Group #20290633 — subgroups

Subgroups — #20290633

Order 6784.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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	C₂×#13133284	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#88324	C₂	1	1	yes	maximal, characteristic
3	#16811489	C₂	1	4	yes	maximal
4	#16810468	C₂	1	1	yes	maximal, characteristic
5	C₂²×#88324	C₂²	1	2	yes	—
6	C₂²×#88324	C₂²	1	2	yes	—
7	#13133284	—	2	2	no	—
8	C₄⋊#88324	—	2	2	no	—
9	C₂×C₄×Dic₅₃	C₂²	1	2	yes	—
10	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
11	#13133124	C₄	1	1	yes	characteristic
12	#13133124	C₄	1	2	yes	—
13	#95×C₅₃	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₅₃	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₅₃	C₂×C₄	1	2	yes	—
17	C₂²×Dic₅₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
19	C₂×#88324	—	2	2	no	—
20	C₂×#88324	—	2	2	no	—
21	C₂×#88324	—	2	4	no	—
22	C₂×#88324	—	2	4	no	—
23	C₄×Dic₅₃	—	2	2	no	—
24	C₄×Dic₅₃	—	2	2	no	—
25	C₄×Dic₅₃	D₄	1	2	yes	—
26	C₄×Dic₅₃	Q₈	1	2	yes	—
27	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₅₃	—	2	2	no	—
29	C₂×C₄×C₅₃	—	2	2	no	—
30	C₂×C₄×C₅₃	—	2	2	no	—
31	C₂×C₄×C₅₃	—	2	2	no	—
32	C₂×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
33	C₂×Dic₅₃	—	2	1	no	—
34	C₂×Dic₅₃	—	2	1	no	—
35	C₂×Dic₅₃	—	2	2	no	—
36	C₂×Dic₅₃	—	2	2	no	—
37	C₂×Dic₅₃	—	2	2	no	—
38	C₂×Dic₅₃	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×Dic₅₃	#41	1	2	yes	—
42	C₂×Dic₅₃	#41	1	2	yes	—
43	#88324	—	4	2	no	—
44	#88324	—	4	2	no	—
45	C₂²×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₅₃	#117	1	2	yes	—
47	C₂²×C₅₃	#131	1	2	yes	—
48	C₂²×C₅₃	#131	1	1	yes	characteristic
49	C₂²×C₅₃	#131	1	1	yes	characteristic
50	C₄×C₅₃	—	2	2	no	—
51	C₄×C₅₃	—	4	2	no	—
52	Dic₅₃	—	2	2	no	—
53	Dic₅₃	—	4	2	no	—
54	Dic₅₃	#124	1	1	yes	characteristic
55	Dic₅₃	#124	1	1	yes	characteristic
56	Dic₅₃	#125	1	2	yes	—
57	#1832	—	53	1	no	maximal, Sylow
58	C₂×C₅₃	#382	1	1	yes	characteristic
59	C₂×C₅₃	#424	1	1	yes	characteristic
60	C₂×C₅₃	#424	1	1	yes	characteristic
61	C₂×C₅₃	#433	1	2	yes	—
62	C₂×C₅₃	#433	1	2	yes	—
63	C₂×C₄⋊C₈	—	53	1	no	—
64	C₂×C₄⋊C₈	—	53	1	no	—
65	#376	—	53	1	no	—
66	#336	—	53	4	no	—
67	C₅₃	#1832	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₈	—	53	2	no	—
69	C₂²×C₈	—	53	2	no	—
70	C₂×C₄²	—	53	1	no	—
71	C₂×C₄²	—	53	2	no	—
72	C₄⋊C₈	—	106	2	no	—
73	C₄⋊C₈	—	106	2	no	—
74	#95	—	53	2	no	—
75	#95	—	53	1	no	—
76	#95	#6157	1	1	yes	characteristic
77	C₂²×C₄	—	53	1	no	—
78	C₂²×C₄	—	53	1	no	—
79	C₂²×C₄	—	53	2	no	—
80	C₂²×C₄	C₂×#6157	1	2	yes	—
81	C₂²×C₄	C₂×#6157	1	1	yes	characteristic
82	C₂×C₈	—	106	2	no	—
83	C₂×C₈	—	106	2	no	—
84	C₂×C₈	—	106	4	no	—
85	C₂×C₈	—	106	4	no	—
86	C₄²	—	53	2	no	—
87	C₄²	—	53	2	no	—
88	C₄²	—	106	2	no	—
89	C₄²	—	106	2	no	—
90	C₂³	C₂²×#6157	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	53	1	no	—
96	C₂×C₄	—	53	1	no	—
97	C₂×C₄	—	53	2	no	—
98	C₂×C₄	—	53	2	no	—
99	C₂×C₄	—	53	2	no	—
100	C₂×C₄	—	106	1	no	—
101	C₂×C₄	—	106	1	no	—
102	C₂×C₄	—	106	2	no	—
103	C₂×C₄	—	106	2	no	—
104	C₂×C₄	—	106	2	no	—
105	C₂×C₄	C₄⋊#6157	1	2	yes	—
106	C₈	—	212	2	no	—
107	C₈	—	212	2	no	—
108	C₂²	C₂×C₄⋊#6157	1	1	yes	characteristic
109	C₂²	#13133296	1	2	yes	—
110	C₂²	#13133304	1	2	yes	—
111	C₂²	#13133304	1	1	yes	characteristic
112	C₂²	#13133305	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	4	2	no	—
115	C₄	—	53	1	no	—
116	C₄	—	53	1	no	—
117	C₄	—	53	2	no	—
118	C₄	—	106	2	no	—
119	C₄	—	212	2	no	—
120	C₂	#16811567	1	1	yes	characteristic
121	C₂	#16811629	1	1	yes	characteristic
122	C₂	#16811630	1	1	yes	characteristic
123	C₂	#16811647	1	2	yes	—
124	C₂	#16811648	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13133284

