Group #46782882 — subgroups

Subgroups — #46782882

Order 33664.

224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22554381	C₂	1	1	yes	maximal, characteristic
2	#30681804	C₂	1	1	yes	maximal, characteristic
3	#30681700	C₂	1	4	yes	maximal
4	#384×C₂₆₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₂₆₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₂₆₃	C₂²	1	2	yes	—
7	#22554381	C₄	1	4	yes	complemented
8	C₂₆₃⋊#95	—	2	2	no	—
9	C₂×C₄⋊C₄×C₂₆₃	—	2	2	no	—
10	C₂×C₄⋊C₄×C₂₆₃	C₂²	1	2	yes	—
11	C₂×C₄²×C₂₆₃	C₂²	1	1	yes	characteristic
12	C₂²×Dic₂₆₃	—	2	2	no	—
13	C₂×C₂₆₃⋊C₈	—	2	2	no	—
14	C₂×C₂₆₃⋊C₈	—	2	2	no	—
15	C₂×C₂₆₃⋊C₈	C₂×C₄	1	4	yes	—
16	C₄⋊Dic₂₆₃	—	2	4	no	—
17	C₂²×C₄×C₂₆₃	—	2	2	no	—
18	C₂²×C₄×C₂₆₃	D₄	1	2	yes	—
19	C₂²×C₄×C₂₆₃	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₂₆₃	—	2	4	no	—
21	C₄⋊C₄×C₂₆₃	—	4	4	no	—
22	C₄²×C₂₆₃	C₂×C₄	1	2	yes	—
23	C₄²×C₂₆₃	Q₈	1	2	yes	—
24	C₂×Dic₂₆₃	—	4	2	no	—
25	C₂×Dic₂₆₃	—	4	2	no	—
26	C₂×Dic₂₆₃	—	4	2	no	—
27	C₂₆₃⋊C₈	—	2	4	no	—
28	C₂³×C₂₆₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₆₃	—	2	2	no	—
30	C₂×C₄×C₂₆₃	—	2	2	no	—
31	C₂×C₄×C₂₆₃	—	4	2	no	—
32	C₂×C₄×C₂₆₃	—	4	4	no	—
33	C₂×C₄×C₂₆₃	C₄⋊C₄	1	4	yes	—
34	C₂×C₄×C₂₆₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₆₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₂₆₃	#41	1	2	yes	—
37	C₂×C₄×C₂₆₃	#41	1	2	yes	—
38	C₂²×C₂₆₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₂₆₃	#124	1	1	yes	characteristic
40	C₂²×C₂₆₃	#124	1	1	yes	characteristic
41	C₂²×C₂₆₃	AGL(1,ℤ/8)	1	2	yes	—
42	C₂²×C₂₆₃	#137	1	2	yes	—
43	C₄×C₂₆₃	—	2	4	no	—
44	C₄×C₂₆₃	—	8	2	no	—
45	C₄×C₂₆₃	#117	1	2	yes	—
46	C₄×C₂₆₃	#125	1	2	yes	—
47	Dic₂₆₃	—	8	2	no	—
48	C₂×C₂₆₃	#382	1	1	yes	characteristic
49	C₂×C₂₆₃	#428	1	2	yes	—
50	C₂×C₂₆₃	#489	1	2	yes	—
51	C₂×C₂₆₃	#490	1	1	yes	characteristic
52	C₂×C₂₆₃	#491	1	1	yes	characteristic
53	C₂₆₃	#1836	1	1	yes	characteristic, complemented, Sylow
54	#1836	—	263	1	no	maximal, Sylow
55	C₂×#97	—	263	1	no	—
56	#384	D₂₆₃	1	1	yes	characteristic
57	#382	—	263	1	no	—
58	#340	—	263	4	no	—
59	C₂²×C₈	—	263	2	no	—
60	C₂×C₄⋊C₄	—	2	2	no	—
61	C₂×C₄⋊C₄	—	263	2	no	—
62	C₂×C₄⋊C₄	C₂×D₂₆₃	1	2	yes	—
63	C₂×C₄²	C₂×D₂₆₃	1	1	yes	characteristic
64	#97	—	263	4	no	—
65	#95	—	526	2	no	—
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	—	526	2	no	—
68	C₂²×C₄	C₂²⋊D₂₆₃	1	2	yes	—
69	C₂²×C₄	C₂²×D₂₆₃	1	1	yes	characteristic
70	C₂×C₈	—	263	4	no	—
71	C₂×C₈	—	526	2	no	—
72	C₂×C₈	—	526	2	no	—
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	4	4	no	—
75	C₄⋊C₄	—	526	4	no	—
76	C₄²	C₄×D₂₆₃	1	2	yes	—
77	C₄²	Dic₅₂₆	1	2	yes	—
78	C₂³	C₂×C₂²⋊D₂₆₃	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	4	4	no	—
83	C₂×C₄	—	1052	2	no	—
84	C₂×C₄	—	1052	2	no	—
85	C₂×C₄	—	1052	2	no	—
86	C₂×C₄	Dic₂₆₃⋊C₄	1	4	yes	—
87	C₂×C₄	C₂×C₄×D₂₆₃	1	1	yes	characteristic
88	C₂×C₄	C₂×Dic₅₂₆	1	1	yes	characteristic
89	C₂×C₄	#16862375	1	2	yes	—
90	C₂×C₄	#16862377	1	2	yes	—
91	C₈	—	526	4	no	—
92	C₂²	C₂×Dic₂₆₃⋊C₄	1	1	yes	characteristic
93	C₂²	#22554457	1	1	yes	characteristic
94	C₂²	#22554459	1	1	yes	characteristic
95	C₂²	#22554496	1	2	yes	—
96	C₂²	#22554501	1	2	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	8	2	no	—
99	C₄	—	2104	2	no	—
100	C₄	#22554428	1	2	yes	—
101	C₄	#22554461	1	2	yes	—
102	C₂	#30681803	1	1	yes	characteristic
103	C₂	#30681978	1	2	yes	—
104	C₂	#30682300	1	2	yes	—
105	C₂	#30682302	1	1	yes	characteristic
106	C₂	#30682306	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22554381

