2	no	—
97	C₄	C₂×C₁₁×#106	1	2	yes	—
98	C₄	C₁₁×#430	1	4	yes	—
99	C₄	C₁₁×#492	1	2	yes	—
100	C₂	—	2	2	no	—
101	C₂	C₁₁×#1844	1	1	yes	characteristic
102	C₂	C₁₁×#1849	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#1848

C₂

yes

maximal

C₁₁×#1566

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×#334

—

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

—

#8825

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

SD₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#1848

C₂×C₁₁

yes

—

#1566

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×SD₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#106

yes

—

C₂×#108

—

#423

C₂²×C₁₁

yes

—

C₂×C₄×C₈

C₂²×C₁₁

yes

—

C₂×C₄×C₈

C₂²×C₁₁

yes

characteristic

#334

—

#322

C₄×C₁₁

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

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

#1844

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×SD₁₆

yes

—

C₄²

C₂²×C₄×C₁₁

yes

characteristic

C₄²

C₂×D₄×C₁₁

yes

—

C₄²

C₂×Q₈×C₁₁

yes

characteristic

C₁₁

#8825

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×SD₁₆

yes

—

C₈

—

C₈

—

C₈

C₁₁×#106

yes

—

C₂²

—

C₂²

C₁₁×#384

yes

characteristic

C₂²

C₁₁×#498

yes

—

C₄

—

C₄

C₂×C₁₁×#106

yes

—

C₄

C₁₁×#430

yes

—

C₄

C₁₁×#492

yes

—

100

C₂

—

101

C₂

C₁₁×#1844

yes

characteristic

102

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. #8825	C₁₁	direct (N × H)
82. C₁₁	#8825	direct (N × H)

H ≅ G/N

type

20. #8825

C₁₁

direct (N × H)

82. C₁₁

#8825

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×#1566	2
C₂×C₁₁×#322	2
#8825	11

subgroup

index

C₁₁×#1848

C₁₁×#1566

C₂×C₁₁×#322

#8825

Subgroups — C₁₁×#8825 #14586018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C11×#8825 #14586018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#8825 #14586018