Group #20290215 — subgroups

Subgroups — D₅₃⋊#333 #20290215

Order 6784.

256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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	D₅₃⋊(C₄⋊C₈)	C₂	1	2	yes	maximal
2	#16811483	C₂	1	4	yes	maximal, complemented
3	C₄⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×D₅₃⋊C₈	—	2	2	no	—
5	#13133284	C₂²	1	4	yes	—
6	C₄⋊#88324	—	2	2	no	—
7	C₂×Q₈×D₅₃	C₄	1	2	yes	—
8	#13133217	C₄	1	1	yes	characteristic
9	#13133216	—	2	2	no	—
10	#13133215	C₂²	1	2	yes	—
11	C₄⋊C₄×D₅₃	—	2	2	no	—
12	C₄²×D₅₃	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×C₅₃	C₄	1	1	yes	characteristic
14	C₂×Q₈×C₅₃	C₂×C₄	1	2	yes	—
15	Q₈×D₅₃	—	4	4	no	—
16	C₂×C₄×D₅₃	—	2	2	no	—
17	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₅₃	D₄	1	2	yes	—
19	C₂×Dic₁₀₆	—	2	2	no	—
20	C₂×Dic₁₀₆	C₂×C₄	1	2	yes	—
21	C₂×#88324	—	2	4	no	—
22	D₅₃⋊C₈	—	4	4	no	—
23	C₄⋊C₄×C₅₃	—	2	2	no	—
24	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
25	C₄⋊Dic₅₃	—	2	2	no	—
26	#11719919	—	2	4	no	—
27	C₄×Dic₅₃	D₄	1	2	yes	—
28	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
29	C₂²×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
30	Q₈×C₅₃	—	4	2	no	—
31	C₂×C₄×C₅₃	—	2	2	no	—
32	C₂×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
33	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₅₃	—	2	2	no	—
35	C₂×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₅₃	C₂×D₄	1	2	yes	—
37	C₄×D₅₃	—	2	2	no	—
38	C₄×D₅₃	—	4	4	no	—
39	C₄×D₅₃	SD₁₆	1	4	yes	—
40	C₄×D₅₃	Q₁₆	1	4	yes	—
41	Dic₁₀₆	—	4	4	no	—
42	Dic₁₀₆	—	4	2	no	—
43	#88324	—	4	4	no	—
44	C₂²×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₅₃	#100	1	2	yes	—
46	C₂×D₅₃	#103	1	4	yes	—
47	C₄×C₅₃	—	2	1	no	—
48	C₄×C₅₃	—	4	2	no	—
49	C₄×C₅₃	#103	1	4	yes	—
50	Dic₅₃	—	2	1	no	—
51	Dic₅₃	—	4	2	no	—
52	Dic₅₃	C₂×SD₁₆	1	2	yes	—
53	Dic₅₃	C₂×Q₁₆	1	2	yes	—
54	C₂×#333	—	53	1	no	maximal, Sylow
55	C₂×C₅₃	C₂×#100	1	1	yes	characteristic
56	C₂×C₅₃	C₂×#103	1	2	yes	—
57	D₅₃	#333	1	4	yes	complemented
58	C₂×C₄⋊Q₈	—	53	1	no	—
59	C₂×C₄⋊C₈	—	53	2	no	—
60	#333	—	53	4	no	—
61	C₅₃	C₂×#333	1	1	yes	characteristic, complemented, Sylow
62	C₂²×Q₈	—	53	2	no	—
63	C₂²×C₈	—	106	2	no	—
64	C₄⋊Q₈	—	53	2	no	—
65	C₄⋊Q₈	—	53	1	no	—
66	C₄⋊Q₈	—	106	2	no	—
67	C₄⋊Q₈	#6157	1	1	yes	characteristic
68	C₂×C₄⋊C₄	—	106	2	no	—
69	C₂×C₄²	—	53	1	no	—
70	C₄⋊C₈	—	53	4	no	—
71	C₄⋊C₈	—	106	2	no	—
72	C₂×Q₈	—	53	2	no	—
73	C₂×Q₈	—	106	2	no	—
74	C₂×Q₈	—	212	4	no	—
75	C₂×Q₈	C₂×#6157	1	2	yes	—
76	C₂²×C₄	—	53	2	no	—
77	C₂²×C₄	—	53	1	no	—
78	C₂²×C₄	—	106	2	no	—
79	C₂×C₈	—	106	4	no	—
80	C₂×C₈	—	212	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	106	4	no	—
83	C₄⋊C₄	—	106	2	no	—
84	C₄²	—	53	2	no	—
85	C₄²	—	53	1	no	—
86	C₄²	C₂×#6157	1	1	yes	characteristic
87	C₂³	—	53	1	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	212	2	no	—
90	Q₈	—	212	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	53	2	no	—
93	C₂×C₄	—	53	4	no	—
94	C₂×C₄	—	53	4	no	—
95	C₂×C₄	—	53	1	no	—
96	C₂×C₄	—	106	2	no	—
97	C₂×C₄	—	106	2	no	—
98	C₂×C₄	—	212	4	no	—
99	C₂×C₄	C₂²⋊#6157	1	2	yes	—
100	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
101	C₈	—	212	4	no	—
102	C₂²	—	53	2	no	—
103	C₂²	—	53	4	no	—
104	C₂²	C₂×C₂²⋊#6157	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	4	2	no	—
107	C₄	—	53	2	no	—
108	C₄	—	53	2	no	—
109	C₄	—	106	1	no	—
110	C₄	—	212	2	no	—
111	C₄	#13133280	1	4	yes	—
112	C₂	—	53	4	no	—
113	C₂	D₅₃⋊#100	1	1	yes	characteristic
114	C₂	C₂×#13133280	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

