Group #46782866 — subgroups

Subgroups — #46782866

Order 33664.

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

normal subgroups only

This group has 216 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×C₄⋊(C₂₆₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	#30681784	C₂	1	1	yes	maximal, characteristic
3	#30681692	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₈×C₂₆₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₂₆₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×Dic₂₆₃	C₂²	1	2	yes	—
7	C₄⋊(C₂₆₃⋊C₈)	—	2	2	no	—
8	C₂₆₃⋊#95	C₄	1	2	yes	—
9	C₂₆₃⋊#95	C₄	1	2	yes	—
10	C₂²×C₈×C₂₆₃	C₂²	1	2	yes	—
11	C₂×C₄²×C₂₆₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₂₆₃	—	2	2	no	—
13	C₂²×Dic₂₆₃	C₂×C₄	1	4	yes	—
14	C₂×C₂₆₃⋊C₈	—	2	2	no	—
15	C₂×C₂₆₃⋊C₈	—	2	4	no	—
16	C₄×Dic₂₆₃	—	2	2	no	—
17	C₄×Dic₂₆₃	—	2	2	no	—
18	C₂²×C₄×C₂₆₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₆₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₆₃	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₂₆₃	—	2	2	no	—
22	C₂×C₈×C₂₆₃	—	2	4	no	—
23	C₄²×C₂₆₃	D₄	1	2	yes	—
24	C₄²×C₂₆₃	Q₈	1	2	yes	—
25	C₂×Dic₂₆₃	—	2	4	no	—
26	C₂×Dic₂₆₃	—	2	4	no	—
27	C₂×Dic₂₆₃	—	2	4	no	—
28	C₂₆₃⋊C₈	—	4	2	no	—
29	C₂³×C₂₆₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₆₃	—	2	2	no	—
31	C₂×C₄×C₂₆₃	—	2	2	no	—
32	C₂×C₄×C₂₆₃	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₂₆₃	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₆₃	C₂×D₄	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	C₈×C₂₆₃	—	4	2	no	—
39	C₂²×C₂₆₃	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₂₆₃	#117	1	2	yes	—
41	C₂²×C₂₆₃	#131	1	2	yes	—
42	C₂²×C₂₆₃	#131	1	2	yes	—
43	C₄×C₂₆₃	—	2	2	no	—
44	C₄×C₂₆₃	—	2	2	no	—
45	C₄×C₂₆₃	#124	1	1	yes	characteristic
46	C₄×C₂₆₃	#124	1	1	yes	characteristic
47	C₄×C₂₆₃	#125	1	2	yes	—
48	Dic₂₆₃	—	4	4	no	—
49	C₂×C₂₆₃	#382	1	1	yes	characteristic
50	C₂×C₂₆₃	#424	1	1	yes	characteristic
51	C₂×C₂₆₃	#424	1	1	yes	characteristic
52	C₂×C₂₆₃	#433	1	4	yes	—
53	C₂₆₃	#1832	1	1	yes	characteristic, complemented, Sylow
54	#1832	—	263	1	no	maximal, Sylow
55	C₂×C₄⋊C₈	—	263	1	no	—
56	C₂×C₄⋊C₈	D₂₆₃	1	1	yes	characteristic
57	#376	—	263	1	no	—
58	#336	—	263	4	no	—
59	C₂²×C₈	—	263	2	no	—
60	C₂²×C₈	C₂×D₂₆₃	1	2	yes	—
61	C₂×C₄²	—	263	2	no	—
62	C₂×C₄²	C₂×D₂₆₃	1	1	yes	characteristic
63	C₄⋊C₈	—	2	2	no	—
64	C₄⋊C₈	—	526	2	no	—
65	#95	—	263	2	no	—
66	#95	—	263	2	no	—
67	C₂²×C₄	—	263	4	no	—
68	C₂²×C₄	C₄×D₂₆₃	1	1	yes	characteristic
69	C₂²×C₄	C₄×D₂₆₃	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₂₆₃	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	4	no	—
73	C₂×C₈	—	526	2	no	—
74	C₂×C₈	—	526	4	no	—
75	C₄²	—	526	2	no	—
76	C₄²	—	526	2	no	—
77	C₄²	C₂²⋊D₂₆₃	1	2	yes	—
78	C₄²	Dic₅₂₆	1	2	yes	—
79	C₂³	C₂×C₄×D₂₆₃	1	1	yes	characteristic
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	526	4	no	—
83	C₂×C₄	—	526	4	no	—
84	C₂×C₄	—	526	4	no	—
85	C₂×C₄	Dic₂₆₃⋊C₄	1	2	yes	—
86	C₂×C₄	Dic₂₆₃⋊C₄	1	2	yes	—
87	C₂×C₄	C₂×C₂²⋊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	—	4	2	no	—
92	C₈	—	1052	2	no	—
93	C₂²	C₂×Dic₂₆₃⋊C₄	1	1	yes	characteristic
94	C₂²	#22554428	1	2	yes	—
95	C₂²	#22554476	1	2	yes	—
96	C₂²	#22554478	1	2	yes	—
97	C₄	—	2	2	no	—
98	C₄	—	2	2	no	—
99	C₄	—	1052	4	no	—
100	C₄	#22554457	1	1	yes	characteristic
101	C₄	#22554459	1	1	yes	characteristic
102	C₄	#22554461	1	2	yes	—
103	C₂	#30681803	1	1	yes	characteristic
104	C₂	#30681964	1	1	yes	characteristic
105	C₂	#30681966	1	1	yes	characteristic
106	C₂	#30681998	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₂₆₃⋊C₈)

