Group #46783740 — subgroups

Subgroups — #46783740

Order 33664.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#22554462	C₂	1	1	yes	maximal, characteristic
2	#30681962	C₂	1	1	yes	maximal, characteristic
3	#30681706	C₂	1	4	yes	maximal
4	C₄×M₁₆×C₂₆₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#16862360	C₂²	1	2	yes	—
6	#22554462	—	2	1	no	—
7	#22554462	—	2	1	no	—
8	#22554462	—	2	2	no	—
9	C₂×C₄⋊Dic₂₆₃	C₂²	1	2	yes	—
10	C₂×Dic₂₆₃⋊C₄	C₄	1	4	yes	—
11	C₄⋊(C₂₆₃⋊C₈)	—	2	2	no	—
12	C₂×M₁₆×C₂₆₃	C₂²	1	2	yes	—
13	C₂×C₄²×C₂₆₃	C₂²	1	1	yes	characteristic
14	#97×C₂₆₃	—	2	1	no	—
15	C₄×C₈×C₂₆₃	—	2	1	no	—
16	C₂²×Dic₂₆₃	C₂×C₄	1	4	yes	—
17	#16862360	—	2	4	no	—
18	C₂×C₂₆₃⋊C₈	—	2	2	no	—
19	C₄⋊Dic₂₆₃	—	2	2	no	—
20	C₄⋊Dic₂₆₃	—	2	2	no	—
21	Dic₂₆₃⋊C₄	—	2	4	no	—
22	Dic₂₆₃⋊C₄	—	2	4	no	—
23	C₂²×C₄×C₂₆₃	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₂₆₃	C₂³	1	1	yes	characteristic
25	M₁₆×C₂₆₃	—	2	2	no	—
26	M₁₆×C₂₆₃	Q₈	1	4	yes	—
27	C₂×C₈×C₂₆₃	—	2	2	no	—
28	C₄²×C₂₆₃	D₄	1	1	yes	characteristic
29	C₄²×C₂₆₃	D₄	1	1	yes	characteristic
30	C₄²×C₂₆₃	D₄	1	2	yes	—
31	C₂×Dic₂₆₃	—	2	4	no	—
32	C₂×Dic₂₆₃	—	4	4	no	—
33	C₂₆₃⋊C₈	—	4	2	no	—
34	C₂³×C₂₆₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₆₃	—	4	2	no	—
36	C₂×C₄×C₂₆₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₂₆₃	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₆₃	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₂₆₃	#41	1	2	yes	—
42	C₈×C₂₆₃	—	2	4	no	—
43	C₂²×C₂₆₃	—	2	2	no	—
44	C₂²×C₂₆₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₂₆₃	C₄×Q₈	1	2	yes	—
46	C₄×C₂₆₃	—	2	2	no	—
47	C₄×C₂₆₃	—	2	2	no	—
48	C₄×C₂₆₃	C₂²⋊Q₈	1	2	yes	—
49	C₄×C₂₆₃	#124	1	1	yes	characteristic
50	C₄×C₂₆₃	C₄⋊Q₈	1	1	yes	characteristic
51	Dic₂₆₃	—	4	4	no	—
52	C₂×C₂₆₃	—	2	2	no	—
53	C₂×C₂₆₃	#391	1	1	yes	characteristic
54	C₂×C₂₆₃	#413	1	2	yes	—
55	C₂₆₃	#1998	1	1	yes	characteristic, complemented, Sylow
56	#1998	—	263	1	no	maximal, Sylow
57	C₂×#125	—	263	1	no	—
58	#423	—	263	1	no	—
59	C₄×M₁₆	D₂₆₃	1	1	yes	characteristic
60	#343	—	263	4	no	—
61	C₂×M₁₆	—	263	2	no	—
62	C₂×M₁₆	C₂×D₂₆₃	1	2	yes	—
63	#125	—	526	1	no	—
64	#125	—	526	1	no	—
65	#125	—	526	2	no	—
66	C₂×C₄⋊C₄	—	263	4	no	—
67	C₂×C₄⋊C₄	—	263	2	no	—
68	C₂×C₄²	C₂×D₂₆₃	1	1	yes	characteristic
69	C₄⋊C₈	—	526	2	no	—
70	#97	—	2	1	no	—
71	C₄×C₈	—	2	1	no	—
72	C₂²×C₄	—	263	4	no	—
73	C₂²×C₄	C₄×D₂₆₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₂₆₃	1	1	yes	characteristic
75	M₁₆	—	2	2	no	—
76	M₁₆	—	526	4	no	—
77	M₁₆	Dic₅₂₆	1	4	yes	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	526	2	no	—
80	C₄⋊C₄	—	526	4	no	—
81	C₄⋊C₄	—	526	4	no	—
82	C₄⋊C₄	—	526	2	no	—
83	C₄⋊C₄	—	526	2	no	—
84	C₄²	C₂²⋊D₂₆₃	1	1	yes	characteristic
85	C₄²	C₂²⋊D₂₆₃	1	1	yes	characteristic
86	C₄²	D₁₀₅₂	1	2	yes	—
87	C₂³	C₂×C₄×D₂₆₃	1	1	yes	characteristic
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	526	4	no	—
90	C₂×C₄	—	1052	4	no	—
91	C₂×C₄	(C₂×D₂₆₃)⋊C₄	1	2	yes	—
92	C₂×C₄	(C₂×D₂₆₃)⋊C₄	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₂₆₃	1	1	yes	characteristic
94	C₂×C₄	C₂×D₁₀₅₂	1	1	yes	characteristic
95	C₂×C₄	C₂×Dic₅₂₆	1	2	yes	—
96	C₂×C₄	#16862376	1	2	yes	—
97	C₈	—	2	4	no	—
98	C₈	—	1052	2	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₂×(C₂×D₂₆₃)⋊C₄	1	1	yes	characteristic
101	C₂²	C₄×Dic₅₂₆	1	2	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	1052	4	no	—
105	C₄	#22554449	1	2	yes	—
106	C₄	#22554458	1	1	yes	characteristic
107	C₄	#22554470	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#30681844	1	1	yes	characteristic
110	C₂	#30681920	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22554462

