Group #20289690 — subgroups

Subgroups — #20289690

Order 6784.

110 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 26 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	#16811520	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811492	C₂	1	1	yes	maximal, characteristic, complemented
3	#16810877	C₂	1	1	yes	maximal, characteristic
4	D₅₃⋊M₁₆	—	2	1	no	—
5	#13133291	—	2	1	no	—
6	C₂×D₄₂₄	C₄	1	1	yes	characteristic
7	C₂×#11719912	C₂²	1	1	yes	characteristic
8	#13133192	—	2	1	no	—
9	#13133137	—	2	1	no	—
10	#106×C₅₃	C₄	1	1	yes	characteristic
11	C₂×D₂₁₂	—	2	1	no	—
12	C₂×D₂₁₂	—	4	1	no	—
13	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
14	#11719940	—	4	1	no	—
15	#11719936	—	4	1	no	—
16	D₅₃⋊C₈	—	2	2	no	—
17	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
18	C₄⋊C₄×C₅₃	—	2	1	no	—
19	#11719921	—	4	1	no	—
20	C₂×#88322	D₄	1	1	yes	characteristic
21	D₄₂₄	—	4	1	no	—
22	#11719912	—	4	1	no	—
23	#11719910	—	4	1	no	—
24	C₂²×D₅₃	—	4	1	no	—
25	C₂²×D₅₃	SD₁₆	1	1	yes	characteristic
26	C₂×C₄×C₅₃	—	4	1	no	—
27	C₂×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₅₃	D₈	1	1	yes	characteristic
29	D₂₁₂	—	4	1	no	—
30	D₂₁₂	—	4	1	no	—
31	D₂₁₂	—	8	2	no	—
32	C₄×D₅₃	—	2	1	no	—
33	C₄×D₅₃	—	2	1	no	—
34	#88324	—	4	2	no	—
35	C₈×C₅₃	—	2	1	no	—
36	#88322	—	2	1	no	—
37	C₂²×C₅₃	#102	1	1	yes	characteristic
38	C₂×D₅₃	—	2	1	no	—
39	C₂×D₅₃	—	4	1	no	—
40	C₂×D₅₃	—	8	1	no	—
41	C₂×D₅₃	—	8	1	no	—
42	C₂×D₅₃	—	8	1	no	—
43	C₄×C₅₃	—	8	1	no	—
44	C₄×C₅₃	#99	1	1	yes	characteristic
45	C₄×C₅₃	#104	1	1	yes	characteristic
46	Dic₅₃	—	2	1	no	—
47	#1341	—	53	1	no	maximal, Sylow
48	C₂×C₅₃	—	2	1	no	—
49	C₂×C₅₃	#327	1	1	yes	characteristic
50	D₅₃	—	4	1	no	—
51	D₅₃	—	16	1	no	—
52	#469	—	53	1	no	—
53	#349	—	53	1	no	—
54	#338	—	53	1	no	—
55	C₅₃	#1341	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	53	1	no	—
57	C₂×M₁₆	—	53	1	no	—
58	C₂×M₁₆	—	106	1	no	—
59	#121	—	106	1	no	—
60	M₃₂	—	106	1	no	—
61	#106	#6157	1	1	yes	characteristic
62	#102	—	106	1	no	—
63	C₂×D₄	—	106	1	no	—
64	C₂×D₄	—	212	1	no	—
65	C₂²×C₄	—	53	1	no	—
66	D₈	—	212	1	no	—
67	M₁₆	—	212	1	no	—
68	M₁₆	—	212	1	no	—
69	M₁₆	—	212	1	no	—
70	C₂×C₈	—	53	1	no	—
71	C₂×C₈	—	106	2	no	—
72	C₂×C₈	C₂×#6157	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₂²⋊C₄	—	212	1	no	—
75	C₁₆	—	212	1	no	—
76	C₂³	—	53	1	no	—
77	C₂³	—	212	1	no	—
78	D₄	—	424	2	no	—
79	D₄	—	212	1	no	—
80	D₄	—	212	1	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	—	53	1	no	—
83	C₂×C₄	—	106	1	no	—
84	C₂×C₄	—	106	1	no	—
85	C₂×C₄	C₂²⋊#6157	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	106	1	no	—
88	C₈	—	212	2	no	—
89	C₂²	—	106	1	no	—
90	C₂²	—	424	1	no	—
91	C₂²	—	424	1	no	—
92	C₂²	—	424	1	no	—
93	C₂²	—	212	1	no	—
94	C₂²	#13133279	1	1	yes	characteristic
95	C₄	—	8	1	no	—
96	C₄	—	106	1	no	—
97	C₄	#13133276	1	1	yes	characteristic
98	C₄	#13133282	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	848	1	no	—
101	C₂	—	212	1	no	—
102	C₂	#16811475	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16811520

