Group #20276932 — subgroups

Subgroups — #20276932

Order 6784.

124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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	#16810672	C₂	1	1	yes	maximal, characteristic
2	#16810445	C₂	1	2	yes	maximal, complemented
3	#16810439	C₂	1	2	yes	maximal, complemented
4	#16810405	C₂	1	1	yes	maximal, characteristic
5	C₅₃×#470	C₂	1	1	yes	maximal, characteristic
6	C₂×#11719917	—	2	1	no	—
7	#13133157	C₂²	1	2	yes	—
8	#13133153	—	2	1	no	—
9	#13133153	C₂²	1	2	yes	—
10	C₂×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
12	C₂²⋊Q₈×C₅₃	—	2	1	no	—
13	#106×C₅₃	C₂²	1	1	yes	characteristic
14	#103×C₅₃	—	2	1	no	—
15	C₂×Q₈×C₅₃	—	2	1	no	—
16	C₂²×C₄×C₅₃	D₄	1	1	yes	characteristic
17	Q₁₆×C₅₃	—	2	2	no	—
18	M₁₆×C₅₃	—	2	2	no	—
19	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₅₃	—	2	1	no	—
22	C₄⋊C₄×C₅₃	—	4	1	no	—
23	C₂²⋊C₄×C₅₃	—	4	1	no	—
24	#11719917	—	2	2	no	—
25	#11719917	—	4	1	no	—
26	C₂×#88322	—	4	1	no	—
27	#11719908	—	2	2	no	—
28	C₂³×C₅₃	SD₁₆	1	1	yes	characteristic
29	Q₈×C₅₃	—	4	1	no	—
30	Q₈×C₅₃	—	4	1	no	—
31	C₂×C₄×C₅₃	—	2	1	no	—
32	C₂×C₄×C₅₃	—	2	1	no	—
33	C₂×C₄×C₅₃	—	4	1	no	—
34	C₂×C₄×C₅₃	—	4	1	no	—
35	C₂×C₄×C₅₃	SD₁₆	1	1	yes	characteristic
36	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
37	C₈×C₅₃	—	2	1	no	—
38	C₈×C₅₃	#41	1	2	yes	—
39	#88322	—	4	2	no	—
40	C₂²×C₅₃	—	2	1	no	—
41	C₂²×C₅₃	—	4	1	no	—
42	C₂²×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
43	C₄×C₅₃	—	2	1	no	—
44	C₄×C₅₃	—	8	1	no	—
45	C₄×C₅₃	—	8	1	no	—
46	C₄×C₅₃	#123	1	1	yes	characteristic
47	C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
48	#2239	—	53	1	no	maximal, Sylow
49	C₂×C₅₃	—	2	1	no	—
50	C₂×C₅₃	—	4	1	no	—
51	C₂×C₅₃	#481	1	1	yes	characteristic
52	#470	D₅₃	1	1	yes	characteristic
53	#430	—	53	1	no	—
54	#365	—	53	2	no	—
55	#362	—	53	2	no	—
56	#349	—	53	1	no	—
57	C₅₃	#2239	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	C₂×D₅₃	1	1	yes	characteristic
59	C₂×M₁₆	—	106	1	no	—
60	C₂×M₁₆	C₂×D₅₃	1	1	yes	characteristic
61	C₂²⋊Q₈	—	2	1	no	—
62	M₃₂	—	53	2	no	—
63	#108	—	53	2	no	—
64	#108	—	106	1	no	—
65	#106	C₂×D₅₃	1	1	yes	characteristic
66	#103	—	2	1	no	—
67	C₂×Q₈	—	2	1	no	—
68	C₂²×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
69	Q₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	106	2	no	—
72	M₁₆	—	212	1	no	—
73	C₂×C₈	—	212	1	no	—
74	C₂×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
76	C₄⋊C₄	—	2	1	no	—
77	C₄⋊C₄	—	4	1	no	—
78	C₂²⋊C₄	—	4	1	no	—
79	C₁₆	—	106	2	no	—
80	C₂³	#11719923	1	1	yes	characteristic
81	Q₈	—	4	1	no	—
82	Q₈	—	4	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	#11719923	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	212	2	no	—
91	C₈	#11719947	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#11719923	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	8	1	no	—
97	C₄	—	8	1	no	—
98	C₄	#13133198	1	1	yes	characteristic
99	C₄	#13133242	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#16810939	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16810672

C₂

yes

maximal, characteristic

#16810445

C₂

yes

maximal, complemented

#16810439

C₂

yes

maximal, complemented

#16810405

C₂

yes

maximal, characteristic

C₅₃×#470

C₂

yes

maximal, characteristic

C₂×#11719917

—

#13133157

C₂²

yes

—

#13133153

—

#13133153

C₂²

yes

—

C₂×Q₁₆×C₅₃

C₂²

yes

characteristic

C₂×M₁₆×C₅₃

C₂²

yes

characteristic

C₂²⋊Q₈×C₅₃

—

#106×C₅₃

C₂²

yes

characteristic

#103×C₅₃

—

C₂×Q₈×C₅₃

—

C₂²×C₄×C₅₃

D₄

yes

characteristic

Q₁₆×C₅₃

—

M₁₆×C₅₃

—

C₂×C₈×C₅₃

D₄

yes

characteristic

C₂×C₈×C₅₃

C₂³

yes

characteristic

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

—

—

—

—

C₂³×C₅₃

SD₁₆

yes

characteristic

Q₈×C₅₃

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

SD₁₆

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₈×C₅₃

—

C₈×C₅₃

#41

yes

—

#88322

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

C₂×SD₁₆

yes

characteristic

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

yes

C₄×C₅₃

yes

—

C₂×C₅₃

—

C₂×C₅₃

—

C₂×C₅₃

#481

yes

characteristic

#470

D₅₃

yes

—

—

—

—

C₅₃

#2239

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₅₃

yes

characteristic

C₂×M₁₆

—

106

—

C₂×M₁₆

C₂×D₅₃

yes

characteristic

C₂²⋊Q₈

—

M₃₂

—

#108

—

#108

—

106

—

#106

C₂×D₅₃

yes

characteristic

#103

—

C₂×Q₈

—

C₂²×C₄

C₂²⋊D₅₃

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

106

—

M₁₆

—

212

—

C₂×C₈

—

212

—

C₂×C₈

C₂²⋊D₅₃

yes

characteristic

C₂×C₈

C₂²×D₅₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

106

—

C₂³

#11719923

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#11719923

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

C₈

—

C₈

—

212

—

C₈

#11719947

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11719923

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#16810939

yes

characteristic

	subgroup	G/H
center	C₂	#16810939
commutator	C₂×C₈×C₅₃	C₂³
Frattini	C₂×C₈	C₂²×D₅₃
Fitting	C₅₃×#470	C₂
socle	C₂×C₅₃	#481
hypercenter	#470	D₅₃
hypocenter	C₅₃	#2239
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

subgroup

G/H

center

C₂

#16810939

commutator

C₂×C₈×C₅₃

C₂³

Frattini

C₂×C₈

C₂²×D₅₃

Fitting

C₅₃×#470

C₂

C₂×C₅₃

D₅₃

C₅₃

G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

N	H ≅ G/N	type
2. #16810445	C₂	semidirect
3. #16810439	C₂	semidirect
57. C₅₃	#2239	semidirect

H ≅ G/N

type

2. #16810445

C₂

semidirect

3. #16810439

C₂

semidirect

57. C₅₃

#2239

semidirect

Subgroups — #20276932

Conjugacy classes of subgroups

Complements