Group #20290641 — subgroups

Subgroups — #20290641

Order 6784.

180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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	#16811628	C₂	1	1	yes	maximal, characteristic
2	#16811627	C₂	1	1	yes	maximal, characteristic
3	#16811499	C₂	1	4	yes	maximal
4	#97×D₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11719936	C₂²	1	2	yes	—
6	C₂×#11719936	C₂²	1	2	yes	—
7	#13133284	—	2	2	no	—
8	C₄⋊#88324	—	2	2	no	—
9	C₂×C₈×D₅₃	C₂²	1	2	yes	—
10	C₄²×D₅₃	C₂²	1	1	yes	characteristic
11	#13133128	C₄	1	1	yes	characteristic
12	#13133127	C₄	1	2	yes	—
13	#97×C₅₃	C₄	1	1	yes	characteristic
14	C₂×C₄×D₅₃	Q₈	1	2	yes	—
15	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
16	C₂×#88324	—	2	2	no	—
17	C₂×#88324	—	2	2	no	—
18	#11719936	—	2	4	no	—
19	#11719936	—	2	4	no	—
20	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
21	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₅₃	D₄	1	2	yes	—
24	C₂×#88322	C₂×C₄	1	2	yes	—
25	C₈×D₅₃	—	2	2	no	—
26	C₈×D₅₃	—	2	2	no	—
27	C₂²×D₅₃	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₅₃	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
32	C₄×D₅₃	—	4	2	no	—
33	C₄×D₅₃	#41	1	2	yes	—
34	C₄×D₅₃	#41	1	2	yes	—
35	#88324	—	4	2	no	—
36	#88324	—	4	2	no	—
37	C₈×C₅₃	—	2	2	no	—
38	#88322	—	2	2	no	—
39	C₂²×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×D₅₃	—	2	2	no	—
41	C₂×D₅₃	#125	1	2	yes	—
42	C₄×C₅₃	—	2	2	no	—
43	C₄×C₅₃	#117	1	2	yes	—
44	Dic₅₃	—	2	2	no	—
45	Dic₅₃	#124	1	1	yes	characteristic
46	Dic₅₃	#124	1	1	yes	characteristic
47	#1838	—	53	1	no	maximal, Sylow
48	C₂×C₅₃	#382	1	1	yes	characteristic
49	C₂×C₅₃	#430	1	2	yes	—
50	D₅₃	—	2	2	no	—
51	#423	—	53	1	no	—
52	#423	—	53	1	no	—
53	C₂×#97	—	53	1	no	—
54	#341	—	53	4	no	—
55	C₅₃	#1838	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	—	53	2	no	—
57	C₂×M₁₆	—	53	2	no	—
58	C₂²×C₈	—	53	2	no	—
59	C₂×C₄²	—	53	1	no	—
60	C₄⋊C₈	—	106	2	no	—
61	C₄⋊C₈	—	106	2	no	—
62	#97	—	53	2	no	—
63	#97	—	53	1	no	—
64	#97	#6157	1	1	yes	characteristic
65	C₂²×C₄	—	53	1	no	—
66	C₂²×C₄	—	53	2	no	—
67	M₁₆	—	106	4	no	—
68	M₁₆	—	106	4	no	—
69	C₂×C₈	—	53	2	no	—
70	C₂×C₈	—	106	2	no	—
71	C₂×C₈	—	106	2	no	—
72	C₂×C₈	—	106	2	no	—
73	C₂×C₈	—	106	2	no	—
74	C₂×C₈	C₂×#6157	1	2	yes	—
75	C₄²	—	53	2	no	—
76	C₄²	—	53	1	no	—
77	C₄²	C₂×#6157	1	1	yes	characteristic
78	C₂³	—	53	1	no	—
79	C₂×C₄	—	53	1	no	—
80	C₂×C₄	—	53	2	no	—
81	C₂×C₄	—	53	2	no	—
82	C₂×C₄	—	53	2	no	—
83	C₂×C₄	—	212	2	no	—
84	C₂×C₄	C₄⋊#6157	1	2	yes	—
85	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	106	2	no	—
88	C₈	—	212	2	no	—
89	C₈	—	212	2	no	—
90	C₂²	—	53	2	no	—
91	C₂²	—	106	2	no	—
92	C₂²	C₂×C₄⋊#6157	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	53	1	no	—
95	C₄	—	53	1	no	—
96	C₄	—	106	2	no	—
97	C₄	#13133296	1	2	yes	—
98	C₂	—	106	2	no	—
99	C₂	#16811567	1	1	yes	characteristic
100	C₂	#16811638	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16811628

