Group #46782873 — subgroups

Subgroups — #46782873

Order 33664.

248 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 109 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×C₈×Dic₂₆₃	C₂	1	1	yes	maximal, characteristic
2	#30681807	C₂	1	2	yes	maximal
3	#30681701	C₂	1	1	yes	maximal, characteristic
4	#30681700	C₂	1	2	yes	maximal
5	#340×C₂₆₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₂₆₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₂₆₃	C₂²	1	2	yes	—
8	C₂×Dic₂₆₃⋊C₄	—	2	2	no	—
9	C₂×Dic₂₆₃⋊C₄	—	2	2	no	—
10	C₂×C₄×Dic₂₆₃	C₂²	1	1	yes	characteristic
11	C₈×Dic₂₆₃	C₄	1	4	yes	complemented
12	C₂²×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₂₆₃	C₂²	1	2	yes	—
14	C₂²×Dic₂₆₃	—	2	2	no	—
15	C₂²×Dic₂₆₃	D₄	1	1	yes	characteristic
16	C₂²×Dic₂₆₃	D₄	1	1	yes	characteristic
17	C₂×C₂₆₃⋊C₈	—	2	2	no	—
18	C₂×C₂₆₃⋊C₈	C₂×C₄	1	2	yes	—
19	C₄⋊Dic₂₆₃	—	2	2	no	—
20	C₄⋊Dic₂₆₃	—	2	2	no	—
21	Dic₂₆₃⋊C₄	—	4	4	no	—
22	Dic₂₆₃⋊C₄	—	4	4	no	—
23	C₄×Dic₂₆₃	C₂×C₄	1	2	yes	—
24	C₄×Dic₂₆₃	Q₈	1	2	yes	—
25	C₂²×C₄×C₂₆₃	—	2	2	no	—
26	C₂²×C₄×C₂₆₃	C₂³	1	1	yes	characteristic
27	C₂×C₈×C₂₆₃	—	2	2	no	—
28	C₂×C₈×C₂₆₃	C₂×C₄	1	2	yes	—
29	C₄⋊C₄×C₂₆₃	—	2	2	no	—
30	C₄⋊C₄×C₂₆₃	—	2	2	no	—
31	C₂×Dic₂₆₃	—	4	2	no	—
32	C₂×Dic₂₆₃	—	4	2	no	—
33	C₂×Dic₂₆₃	—	4	2	no	—
34	C₂×Dic₂₆₃	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₂₆₃	C₄⋊C₄	1	2	yes	—
36	C₂×Dic₂₆₃	D₈	1	2	yes	—
37	C₂×Dic₂₆₃	SD₁₆	1	4	yes	—
38	C₂×Dic₂₆₃	Q₁₆	1	2	yes	—
39	C₂₆₃⋊C₈	—	2	2	no	—
40	C₂³×C₂₆₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₂₆₃	—	4	2	no	—
42	C₂×C₄×C₂₆₃	—	4	2	no	—
43	C₂×C₄×C₂₆₃	—	4	2	no	—
44	C₂×C₄×C₂₆₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₂₆₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₂₆₃	#41	1	2	yes	—
47	C₂×C₄×C₂₆₃	#41	1	2	yes	—
48	C₈×C₂₆₃	—	2	2	no	—
49	C₂²×C₂₆₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₂₆₃	#124	1	2	yes	—
51	C₂²×C₂₆₃	C₂×D₈	1	1	yes	characteristic
52	C₂²×C₂₆₃	C₂×SD₁₆	1	2	yes	—
53	C₂²×C₂₆₃	C₂×Q₁₆	1	1	yes	characteristic
54	C₄×C₂₆₃	—	8	2	no	—
55	C₄×C₂₆₃	#117	1	1	yes	characteristic
56	C₄×C₂₆₃	#117	1	1	yes	characteristic
57	C₄×C₂₆₃	#125	1	2	yes	—
58	Dic₂₆₃	—	8	2	no	—
59	Dic₂₆₃	#106	1	4	yes	—
60	Dic₂₆₃	#107	1	4	yes	—
61	C₂×C₂₆₃	#382	1	1	yes	characteristic
62	C₂×C₂₆₃	C₂×#106	1	1	yes	characteristic
63	C₂×C₂₆₃	C₂×#107	1	1	yes	characteristic
64	C₂×C₂₆₃	#486	1	2	yes	—
65	C₂×C₂₆₃	#487	1	2	yes	—
66	C₂₆₃	#1834	1	1	yes	characteristic, complemented, Sylow
67	#1834	—	263	1	no	maximal, Sylow
68	C₂×C₄×C₈	—	263	1	no	—
69	#384	—	263	2	no	—
70	#340	—	263	1	no	—
71	#340	—	263	2	no	—
72	#340	D₂₆₃	1	1	yes	characteristic
73	C₂²×C₈	—	263	1	no	—
74	C₂²×C₈	C₂×D₂₆₃	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	263	2	no	—
76	C₂×C₄⋊C₄	—	526	2	no	—
77	C₂×C₄⋊C₄	—	526	2	no	—
78	C₂×C₄⋊C₄	C₂×D₂₆₃	1	2	yes	—
79	C₂×C₄²	—	263	1	no	—
80	C₄×C₈	—	263	4	no	—
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	—	263	1	no	—
83	C₂²×C₄	—	263	1	no	—
84	C₂²×C₄	—	526	2	no	—
85	C₂²×C₄	C₂²×D₂₆₃	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	263	2	no	—
88	C₂×C₈	—	526	2	no	—
89	C₂×C₈	C₄×D₂₆₃	1	2	yes	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	526	2	no	—
93	C₄⋊C₄	—	526	2	no	—
94	C₄⋊C₄	—	1052	4	no	—
95	C₄⋊C₄	—	1052	4	no	—
96	C₄²	—	263	2	no	—
97	C₄²	—	263	2	no	—
98	C₂³	D₄×D₂₆₃	1	1	yes	characteristic
99	C₂×C₄	—	4	2	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	263	2	no	—
103	C₂×C₄	—	263	2	no	—
104	C₂×C₄	—	263	2	no	—
105	C₂×C₄	—	263	4	no	—
106	C₂×C₄	—	263	2	no	—
107	C₂×C₄	—	1052	2	no	—
108	C₂×C₄	—	1052	2	no	—
109	C₂×C₄	—	1052	2	no	—
110	C₂×C₄	C₂×C₄×D₂₆₃	1	1	yes	characteristic
111	C₂×C₄	Q₈×D₂₆₃	1	1	yes	characteristic
112	C₂×C₄	#16862375	1	2	yes	—
113	C₂×C₄	#16862376	1	2	yes	—
114	C₈	—	2	2	no	—
115	C₈	—	526	2	no	—
116	C₂²	C₄⋊C₄×D₂₆₃	1	1	yes	characteristic
117	C₂²	#22554456	1	2	yes	—
118	C₂²	D₈×D₂₆₃	1	1	yes	characteristic
119	C₂²	SD₁₆×D₂₆₃	1	2	yes	—
120	C₂²	Q₁₆×D₂₆₃	1	1	yes	characteristic
121	C₄	—	263	4	no	—
122	C₄	—	263	4	no	—
123	C₄	—	8	2	no	—
124	C₄	—	2104	2	no	—
125	C₄	#22554426	1	1	yes	characteristic
126	C₄	#22554427	1	1	yes	characteristic
127	C₄	#22554460	1	2	yes	—
128	C₂	#30681802	1	1	yes	characteristic
129	C₂	#106×D₂₆₃	1	1	yes	characteristic
130	C₂	#107×D₂₆₃	1	1	yes	characteristic
131	C₂	#30682283	1	2	yes	—
132	C₂	#30682287	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₂₆₃