D₅₃⋊(C₄⋊C₈)

C₂

yes

maximal

#16811483

C₂

yes

maximal, complemented

C₄⋊Q₈×D₅₃

C₂

yes

maximal, characteristic

C₂×D₅₃⋊C₈

—

#13133284

C₂²

yes

—

C₄⋊#88324

—

C₂×Q₈×D₅₃

C₄

yes

—

#13133217

C₄

yes

characteristic

#13133216

—

#13133215

C₂²

yes

—

C₄⋊C₄×D₅₃

—

C₄²×D₅₃

C₂²

yes

characteristic

C₄⋊Q₈×C₅₃

C₄

yes

characteristic

C₂×Q₈×C₅₃

C₂×C₄

yes

—

Q₈×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

C₂×C₄

yes

characteristic

C₂×C₄×D₅₃

D₄

yes

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

C₂×C₄

yes

—

C₂×#88324

—

D₅₃⋊C₈

—

C₄⋊C₄×C₅₃

—

C₄²×C₅₃

C₂×C₄

yes

characteristic

C₄⋊Dic₅₃

—

#11719919

—

C₄×Dic₅₃

D₄

yes

—

C₄×Dic₅₃

C₂³

yes

characteristic

C₂²×D₅₃

C₂²⋊C₄

yes

characteristic

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂²⋊C₄

yes

—

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₅₃

C₂×D₄

yes

—

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

SD₁₆

yes

—

C₄×D₅₃

Q₁₆

yes

—

Dic₁₀₆

—

Dic₁₀₆

—

#88324

—

C₂²×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₅₃

#100

yes

—

C₂×D₅₃

#103

yes

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

#103

yes

—

Dic₅₃

—

Dic₅₃

—

Dic₅₃

C₂×SD₁₆

yes

—

Dic₅₃

C₂×Q₁₆

yes

—

—

C₂×C₅₃

yes

C₂×C₅₃

yes

—

D₅₃

#333

yes

complemented

C₂×C₄⋊Q₈

—

C₂×C₄⋊C₈

—

#333

—

C₅₃

C₂×#333

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

106

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

106

—

C₄⋊Q₈

#6157

yes

characteristic

C₂×C₄⋊C₄

—

106

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

106

—

C₂×Q₈

—

C₂×Q₈

—

106

—

C₂×Q₈

—

212

—

C₂×Q₈

C₂×#6157

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

106

—

C₂×C₈

—

106

—

C₂×C₈

—

212

—

C₄⋊C₄

—

C₄⋊C₄

—

106

—

C₄⋊C₄

—

106

—

C₄²

—

C₄²

—

C₄²

C₂×#6157

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

212

—

Q₈

—

212

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

106

—

C₂×C₄

—

106

—

C₂×C₄

—

212

—

C₂×C₄

C₂²⋊#6157

yes

—

100

C₂×C₄

C₂²×#6157

yes

characteristic

101

C₈

—

212

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊#6157

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

106

—

110

C₄

—

212

—

111

C₄

#13133280

yes

—

112

C₂

—

113

C₂

D₅₃⋊#100

yes

characteristic

114

C₂

C₂×#13133280

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#6157
commutator	C₂×C₄×C₅₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6157
Fitting	C₄⋊Q₈×C₅₃	C₄
socle	C₂²×C₅₃	C₂×C₂²⋊C₄
hypercenter	C₄⋊Q₈	#6157
hypocenter	C₅₃	C₂×#333
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊#6157

commutator

C₂×C₄×C₅₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6157

Fitting

C₄⋊Q₈×C₅₃

C₄

socle

C₂²×C₅₃

C₂×C₂²⋊C₄

C₄⋊Q₈

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
2. #16811483	C₂	semidirect
57. D₅₃	#333	semidirect
61. C₅₃	C₂×#333	semidirect

H ≅ G/N

type

2. #16811483

C₂

semidirect

57. D₅₃

#333

semidirect

61. C₅₃

C₂×#333

semidirect

Subgroups — D₅₃⋊#333 #20290215

Conjugacy classes of subgroups

Complements

Subgroups — D53⋊#333 #20290215

Conjugacy classes of subgroups

Complements

Subgroups — D₅₃⋊#333 #20290215