C₂

yes

maximal, characteristic

#16811627

C₂

yes

maximal, characteristic

#16811499

C₂

yes

maximal

#97×D₅₃

C₂

yes

maximal, characteristic

C₂×#11719936

C₂²

yes

—

C₂×#11719936

C₂²

yes

—

#13133284

—

C₄⋊#88324

—

C₂×C₈×D₅₃

C₂²

yes

—

C₄²×D₅₃

C₂²

yes

characteristic

#13133128

C₄

yes

characteristic

#13133127

C₄

yes

—

#97×C₅₃

C₄

yes

characteristic

C₂×C₄×D₅₃

Q₈

yes

—

C₂×C₄×D₅₃

C₂³

yes

—

—

—

—

C₂×C₈×C₅₃

C₂×C₄

yes

—

C₄²×C₅₃

C₂×C₄

yes

characteristic

C₄×Dic₅₃

C₂×C₄

yes

characteristic

C₄×Dic₅₃

D₄

yes

—

C₂×#88322

C₂×C₄

yes

—

C₈×D₅₃

—

C₈×D₅₃

—

C₂²×D₅₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₃

C₄⋊C₄

yes

—

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×Dic₅₃

C₄⋊C₄

yes

—

C₂×Dic₅₃

C₂×D₄

yes

characteristic

C₄×D₅₃

—

C₄×D₅₃

#41

yes

—

C₄×D₅₃

#41

yes

—

#88324

—

#88324

—

C₈×C₅₃

—

#88322

—

C₂²×C₅₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₅₃

—

C₂×D₅₃

#125

yes

—

C₄×C₅₃

—

C₄×C₅₃

#117

yes

—

Dic₅₃

—

Dic₅₃

yes

Dic₅₃

yes

—

C₂×C₅₃

yes

C₂×C₅₃

yes

—

D₅₃

—

#423

—

#423

—

C₂×#97

—

#341

—

C₅₃

#1838

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

106

—

C₄⋊C₈

—

106

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

106

—

M₁₆

—

106

—

C₂×C₈

—

C₂×C₈

—

106

—

C₂×C₈

—

106

—

C₂×C₈

—

106

—

C₂×C₈

—

106

—

C₂×C₈

C₂×#6157

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#6157

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

212

—

C₂×C₄

C₄⋊#6157

yes

—

C₂×C₄

C₂²×#6157

yes

characteristic

C₈

—

C₈

—

106

—

C₈

—

212

—

C₈

—

212

—

C₂²

—

C₂²

—

106

—

C₂²

C₂×C₄⋊#6157

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

106

—

C₄

#13133296

yes

—

C₂

—

106

—

C₂

#16811567

yes

characteristic

100

C₂

#16811638

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6157
commutator	C₂×C₄×C₅₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6157
Fitting	#97×C₅₃	C₄
socle	C₂²×C₅₃	C₂×C₄⋊C₄
hypercenter	#97	#6157
hypocenter	C₅₃	#1838
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#6157

commutator

C₂×C₄×C₅₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6157

Fitting

#97×C₅₃

C₄

socle

C₂²×C₅₃

C₂×C₄⋊C₄

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
55. C₅₃	#1838	semidirect

H ≅ G/N

type

55. C₅₃

#1838

semidirect

Subgroups — #20290641

Conjugacy classes of subgroups

Complements