C₂

yes

maximal, characteristic

#30681807

C₂

yes

maximal

#30681701

C₂

yes

maximal, characteristic

#30681700

C₂

yes

maximal

#340×C₂₆₃

C₂

yes

maximal, characteristic

C₂²×C₂₆₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₆₃

C₂²

yes

—

C₂×Dic₂₆₃⋊C₄

—

C₂×Dic₂₆₃⋊C₄

—

C₂×C₄×Dic₂₆₃

C₂²

yes

characteristic

C₈×Dic₂₆₃

C₄

yes

complemented

C₂²×C₈×C₂₆₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₂₆₃

C₂²

yes

—

C₂²×Dic₂₆₃

—

C₂²×Dic₂₆₃

D₄

yes

characteristic

C₂²×Dic₂₆₃

D₄

yes

characteristic

C₂×C₂₆₃⋊C₈

—

C₂×C₂₆₃⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₂₆₃

—

C₄⋊Dic₂₆₃

—

Dic₂₆₃⋊C₄

—

Dic₂₆₃⋊C₄

—

C₄×Dic₂₆₃

C₂×C₄

yes

—

C₄×Dic₂₆₃

Q₈

yes

—

C₂²×C₄×C₂₆₃

—

C₂²×C₄×C₂₆₃

C₂³

yes

characteristic

C₂×C₈×C₂₆₃

—

C₂×C₈×C₂₆₃

C₂×C₄

yes

—

C₄⋊C₄×C₂₆₃

—

C₄⋊C₄×C₂₆₃

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

C₄⋊C₄

yes

—

C₂×Dic₂₆₃

C₄⋊C₄

yes

—

C₂×Dic₂₆₃

D₈

yes

—

C₂×Dic₂₆₃

SD₁₆

yes

—

C₂×Dic₂₆₃

Q₁₆

yes

—

C₂₆₃⋊C₈

—

C₂³×C₂₆₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₆₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₆₃