C₂

yes

maximal, characteristic

C₂×C₄⋊#88324

C₂

yes

maximal, characteristic

#16811489

C₂

yes

maximal

#16810468

C₂

yes

maximal, characteristic

C₂²×#88324

C₂²

yes

—

C₂²×#88324

C₂²

yes

—

#13133284

—

C₄⋊#88324

—

C₂×C₄×Dic₅₃

C₂²

yes

—

C₂×C₄×Dic₅₃

C₂²

yes

characteristic

#13133124

C₄

yes

characteristic

#13133124

C₄

yes

—

#95×C₅₃

C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×C₄

yes

—

C₂²×C₄×C₅₃

C₂×C₄

yes

characteristic

C₂²×Dic₅₃

C₂×C₄

yes

—

C₂²×Dic₅₃

C₂×C₄

yes

characteristic

C₂²×Dic₅₃

C₂³

yes

—

—

—

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

D₄

yes

—

C₄×Dic₅₃

Q₈

yes

—

C₂³×C₅₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₄⋊C₄

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₄⋊C₄

yes

—

C₂×Dic₅₃

C₂×D₄

yes

characteristic

C₂×Dic₅₃

C₂×Q₈

yes

characteristic

C₂×Dic₅₃

#41

yes

—

C₂×Dic₅₃

#41

yes

—

#88324

—

#88324

—

C₂²×C₅₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₅₃

#117

yes

—

C₂²×C₅₃

#131

yes

—

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₄×C₅₃

—

C₄×C₅₃

—

Dic₅₃

—

Dic₅₃

—

Dic₅₃

yes

Dic₅₃

yes

Dic₅₃

yes

—

—

C₂×C₅₃

yes

C₂×C₅₃

yes

C₂×C₅₃

yes

C₂×C₅₃

yes

—

C₂×C₅₃

#433

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#376

—

#336

—

C₅₃

#1832

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

106

—

C₄⋊C₈

—

106

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6157

yes

—

C₂²×C₄

C₂×#6157

yes

characteristic

C₂×C₈

—

106

—

C₂×C₈

—

106

—

C₂×C₈

—

106

—

C₂×C₈

—

106

—

C₄²

—

C₄²

—

C₄²

—

106

—

C₄²

—

106

—

C₂³

C₂²×#6157

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

106

—

101

C₂×C₄

—

106

—

102

C₂×C₄

—

106

—

103

C₂×C₄

—

106

—

104

C₂×C₄

—

106

—

105

C₂×C₄

C₄⋊#6157

yes

—

106

C₈

—

212

—

107

C₈

—

212

—

108

C₂²

C₂×C₄⋊#6157

yes

characteristic

109

C₂²

#13133296

yes

—

110

C₂²

#13133304

yes

—

111

C₂²

#13133304

yes

characteristic

112

C₂²

#13133305

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

106

—

119

C₄

—

212

—

120

C₂

#16811567

yes

characteristic

121

C₂

#16811629

yes

characteristic

122

C₂

#16811630

yes

characteristic

123

C₂

#16811647

yes

—

124

C₂

#16811648

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#6157
commutator, socle	C₂³×C₅₃	C₂²×C₄
Fitting	#95×C₅₃	C₄
hypercenter	#95	#6157
hypocenter	C₅₃	#1832
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#6157

commutator, socle

C₂³×C₅₃

C₂²×C₄

Fitting

#95×C₅₃

C₄

C₅₃

G ▷ C₂³×C₅₃ ▷ C₅₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
67. C₅₃	#1832	semidirect

H ≅ G/N

type

67. C₅₃

#1832

semidirect

Subgroups — #20290633

Conjugacy classes of subgroups

Complements