C₂

yes

maximal, characteristic

#30681784

C₂

yes

maximal, characteristic

#30681692

C₂

yes

maximal

C₂×C₄⋊C₈×C₂₆₃

C₂

yes

maximal, characteristic

C₂²×C₂₆₃⋊C₈

C₂²

yes

—

C₂×C₄×Dic₂₆₃

C₂²

yes

—

C₄⋊(C₂₆₃⋊C₈)

—

C₂₆₃⋊#95

C₄

yes

—

C₂₆₃⋊#95

C₄

yes

—

C₂²×C₈×C₂₆₃

C₂²

yes

—

C₂×C₄²×C₂₆₃

C₂²

yes

characteristic

C₄⋊C₈×C₂₆₃

—

C₂²×Dic₂₆₃

C₂×C₄

yes

—

C₂×C₂₆₃⋊C₈

—

C₂×C₂₆₃⋊C₈

—

C₄×Dic₂₆₃

—

C₄×Dic₂₆₃

—

C₂²×C₄×C₂₆₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₆₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₆₃

C₂³

yes

characteristic

C₂×C₈×C₂₆₃

—

C₂×C₈×C₂₆₃

—

C₄²×C₂₆₃

D₄

yes

—

C₄²×C₂₆₃

Q₈

yes

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

—

C₂₆₃⋊C₈

—

C₂³×C₂₆₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

C₄⋊C₄

yes

—

C₂×C₄×C₂₆₃

C₄⋊C₄

yes

—

C₂×C₄×C₂₆₃

C₂×D₄

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

#117

yes

—

C₂²×C₂₆₃

#131

yes

—

C₂²×C₂₆₃

#131

yes

—

C₄×C₂₆₃

—

C₄×C₂₆₃

—

C₄×C₂₆₃

yes

C₄×C₂₆₃

yes

C₄×C₂₆₃

yes

—

Dic₂₆₃

—

C₂×C₂₆₃

yes

C₂×C₂₆₃

yes

C₂×C₂₆₃

yes

C₂×C₂₆₃

yes

—

C₂₆₃

#1832

yes

characteristic, complemented, Sylow

#1832

—

263

maximal, Sylow

C₂×C₄⋊C₈

—

263

—

C₂×C₄⋊C₈

D₂₆₃

yes

characteristic

#376

—

263

—

#336

—

263

—

C₂²×C₈

—

263

—

C₂²×C₈

C₂×D₂₆₃

yes

—

C₂×C₄²

—

263

—

C₂×C₄²

C₂×D₂₆₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

526

—

#95

—

263

—

#95

—

263

—

C₂²×C₄

—

263

—

C₂²×C₄

C₄×D₂₆₃

yes

characteristic

C₂²×C₄

C₄×D₂₆₃

yes

characteristic

C₂²×C₄

C₂²×D₂₆₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

526

—

C₂×C₈

—

526

—

C₄²

—

526

—

C₄²

—

526

—

C₄²

C₂²⋊D₂₆₃

yes

—

C₄²

Dic₅₂₆

yes

—

C₂³

C₂×C₄×D₂₆₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

526

—

C₂×C₄

—

526

—

C₂×C₄

—

526

—

C₂×C₄

Dic₂₆₃⋊C₄

yes

—

C₂×C₄

Dic₂₆₃⋊C₄

yes

—

C₂×C₄

C₂×C₂²⋊D₂₆₃

yes

characteristic

C₂×C₄

C₂×Dic₅₂₆

yes

characteristic

C₂×C₄

#16862375

yes

—

C₂×C₄

#16862377

yes

—

C₈

—

C₈

—

1052

—

C₂²

C₂×Dic₂₆₃⋊C₄

yes

characteristic

C₂²

#22554428

yes

—

C₂²

#22554476

yes

—

C₂²

#22554478

yes

—

C₄

—

C₄

—

C₄

—

1052

—

100

C₄

#22554457

yes

characteristic

101

C₄

#22554459

yes

characteristic

102

C₄

#22554461

yes

—

103

C₂

#30681803

yes

characteristic

104

C₂

#30681964

yes

characteristic

105

C₂

#30681966

yes

characteristic

106

C₂

#30681998

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₆₃
commutator, socle, prime radical	C₂³×C₂₆₃	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₂₆₃	C₂
cosocle	C₂²×C₄×C₂₆₃	C₂³
hypercenter	C₂×C₄⋊C₈	D₂₆₃
hypocenter	C₂₆₃	#1832
LCS	G ▷ C₂³×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₆₃

commutator, socle, prime radical

C₂³×C₂₆₃

C₂²×C₄

Fitting

C₂×C₄⋊C₈×C₂₆₃

C₂

cosocle

C₂²×C₄×C₂₆₃

C₂³

hypercenter

C₂×C₄⋊C₈

D₂₆₃

C₂₆₃

G ▷ C₂³×C₂₆₃ ▷ C₂₆₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
53. C₂₆₃	#1832	semidirect

H ≅ G/N

type

53. C₂₆₃

#1832

semidirect

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

subgroup	index
C₂×C₄⋊(C₂₆₃⋊C₈)	2
#30681784	2
#30681692	2
C₂×C₄⋊C₈×C₂₆₃	2
#1832	263

subgroup

index

C₂×C₄⋊(C₂₆₃⋊C₈)

#30681784

#30681692

C₂×C₄⋊C₈×C₂₆₃

#1832

263

Subgroups — #46782866

Conjugacy classes of subgroups

Complements

Maximal subgroups