Group #14674764 — subgroups

Subgroups — #14674764

Order 2816.

174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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	#13070895	C₂	1	1	yes	maximal, characteristic
2	#13070869	C₂	1	1	yes	maximal, characteristic
3	#13066798	C₂	1	4	yes	maximal
4	C₁₁×#1397	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₈₈	—	2	1	no	—
6	C₂×Dic₈₈	C₂²	1	2	yes	—
7	#10622312	—	2	1	no	—
8	#10622296	—	2	1	no	—
9	C₂×C₁₁×C₃₂	C₂²	1	2	yes	—
10	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	#10622143	—	2	1	no	—
12	#10622142	C₂²	1	2	yes	—
13	C₂×Dic₄₄	—	2	2	no	—
14	C₂×Dic₄₄	—	4	1	no	—
15	#66923	—	4	1	no	—
16	#66922	—	4	1	no	—
17	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
18	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
19	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
20	#66882	—	2	2	no	—
21	#66881	—	4	1	no	—
22	Dic₈₈	—	2	4	no	—
23	Dic₈₈	—	4	2	no	—
24	C₁₁×C₃₂	—	2	2	no	—
25	#13724	—	11	1	no	maximal, Sylow
26	C₂×Dic₂₂	—	4	2	no	—
27	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
28	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
29	C₄²×C₁₁	D₈	1	1	yes	characteristic
30	C₄⋊Dic₁₁	—	4	2	no	—
31	C₄⋊Dic₁₁	—	8	2	no	—
32	Dic₁₁⋊C₄	—	8	2	no	—
33	Dic₄₄	—	4	2	no	—
34	Dic₄₄	—	4	2	no	—
35	Dic₄₄	—	8	2	no	—
36	C₁₁×C₁₆	SD₁₆	1	2	yes	—
37	C₁₁×C₁₆	#41	1	2	yes	—
38	#2253	—	11	1	no	—
39	#2247	—	11	1	no	—
40	#1416	—	11	4	no	—
41	#1397	D₁₁	1	1	yes	characteristic
42	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
43	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
44	C₂×Dic₁₁	—	8	2	no	—
45	C₂×Dic₁₁	—	8	2	no	—
46	Dic₂₂	—	8	2	no	—
47	Dic₂₂	—	8	2	no	—
48	C₈×C₁₁	SD₃₂	1	2	yes	—
49	C₈×C₁₁	#124	1	1	yes	characteristic
50	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
51	C₂×Q₃₂	—	11	2	no	—
52	C₂×Q₃₂	—	22	1	no	—
53	#499	—	22	1	no	—
54	#494	—	22	1	no	—
55	C₂×C₃₂	C₂×D₁₁	1	2	yes	—
56	#367	—	22	1	no	—
57	#366	—	11	2	no	—
58	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
59	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
60	C₄×C₁₁	—	2	2	no	—
61	C₄×C₁₁	#486	1	1	yes	characteristic
62	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
63	Dic₁₁	—	16	2	no	—
64	Dic₁₁	—	16	2	no	—
65	C₂×Q₁₆	—	22	2	no	—
66	C₂×Q₁₆	—	44	1	no	—
67	C₄⋊Q₈	—	44	1	no	—
68	#125	—	44	1	no	—
69	Q₃₂	—	22	4	no	—
70	Q₃₂	—	44	2	no	—
71	C₂×C₁₆	D₄₄	1	1	yes	characteristic
72	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
73	#107	—	22	2	no	—
74	#106	—	44	1	no	—
75	C₄×C₈	D₄₄	1	1	yes	characteristic
76	C₃₂	—	2	2	no	—
77	C₂×C₁₁	#2240	1	1	yes	characteristic
78	C₂×C₁₁	#2264	1	2	yes	—
79	C₂×Q₈	—	44	2	no	—
80	Q₁₆	—	44	2	no	—
81	Q₁₆	—	44	2	no	—
82	Q₁₆	—	88	2	no	—
83	C₂×C₈	D₈₈	1	1	yes	characteristic
84	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
85	C₄⋊C₄	—	44	2	no	—
86	C₄⋊C₄	—	88	2	no	—
87	C₄⋊C₄	—	88	2	no	—
88	C₄²	D₈₈	1	1	yes	characteristic
89	C₁₆	#4314	1	2	yes	—
90	C₁₆	#4339	1	2	yes	—
91	C₁₁	#13724	1	1	yes	characteristic, complemented, Sylow
92	Q₈	—	88	2	no	—
93	Q₈	—	88	2	no	—
94	C₂×C₄	—	88	2	no	—
95	C₂×C₄	—	88	2	no	—
96	C₂×C₄	D₁₇₆	1	2	yes	—
97	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
98	C₈	#66864	1	2	yes	—
99	C₈	#66928	1	1	yes	characteristic
100	C₈	C₂×#4314	1	1	yes	characteristic
101	C₂²	C₂×D₁₇₆	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	176	2	no	—
104	C₄	—	176	2	no	—
105	C₄	#10622307	1	1	yes	characteristic
106	C₄	C₂×#66864	1	1	yes	characteristic
107	C₂	#13070840	1	1	yes	characteristic
108	C₂	#13070936	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13070895