C₂

yes

maximal, characteristic, complemented

#16811492

C₂

yes

maximal, characteristic, complemented

#16810877

C₂

yes

maximal, characteristic

D₅₃⋊M₁₆

—

#13133291

—

C₂×D₄₂₄

C₄

yes

characteristic

C₂×#11719912

C₂²

yes

characteristic

#13133192

—

#13133137

—

#106×C₅₃

C₄

yes

characteristic

C₂×D₂₁₂

—

C₂×D₂₁₂

—

C₂×C₄×D₅₃

D₄

yes

characteristic

#11719940

—

#11719936

—

D₅₃⋊C₈

—

C₂×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₅₃

—

#11719921

—

C₂×#88322

D₄

yes

characteristic

D₄₂₄

—

#11719912

—

#11719910

—

C₂²×D₅₃

—

C₂²×D₅₃

SD₁₆

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₅₃

D₈

yes

characteristic

D₂₁₂

—

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

—

C₄×D₅₃

—

#88324

—

C₈×C₅₃

—

#88322

—

C₂²×C₅₃

#102

yes

characteristic

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₄×C₅₃

—

C₄×C₅₃

yes

C₄×C₅₃

yes

Dic₅₃

—

#1341

—

maximal, Sylow

C₂×C₅₃

—

C₂×C₅₃

#327

yes

characteristic

D₅₃

—

D₅₃

—

#469

—

#349

—

#338

—

C₅₃

#1341

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

—

106

—

#121

—

106

—

M₃₂

—

106

—

yes

—

106

—

C₂×D₄

—

106

—

C₂×D₄

—

212

—

C₂²×C₄

—

D₈

—

212

—

M₁₆

—

212

—

M₁₆

—

212

—

M₁₆

—

212

—

C₂×C₈

—

C₂×C₈

—

106

—

C₂×C₈

C₂×#6157

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

212

—

C₁₆

—

212

—

C₂³

—

C₂³

—

212

—

D₄

—

424

—

D₄

—

212

—

D₄

—

212

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

106

—

C₂×C₄

—

106

—

C₂×C₄

C₂²⋊#6157

yes

characteristic

C₈

—

C₈

—

106

—

C₈

—

212

—

C₂²

—

106

—

C₂²

—

424

—

C₂²

—

424

—

C₂²

—

424

—

C₂²

—

212

—

C₂²

#13133279

yes

characteristic

C₄

—

C₄

—

106

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

848

—

101

C₂

—

212

—

102

C₂

#16811475

yes

characteristic

	subgroup	G/H
center	C₂	#16811475
commutator	C₂×C₈×C₅₃	C₂×C₄
Frattini	C₂×C₈	C₂×#6157
Fitting	#106×C₅₃	C₄
socle	C₂×C₅₃	#327
hypercenter	#106	#6157
hypocenter	C₅₃	#1341
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

subgroup

G/H

center

C₂

#16811475

commutator

C₂×C₈×C₅₃

C₂×C₄

Frattini

C₂×C₈

C₂×#6157

Fitting

#106×C₅₃

C₄

C₂×C₅₃

C₅₃

G ▷ C₂×C₈×C₅₃ ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

N	H ≅ G/N	type
1. #16811520	C₂	semidirect
2. #16811492	C₂	semidirect
55. C₅₃	#1341	semidirect

H ≅ G/N

type

1. #16811520

C₂

semidirect

2. #16811492

C₂

semidirect

55. C₅₃

#1341

semidirect

Subgroups — #20289690

Conjugacy classes of subgroups

Complements