#41

yes

—

C₂×C₄×C₂₆₃

#41

yes

—

C₈×C₂₆₃

—

C₂²×C₂₆₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₆₃

#124

yes

—

C₂²×C₂₆₃

C₂×D₈

yes

characteristic

C₂²×C₂₆₃

C₂×SD₁₆

yes

—

C₂²×C₂₆₃

C₂×Q₁₆

yes

characteristic

C₄×C₂₆₃

—

C₄×C₂₆₃

yes

C₄×C₂₆₃

yes

C₄×C₂₆₃

yes

—

Dic₂₆₃

—

Dic₂₆₃

#106

yes

—

Dic₂₆₃

#107

yes

—

C₂×C₂₆₃

yes

C₂×C₂₆₃

yes

C₂×C₂₆₃

yes

C₂×C₂₆₃

yes

—

C₂×C₂₆₃

#487

yes

—

C₂₆₃

#1834

yes

characteristic, complemented, Sylow

#1834

—

263

maximal, Sylow

C₂×C₄×C₈

—

263

—

#384

—

263

—

#340

—

263

—

#340

—

263

—

#340

D₂₆₃

yes

characteristic

C₂²×C₈

—

263

—

C₂²×C₈

C₂×D₂₆₃

yes

characteristic

C₂×C₄⋊C₄

—

263

—

C₂×C₄⋊C₄

—

526

—

C₂×C₄⋊C₄

—

526

—

C₂×C₄⋊C₄

C₂×D₂₆₃

yes

—

C₂×C₄²

—

263

—

C₄×C₈

—

263

—

C₂²×C₄

—

C₂²×C₄

—

263

—

C₂²×C₄

—

263

—

C₂²×C₄

—

526

—

C₂²×C₄

C₂²×D₂₆₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

263

—

C₂×C₈

—

526

—

C₂×C₈

C₄×D₂₆₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

526

—

C₄⋊C₄

—

526

—

C₄⋊C₄

—

1052

—

C₄⋊C₄

—

1052

—

C₄²

—

263

—

C₄²

—

263

—

C₂³

D₄×D₂₆₃

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

263

—

103

C₂×C₄

—

263

—

104

C₂×C₄

—

263

—

105

C₂×C₄

—

263

—

106

C₂×C₄

—

263

—

107

C₂×C₄

—

1052

—

108

C₂×C₄

—

1052

—

109

C₂×C₄

—

1052

—

110

C₂×C₄

C₂×C₄×D₂₆₃

yes

characteristic

111

C₂×C₄

Q₈×D₂₆₃

yes

characteristic

112

C₂×C₄

#16862375

yes

—

113

C₂×C₄

#16862376

yes

—

114

C₈

—

115

C₈

—

526

—

116

C₂²

C₄⋊C₄×D₂₆₃

yes

characteristic

117

C₂²

#22554456

yes

—

118

C₂²

D₈×D₂₆₃

yes

characteristic

119

C₂²

SD₁₆×D₂₆₃

yes

—

120

C₂²

Q₁₆×D₂₆₃

yes

characteristic

121

C₄

—

263

—

122

C₄

—

263

—

123

C₄

—

124

C₄

—

2104

—

125

C₄

#22554426

yes

characteristic

126

C₄

#22554427

yes

characteristic

127

C₄

#22554460

yes

—

128

C₂

#30681802

yes

characteristic

129

C₂

#106×D₂₆₃

yes

characteristic

130

C₂

#107×D₂₆₃

yes

characteristic

131

C₂

#30682283

yes

—

132

C₂

#30682287

yes

—

	subgroup	G/H
center	C₂³	D₄×D₂₆₃
commutator	C₂×C₄×C₂₆₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₆₃
Fitting	#340×C₂₆₃	C₂
socle, prime radical	C₂³×C₂₆₃	C₂×D₄
cosocle	C₂²×C₄×C₂₆₃	C₂³
hypercenter	#340	D₂₆₃
hypocenter	C₂₆₃	#1834
LCS	G ▷ C₂×C₄×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₂₆₃

commutator

C₂×C₄×C₂₆₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₆₃

Fitting

#340×C₂₆₃

C₂

socle, prime radical

C₂³×C₂₆₃

C₂×D₄

cosocle

C₂²×C₄×C₂₆₃

C₂³

D₂₆₃

C₂₆₃

G ▷ C₂×C₄×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
11. C₈×Dic₂₆₃	C₄	semidirect
66. C₂₆₃	#1834	semidirect

H ≅ G/N

type

11. C₈×Dic₂₆₃

C₄

semidirect

66. C₂₆₃

#1834

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₈×Dic₂₆₃	2
#30681807	2
#30681701	2
#30681700	2
#340×C₂₆₃	2
#1834	263

subgroup

index

C₂×C₈×Dic₂₆₃

#340×C₂₆₃

263

Subgroups — #46782873

Conjugacy classes of subgroups

Complements

Maximal subgroups