Group #14670166 — subgroups

Subgroups — #14670166

Order 2816.

274 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 147 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	#13066710	C₂	1	4	yes	maximal
3	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66883	—	2	2	no	—
7	C₂×#66883	C₂²	1	4	yes	—
8	#10622537	—	2	2	no	—
9	C₁₁×#346	C₄	1	4	yes	—
10	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
12	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
13	C₂×#4318	—	2	4	no	—
14	C₂×C₁₁×C₁₆	—	2	4	no	—
15	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
16	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₁	Q₈	1	2	yes	—
18	#66883	—	2	8	no	—
19	#66883	—	4	4	no	—
20	C₄⋊(C₁₁⋊C₈)	—	4	4	no	—
21	#12892	—	11	1	no	maximal, Sylow
22	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
23	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
26	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₈×C₁₁	#41	1	4	yes	—
29	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
30	C₄²×C₁₁	D₈	1	2	yes	—
31	#4318	—	4	4	no	—
32	#4318	—	4	4	no	—
33	C₂×C₁₁⋊C₈	—	4	4	no	—
34	C₁₁×C₁₆	—	2	4	no	—
35	C₂×#346	D₁₁	1	1	yes	characteristic
36	#1848	—	11	2	no	—
37	#1381	—	11	4	no	—
38	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
39	C₂×C₄×C₁₁	—	4	2	no	—
40	C₂×C₄×C₁₁	#107	1	4	yes	—
41	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₁	#124	1	2	yes	—
43	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
44	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
45	C₈×C₁₁	#106	1	4	yes	—
46	C₈×C₁₁	#117	1	2	yes	—
47	C₈×C₁₁	#125	1	2	yes	—
48	C₁₁⋊C₈	—	8	4	no	—
49	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
50	C₂×#108	—	11	4	no	—
51	C₂×#108	—	22	2	no	—
52	#423	—	22	2	no	—
53	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
54	#346	Dic₁₁	1	4	yes	—
55	C₂²×C₁₁	—	2	2	no	—
56	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
57	C₂²×C₁₁	#487	1	2	yes	—
58	C₄×C₁₁	—	2	4	no	—
59	C₄×C₁₁	#382	1	1	yes	characteristic
60	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
61	C₄×C₁₁	#486	1	2	yes	—
62	C₂×M₁₆	—	22	4	no	—
63	C₂²×C₈	D₄₄	1	1	yes	characteristic
64	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
65	C₂×C₄²	D₄₄	1	1	yes	characteristic
66	C₂×C₁₆	—	2	4	no	—
67	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	—
68	#108	—	22	8	no	—
69	#108	—	44	4	no	—
70	C₄⋊C₈	—	44	4	no	—
71	C₄×C₈	Dic₂₂	1	2	yes	—
72	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
73	C₂×C₁₁	—	2	2	no	—
74	C₂×C₁₁	#1834	1	1	yes	characteristic
75	C₂×C₁₁	#2161	1	2	yes	—
76	C₂²×C₄	Dic₄₄	1	2	yes	—
77	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
78	M₁₆	—	44	4	no	—
79	M₁₆	—	44	4	no	—
80	C₂×C₈	—	44	4	no	—
81	C₂×C₈	#4314	1	4	yes	—
82	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
83	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
84	C₂×C₈	#4339	1	4	yes	—
85	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
86	C₄²	D₈₈	1	2	yes	—
87	C₄²	C₄⋊Dic₁₁	1	2	yes	—
88	C₁₆	—	2	4	no	—
89	C₁₁	#12892	1	1	yes	characteristic, complemented, Sylow
90	C₂³	C₂×Dic₄₄	1	1	yes	characteristic
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	#66882	1	4	yes	—
93	C₂×C₄	#66928	1	2	yes	—
94	C₂×C₄	C₂×#4314	1	2	yes	—
95	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
96	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
97	C₈	—	88	4	no	—
98	C₈	#66881	1	4	yes	—
99	C₈	#66923	1	2	yes	—
100	C₈	#66979	1	2	yes	—
101	C₂²	—	2	2	no	—
102	C₂²	#10622294	1	2	yes	—
103	C₂²	C₂×#66882	1	1	yes	characteristic
104	C₄	—	2	4	no	—
105	C₄	#10622307	1	2	yes	—
106	C₄	#10622549	1	1	yes	characteristic
107	C₄	C₂×#66881	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#13068744	1	1	yes	characteristic
110	C₂	#13070411	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068788

C₂

yes

maximal

#13066710

C₂

yes

maximal

C₂×C₁₁×#346

C₂

yes

maximal, characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

C₂×#66883

C₂²

yes

—

#10622537

—

C₁₁×#346

C₄

yes

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×#4318

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

#12892

—

maximal, Sylow

C₂²×C₄×C₁₁

Q₁₆

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

#41

yes

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

D₈

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

C₂×#346

D₁₁

yes

characteristic

#1848

—

#1381

—

C₂³×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#107

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#124

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

#106

yes

—

C₈×C₁₁

#117

yes

—

C₈×C₁₁

#125

yes

—

C₁₁⋊C₈

—

C₂²×C₁₆

C₂×D₁₁

yes

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#346

Dic₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×#107

yes

characteristic

C₂²×C₁₁

#487

yes

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

C₂×M₁₆

—

C₂²×C₈

D₄₄

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₁₁

yes

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

#1834

yes

characteristic

C₂×C₁₁

#2161

yes

—

C₂²×C₄

Dic₄₄

yes

—

C₂²×C₄

C₂×D₄₄

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

#4314

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₂×Dic₂₂

yes

characteristic

C₂×C₈

#4339

yes

—

C₂×C₈

C₂²×Dic₁₁

yes

characteristic

C₄²

D₈₈

yes

—

C₄²

C₄⋊Dic₁₁

yes

—

C₁₆

—

C₁₁

#12892

yes

characteristic, complemented, Sylow

C₂³

C₂×Dic₄₄

yes

characteristic

C₂×C₄

—

C₂×C₄

#66882

yes

—

C₂×C₄

#66928

yes

—

C₂×C₄

C₂×#4314

yes

—

C₂×C₄

C₂×D₈₈

yes

characteristic

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

C₈

—

C₈

#66881

yes

—

C₈

#66923

yes

—

100

C₈

#66979

yes

—

101

C₂²

—

102

C₂²

#10622294

yes

—

103

C₂²

C₂×#66882

yes

characteristic

104

C₄

—

105

C₄

#10622307

yes

—

106

C₄

#10622549

yes

characteristic

107

C₄

C₂×#66881

yes

characteristic

108

C₂

—

109

C₂

#13068744

yes

characteristic

110

C₂

#13070411

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₈₈
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#12892
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₈₈

commutator

C₂×C₈×C₁₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₂×C₁₁×#346

C₂

socle

C₂²×C₁₁

C₂×#107

prime radical

C₂³×C₁₁

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
89. C₁₁	#12892	semidirect

H ≅ G/N

type

89. C₁₁

#12892

semidirect

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

subgroup	index
#13068788	2
#13066710	2
C₂×C₁₁×#346	2
#12892	11

subgroup

index

#13068788

#13066710

C₂×C₁₁×#346

#12892

Subgroups — #14670166

Conjugacy classes of subgroups

Complements

Maximal subgroups