Group #14587496 — subgroups

Subgroups — C₁₁×#10303 #14587496

Order 2816.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3255	C₂	1	3	yes	maximal
2	C₁₁×#1994	C₂	1	3	yes	maximal
3	C₁₁×#1309	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#533	C₂²	1	3	yes	—
5	C₁₁×#475	—	2	6	no	—
6	C₁₁×#470	—	2	6	no	—
7	C₁₁×#462	—	2	6	no	—
8	C₁₁×#423	C₂²	1	3	yes	—
9	C₄³×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×#339	—	2	6	no	—
11	C₂×C₁₁×Q₁₆	—	2	6	no	—
12	C₂×C₁₁×M₁₆	D₄	1	6	yes	—
13	C₁₁×C₄⋊Q₈	D₄	1	6	yes	—
14	C₁₁×#125	—	2	3	no	—
15	C₁₁×C₂²⋊Q₈	—	2	6	no	—
16	C₄×Q₈×C₁₁	—	2	6	no	—
17	C₁₁×#117	—	2	3	no	—
18	C₂×C₄²×C₁₁	—	2	3	no	—
19	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
20	C₁₁×#106	—	2	6	no	—
21	C₁₁×C₄⋊C₈	—	2	6	no	—
22	C₁₁×#103	—	2	12	no	—
23	#10303	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×Q₈×C₁₁	—	2	6	no	—
25	C₂²×C₄×C₁₁	—	4	1	no	—
26	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
27	C₁₁×Q₁₆	—	8	6	no	—
28	C₁₁×M₁₆	—	4	6	no	—
29	C₂×C₈×C₁₁	—	2	6	no	—
30	C₁₁×C₄⋊C₄	—	2	6	no	—
31	C₁₁×C₄⋊C₄	—	2	6	no	—
32	C₁₁×C₄⋊C₄	—	4	6	no	—
33	C₁₁×C₂²⋊C₄	—	4	3	no	—
34	C₄²×C₁₁	—	2	6	no	—
35	C₄²×C₁₁	—	4	3	no	—
36	C₄²×C₁₁	—	4	3	no	—
37	C₄²×C₁₁	C₂×D₄	1	3	yes	—
38	C₄²×C₁₁	#41	1	1	yes	characteristic
39	#3255	C₂×C₁₁	1	3	yes	—
40	#1994	C₂×C₁₁	1	3	yes	—
41	#1309	C₂×C₁₁	1	1	yes	characteristic
42	C₂³×C₁₁	#127	1	1	yes	characteristic
43	Q₈×C₁₁	—	4	6	no	—
44	Q₈×C₁₁	—	4	6	no	—
45	C₂×C₄×C₁₁	—	2	3	no	—
46	C₂×C₄×C₁₁	—	2	3	no	—
47	C₂×C₄×C₁₁	—	4	6	no	—
48	C₂×C₄×C₁₁	—	4	6	no	—
49	C₂×C₄×C₁₁	#120	1	3	yes	—
50	C₂×C₄×C₁₁	#121	1	3	yes	—
51	C₈×C₁₁	—	4	6	no	—
52	#533	C₂²×C₁₁	1	3	yes	—
53	#475	—	2	6	no	—
54	#470	—	2	6	no	—
55	#462	—	2	6	no	—
56	#423	C₂²×C₁₁	1	3	yes	—
57	C₄³	C₂²×C₁₁	1	1	yes	characteristic
58	#339	—	2	6	no	—
59	C₂²×C₁₁	—	2	3	no	—
60	C₂²×C₁₁	#392	1	1	yes	characteristic
61	C₄×C₁₁	—	2	3	no	—
62	C₄×C₁₁	—	4	4	no	—
63	C₄×C₁₁	—	8	6	no	—
64	C₄×C₁₁	#455	1	3	yes	—
65	C₄×C₁₁	#456	1	3	yes	—
66	C₂×Q₁₆	—	2	6	no	—
67	C₂×M₁₆	D₄×C₁₁	1	6	yes	—
68	C₄⋊Q₈	D₄×C₁₁	1	6	yes	—
69	#125	—	2	3	no	—
70	C₂²⋊Q₈	—	2	6	no	—
71	C₄×Q₈	—	2	6	no	—
72	#117	—	2	3	no	—
73	C₂×C₄²	—	2	3	no	—
74	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
75	#106	—	2	6	no	—
76	C₄⋊C₈	—	2	6	no	—
77	#103	—	2	12	no	—
78	C₂×C₁₁	—	4	1	no	—
79	C₂×C₁₁	#2007	1	3	yes	—
80	C₂×Q₈	—	2	6	no	—
81	C₂²×C₄	—	4	1	no	—
82	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
83	Q₁₆	—	8	6	no	—
84	M₁₆	—	4	6	no	—
85	C₂×C₈	—	2	6	no	—
86	C₄⋊C₄	—	2	6	no	—
87	C₄⋊C₄	—	2	6	no	—
88	C₄⋊C₄	—	4	6	no	—
89	C₂²⋊C₄	—	4	3	no	—
90	C₄²	—	2	6	no	—
91	C₄²	—	4	3	no	—
92	C₄²	—	4	3	no	—
93	C₄²	C₂×D₄×C₁₁	1	3	yes	—
94	C₄²	C₁₁×#41	1	1	yes	characteristic
95	C₁₁	#10303	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³	C₁₁×#127	1	1	yes	characteristic
97	Q₈	—	4	6	no	—
98	Q₈	—	4	6	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	4	6	no	—
102	C₂×C₄	—	4	6	no	—
103	C₂×C₄	C₁₁×#120	1	3	yes	—
104	C₂×C₄	C₁₁×#121	1	3	yes	—
105	C₈	—	4	6	no	—
106	C₂²	—	2	3	no	—
107	C₂²	C₁₁×#392	1	1	yes	characteristic
108	C₄	—	2	3	no	—
109	C₄	—	4	4	no	—
110	C₄	—	8	6	no	—
111	C₄	C₁₁×#455	1	3	yes	—
112	C₄	C₁₁×#456	1	3	yes	—
113	C₂	—	4	1	no	—
114	C₂	C₁₁×#2007	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#3255