C₂

yes

maximal, characteristic

#30681804

C₂

yes

maximal, characteristic

#30681700

C₂

yes

maximal

#384×C₂₆₃

C₂

yes

maximal, characteristic

C₂²×C₂₆₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₂₆₃

C₂²

yes

—

#22554381

C₄

yes

complemented

C₂₆₃⋊#95

—

C₂×C₄⋊C₄×C₂₆₃

—

C₂×C₄⋊C₄×C₂₆₃

C₂²

yes

—

C₂×C₄²×C₂₆₃

C₂²

yes

characteristic

C₂²×Dic₂₆₃

—

C₂×C₂₆₃⋊C₈

—

C₂×C₂₆₃⋊C₈

—

C₂×C₂₆₃⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₂₆₃

—

C₂²×C₄×C₂₆₃

—

C₂²×C₄×C₂₆₃

D₄

yes

—

C₂²×C₄×C₂₆₃

C₂³

yes

characteristic

C₄⋊C₄×C₂₆₃

—

C₄⋊C₄×C₂₆₃

—

C₄²×C₂₆₃

C₂×C₄

yes

—

C₄²×C₂₆₃

Q₈

yes

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

—

C₂₆₃⋊C₈

—

C₂³×C₂₆₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

C₄⋊C₄

yes

—

C₂×C₄×C₂₆₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₆₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₆₃

#41

yes

—

C₂×C₄×C₂₆₃

#41

yes

—

C₂²×C₂₆₃

C₂×C₄⋊C₄

yes

C₂²×C₂₆₃

yes

C₂²×C₂₆₃

yes

C₂²×C₂₆₃

yes

—

C₂²×C₂₆₃

#137

yes

—

C₄×C₂₆₃

—

C₄×C₂₆₃

—

C₄×C₂₆₃

#117

yes

—

C₄×C₂₆₃

#125

yes

—

Dic₂₆₃

—

C₂×C₂₆₃

#382

yes

characteristic

C₂×C₂₆₃

#428

yes

—

C₂×C₂₆₃

#489

yes

—

C₂×C₂₆₃

yes

C₂×C₂₆₃

yes

C₂₆₃

yes

characteristic, complemented, Sylow

#1836

—

263

maximal, Sylow

C₂×#97

—

263

—

#384

D₂₆₃

yes

characteristic

#382

—

263

—

#340

—

263

—

C₂²×C₈

—

263

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

263

—

C₂×C₄⋊C₄

C₂×D₂₆₃

yes

—

C₂×C₄²

C₂×D₂₆₃

yes

characteristic

#97

—

263

—

#95

—

526

—

C₂²×C₄

—

C₂²×C₄

—

526

—

C₂²×C₄

C₂²⋊D₂₆₃

yes

—

C₂²×C₄

C₂²×D₂₆₃

yes

characteristic

C₂×C₈

—

263

—

C₂×C₈

—

526

—

C₂×C₈

—

526

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

526

—

C₄²

C₄×D₂₆₃

yes

—

C₄²

Dic₅₂₆

yes

—

C₂³

C₂×C₂²⋊D₂₆₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

1052

—

C₂×C₄

—

1052

—

C₂×C₄

—

1052

—

C₂×C₄

Dic₂₆₃⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₂₆₃

yes

characteristic

C₂×C₄

C₂×Dic₅₂₆

yes

characteristic

C₂×C₄

#16862375

yes

—

C₂×C₄

#16862377

yes

—

C₈

—

526

—

C₂²

C₂×Dic₂₆₃⋊C₄

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#22554501

yes

—

C₄

—

C₄

—

C₄

—

2104

—

100

C₄

#22554428

yes

—

101

C₄

#22554461

yes

—

102

C₂

#30681803

yes

characteristic

103

C₂

#30681978

yes

—

104

C₂

#30682300

yes

—

105

C₂

#30682302

yes

characteristic

106

C₂

#30682306

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₆₃
commutator	C₂×C₄×C₂₆₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₆₃
Fitting	#384×C₂₆₃	C₂
socle, prime radical	C₂³×C₂₆₃	C₂×D₄
cosocle	C₂²×C₄×C₂₆₃	C₂³
hypercenter	#384	D₂₆₃
hypocenter	C₂₆₃	#1836
LCS	G ▷ C₂×C₄×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₆₃

commutator

C₂×C₄×C₂₆₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₆₃

Fitting

#384×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 ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
7. #22554381	C₄	semidirect
53. C₂₆₃	#1836	semidirect

H ≅ G/N

type

7. #22554381

C₄

semidirect

53. C₂₆₃

#1836

semidirect

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

subgroup	index
C₂×#22554381	2
#30681804	2
#30681700	2
#384×C₂₆₃	2
#1836	263

subgroup

index

#384×C₂₆₃

263

Subgroups — #46782882

Conjugacy classes of subgroups

Complements

Maximal subgroups