Group #14586015 — subgroups

Subgroups — C₁₁×#8822 #14586015

Order 2816.

354 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 214 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×C₈²×C₁₁	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	C₈²×C₁₁	C₄	1	1	yes	characteristic
10	C₈²×C₁₁	C₄	1	2	yes	—
11	C₈²×C₁₁	C₄	1	1	yes	characteristic
12	C₂×C₁₁×M₁₆	—	2	4	no	—
13	C₂²×C₈×C₁₁	D₄	1	2	yes	—
14	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
15	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
16	C₁₁×#108	—	4	8	no	—
17	C₁₁×C₄⋊C₈	—	2	8	no	—
18	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₁	D₄	1	4	yes	—
23	C₄×C₈×C₁₁	Q₈	1	2	yes	—
24	#8822	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
27	C₁₁×M₁₆	—	4	8	no	—
28	C₂×C₈×C₁₁	—	2	8	no	—
29	C₂×C₈×C₁₁	—	4	4	no	—
30	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
33	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
34	C₂×C₈×C₁₁	SD₁₆	1	8	yes	—
35	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₁₁	C₂×D₄	1	2	yes	—
37	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
38	#1848	C₂×C₁₁	1	2	yes	—
39	#1566	C₂×C₁₁	1	4	yes	—
40	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic
41	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₁	—	2	4	no	—
43	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
45	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
46	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
47	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
48	C₈×C₁₁	—	2	4	no	—
49	C₈×C₁₁	—	8	4	no	—
50	C₈×C₁₁	#106	1	4	yes	—
51	C₈×C₁₁	#106	1	4	yes	—
52	C₈×C₁₁	#108	1	8	yes	complemented
53	C₂×#108	—	2	4	no	—
54	#423	C₂²×C₁₁	1	4	yes	—
55	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
56	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
57	#334	—	2	8	no	—
58	C₈²	C₄×C₁₁	1	1	yes	characteristic
59	C₈²	C₄×C₁₁	1	2	yes	—
60	C₈²	C₄×C₁₁	1	1	yes	characteristic
61	C₂²×C₁₁	—	2	2	no	—
62	C₂²×C₁₁	#384	1	1	yes	characteristic
63	C₂²×C₁₁	#498	1	2	yes	—
64	C₄×C₁₁	—	2	2	no	—
65	C₄×C₁₁	C₂×#106	1	2	yes	—
66	C₄×C₁₁	C₂×#108	1	4	yes	—
67	C₄×C₁₁	#492	1	2	yes	—
68	C₂×M₁₆	—	2	4	no	—
69	C₂²×C₈	D₄×C₁₁	1	2	yes	—
70	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
71	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
72	#108	—	4	8	no	—
73	C₄⋊C₈	—	2	8	no	—
74	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
75	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
76	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
77	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
78	C₄×C₈	D₄×C₁₁	1	4	yes	—
79	C₄×C₈	Q₈×C₁₁	1	2	yes	—
80	C₂×C₁₁	—	2	2	no	—
81	C₂×C₁₁	#1844	1	1	yes	characteristic
82	C₂×C₁₁	#1848	1	2	yes	—
83	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
84	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
85	M₁₆	—	4	8	no	—
86	C₂×C₈	—	2	8	no	—
87	C₂×C₈	—	4	4	no	—
88	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
89	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
90	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
91	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
92	C₂×C₈	C₁₁×SD₁₆	1	8	yes	—
93	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
94	C₄²	C₂×D₄×C₁₁	1	2	yes	—
95	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
96	C₁₁	#8822	1	1	yes	characteristic, direct product factor, Sylow
97	C₂³	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
101	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
102	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
103	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
104	C₈	—	2	4	no	—
105	C₈	—	8	4	no	—
106	C₈	C₁₁×#106	1	4	yes	—
107	C₈	C₁₁×#106	1	4	yes	—
108	C₈	C₁₁×#108	1	8	yes	complemented
109	C₂²	—	2	2	no	—
110	C₂²	C₁₁×#384	1	1	yes	characteristic
111	C₂²	C₁₁×#498	1	2	yes	—
112	C₄	—	2	2	no	—
113	C₄	C₂×C₁₁×#106	1	2	yes	—
114	C₄	C₂×C₁₁×#108	1	4	yes	—
115	C₄	C₁₁×#492	1	2	yes	—
116	C₂	—	2	2	no	—
117	C₂	C₁₁×#1844	1	1	yes	characteristic
118	C₂	C₁₁×#1848	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#1848

C₂

yes

maximal

C₁₁×#1566

C₂

yes

maximal

C₂×C₈²×C₁₁

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

—

C₈²×C₁₁

C₄

yes

characteristic

C₈²×C₁₁

C₄

yes

—

C₈²×C₁₁

C₄

yes

characteristic

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

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#8822

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

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×C₈²

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

—

C₈×C₁₁

#106

yes

—

C₈×C₁₁

yes

—

C₂²×C₁₁

yes

—

C₂×C₄×C₈

C₂²×C₁₁

yes

—

C₂×C₄×C₈

C₂²×C₁₁

yes

characteristic

#334

—

C₈²

C₄×C₁₁

yes

characteristic

C₈²

C₄×C₁₁

yes

—

C₈²

C₄×C₁₁

yes

characteristic

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#498

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#106

yes

—

C₄×C₁₁

C₂×#108

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

characteristic

C₄×C₈

C₂×C₄×C₁₁

yes

characteristic

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

#1848

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×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

#8822

yes

characteristic, direct product factor, Sylow

C₂³

C₁₁×C₄⋊Q₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₁₁×C₄⋊C₄

yes

characteristic

100

C₂×C₄

C₂×C₁₁×C₄⋊C₄

yes

—

101

C₂×C₄

C₁₁×#127

yes

characteristic

102

C₂×C₄

C₁₁×C₄⋊Q₈

yes

—

103

C₂×C₄

C₂×C₁₁×SD₁₆

yes

—

104

C₈

—

105

C₈

—

106

C₈

C₁₁×#106

yes

—

107

C₈

C₁₁×#106

yes

—

108

C₈

C₁₁×#108

yes

complemented

109

C₂²

—

110

C₂²

C₁₁×#384

yes

characteristic

111

C₂²

C₁₁×#498

yes

—

112

C₄

—

113

C₄

C₂×C₁₁×#106

yes

—

114

C₄

C₂×C₁₁×#108

yes

—

115

C₄

C₁₁×#492

yes

—

116

C₂

—

117

C₂

C₁₁×#1844

yes

characteristic

118

C₂

C₁₁×#1848

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
24. #8822	C₁₁	direct (N × H)
52. C₈×C₁₁	#108	semidirect
96. C₁₁	#8822	direct (N × H)
108. C₈	C₁₁×#108	semidirect

H ≅ G/N

type

24. #8822

C₁₁

direct (N × H)

52. C₈×C₁₁

#108

semidirect

96. C₁₁

#8822

direct (N × H)

108. C₈

C₁₁×#108

semidirect

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×C₈²×C₁₁	2
#8822	11

subgroup

index

C₁₁×#1848

C₁₁×#1566

C₂×C₈²×C₁₁

#8822

Subgroups — C₁₁×#8822 #14586015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C11×#8822 #14586015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#8822 #14586015