C₂

yes

maximal

C₁₁×#1994

C₂

yes

maximal

C₁₁×#1309

C₂

yes

maximal, characteristic

C₁₁×#533

C₂²

yes

—

C₁₁×#475

—

C₁₁×#470

—

C₁₁×#462

—

C₁₁×#423

C₂²

yes

—

C₄³×C₁₁

C₂²

yes

characteristic

C₁₁×#339

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×M₁₆

D₄

yes

—

C₁₁×C₄⋊Q₈

D₄

yes

—

C₁₁×#125

—

C₁₁×C₂²⋊Q₈

—

C₄×Q₈×C₁₁

—

C₁₁×#117

—

C₂×C₄²×C₁₁

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₁₁×#106

—

C₁₁×C₄⋊C₈

—

C₁₁×#103

—

#10303

C₁₁

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₁₁×Q₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

#41

yes

characteristic

#3255

C₂×C₁₁

yes

—

#1994

C₂×C₁₁

yes

—

#1309

C₂×C₁₁

yes

characteristic

C₂³×C₁₁

#127

yes

characteristic

Q₈×C₁₁

—

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#120

yes

—

C₂×C₄×C₁₁

#121

yes

—

C₈×C₁₁

—

#533

C₂²×C₁₁

yes

—

—

—

—

C₂²×C₁₁

yes

—

C₄³

C₂²×C₁₁

yes

characteristic

#339

—

C₂²×C₁₁

—

C₂²×C₁₁

#392

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#455

yes

—

C₄×C₁₁

#456

yes

—

C₂×Q₁₆

—

C₂×M₁₆

D₄×C₁₁

yes

—

C₄⋊Q₈

D₄×C₁₁

yes

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂³×C₁₁

yes

characteristic

#106

—

C₄⋊C₈

—

#103

—

C₂×C₁₁

—

C₂×C₁₁

#2007

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₁

yes

—

Q₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×D₄×C₁₁

yes

—

C₄²

C₁₁×#41

yes

characteristic

C₁₁

#10303

yes

characteristic, direct product factor, Sylow

C₂³

C₁₁×#127

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₁₁×#120

yes

—

104

C₂×C₄

C₁₁×#121

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

C₁₁×#392

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

C₁₁×#455

yes

—

112

C₄

C₁₁×#456

yes

—

113

C₂

—

114

C₂

C₁₁×#2007

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₁

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₁

prime radical

C₂³×C₁₁

#127

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

N	H ≅ G/N	type
23. #10303	C₁₁	direct (N × H)
95. C₁₁	#10303	direct (N × H)

H ≅ G/N

type

23. #10303

C₁₁

direct (N × H)

95. C₁₁

#10303

direct (N × H)

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

subgroup	index
C₁₁×#3255	2
C₁₁×#1994	2
C₁₁×#1309	2
#10303	11

subgroup

index

C₁₁×#3255

C₁₁×#1994

C₁₁×#1309

#10303

Subgroups — C₁₁×#10303 #14587496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C11×#10303 #14587496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#10303 #14587496