C₂

yes

maximal, characteristic

#13070869

C₂

yes

maximal, characteristic

#13066798

C₂

yes

maximal

C₁₁×#1397

C₂

yes

maximal, characteristic

C₂×Dic₈₈

—

C₂×Dic₈₈

C₂²

yes

—

#10622312

—

#10622296

—

C₂×C₁₁×C₃₂

C₂²

yes

—

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

#10622143

—

#10622142

C₂²

yes

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

#66923

—

#66922

—

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₂×C₁₁×C₁₆

C₂³

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

characteristic

#66882

—

#66881

—

Dic₈₈

—

Dic₈₈

—

C₁₁×C₃₂

—

#13724

—

maximal, Sylow

C₂×Dic₂₂

—

C₂×C₈×C₁₁

D₈

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

D₈

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

Dic₄₄

—

Dic₄₄

—

Dic₄₄

—

C₁₁×C₁₆

SD₁₆

yes

—

C₁₁×C₁₆

#41

yes

—

—

—

—

D₁₁

yes

characteristic

C₂×C₄×C₁₁

D₁₆

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

SD₃₂

yes

—

C₈×C₁₁

#124

yes

characteristic

C₈×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×Q₃₂

—

C₂×Q₃₂

—

#499

—

#494

—

C₂×C₃₂

C₂×D₁₁

yes

—

#367

—

#366

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

C₂²×C₁₁

C₂×D₁₆

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

#486

yes

characteristic

C₄×C₁₁

C₂×SD₃₂

yes

characteristic

Dic₁₁

—

Dic₁₁

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

#125

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

D₄₄

yes

characteristic

C₂×C₁₆

C₂²×D₁₁

yes

characteristic

#107

—

#106

—

C₄×C₈

D₄₄

yes

characteristic

C₃₂

—

C₂×C₁₁

#2240

yes

characteristic

C₂×C₁₁

#2264

yes

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₈₈

yes

characteristic

C₂×C₈

C₂×D₄₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₈₈

yes

characteristic

C₁₆

#4314

yes

—

C₁₆

#4339

yes

—

C₁₁

#13724

yes

characteristic, complemented, Sylow

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₇₆

yes

—

C₂×C₄

C₂×D₈₈

yes

characteristic

C₈

#66864

yes

—

C₈

#66928

yes

characteristic

100

C₈

C₂×#4314

yes

characteristic

101

C₂²

C₂×D₁₇₆

yes

characteristic

102

C₄

—

103

C₄

—

176

—

104

C₄

—

176

—

105

C₄

#10622307

yes

characteristic

106

C₄

C₂×#66864

yes

characteristic

107

C₂

#13070840

yes

characteristic

108

C₂

#13070936

yes

—

	subgroup	G/H
center	C₂²	C₂×D₁₇₆
commutator, cosocle	C₂×C₁₁×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₁₁×#1397	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₁₆
hypercenter	#1397	D₁₁
hypocenter	C₁₁	#13724
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₂²

C₂×D₁₇₆

commutator, cosocle

C₂×C₁₁×C₁₆

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₁

Fitting

C₁₁×#1397

C₂

socle, prime radical

C₂²×C₁₁

C₂×D₁₆

D₁₁

C₁₁

G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
91. C₁₁	#13724	semidirect

H ≅ G/N

type

91. C₁₁

#13724

semidirect

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

subgroup	index
#13070895	2
#13070869	2
#13066798	2
C₁₁×#1397	2
#13724	11

subgroup

index

C₁₁×#1397

Subgroups — #14674764

Conjugacy classes of subgroups

Complements

Maximal subgroups