C₂

yes

maximal, characteristic

#30681962

C₂

yes

maximal, characteristic

#30681706

C₂

yes

maximal

C₄×M₁₆×C₂₆₃

C₂

yes

maximal, characteristic

C₂×#16862360

C₂²

yes

—

#22554462

—

#22554462

—

#22554462

—

C₂×C₄⋊Dic₂₆₃

C₂²

yes

—

C₂×Dic₂₆₃⋊C₄

C₄

yes

—

C₄⋊(C₂₆₃⋊C₈)

—

C₂×M₁₆×C₂₆₃

C₂²

yes

—

C₂×C₄²×C₂₆₃

C₂²

yes

characteristic

#97×C₂₆₃

—

C₄×C₈×C₂₆₃

—

C₂²×Dic₂₆₃

C₂×C₄

yes

—

#16862360

—

C₂×C₂₆₃⋊C₈

—

C₄⋊Dic₂₆₃

—

C₄⋊Dic₂₆₃

—

Dic₂₆₃⋊C₄

—

Dic₂₆₃⋊C₄

—

C₂²×C₄×C₂₆₃

C₂×C₄

yes

—

C₂²×C₄×C₂₆₃

C₂³

yes

characteristic

M₁₆×C₂₆₃

—

M₁₆×C₂₆₃

Q₈

yes

—

C₂×C₈×C₂₆₃

—

C₄²×C₂₆₃

D₄

yes

characteristic

C₄²×C₂₆₃

D₄

yes

characteristic

C₄²×C₂₆₃

D₄

yes

—

C₂×Dic₂₆₃

—

C₂×Dic₂₆₃

—

C₂₆₃⋊C₈

—

C₂³×C₂₆₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₆₃

—

C₂×C₄×C₂₆₃

C₂²⋊C₄

yes

—

C₂×C₄×C₂₆₃

C₂²⋊C₄

yes

—

C₂×C₄×C₂₆₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₃

C₂×Q₈

yes

—

C₂×C₄×C₂₆₃

#41

yes

—

C₈×C₂₆₃

—

C₂²×C₂₆₃

—

C₂²×C₂₆₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₆₃

C₄×Q₈

yes

—

C₄×C₂₆₃

—

C₄×C₂₆₃

—

C₄×C₂₆₃

C₂²⋊Q₈

yes

—

C₄×C₂₆₃

#124

yes

characteristic

C₄×C₂₆₃

C₄⋊Q₈

yes

characteristic

Dic₂₆₃

—

C₂×C₂₆₃

—

C₂×C₂₆₃

#391

yes

characteristic

C₂×C₂₆₃

#413

yes

—

C₂₆₃

#1998

yes

characteristic, complemented, Sylow

#1998

—

263

maximal, Sylow

C₂×#125

—

263

—

#423

—

263

—

C₄×M₁₆

D₂₆₃

yes

characteristic

#343

—

263

—

C₂×M₁₆

—

263

—

C₂×M₁₆

C₂×D₂₆₃

yes

—

#125

—

526

—

#125

—

526

—

#125

—

526

—

C₂×C₄⋊C₄

—

263

—

C₂×C₄⋊C₄

—

263

—

C₂×C₄²

C₂×D₂₆₃

yes

characteristic

C₄⋊C₈

—

526

—

#97

—

C₄×C₈

—

C₂²×C₄

—

263

—

C₂²×C₄

C₄×D₂₆₃

yes

—

C₂²×C₄

C₂²×D₂₆₃

yes

characteristic

M₁₆

—

M₁₆

—

526

—

M₁₆

Dic₅₂₆

yes

—

C₂×C₈

—

C₂×C₈

—

526

—

C₄⋊C₄

—

526

—

C₄⋊C₄

—

526

—

C₄⋊C₄

—

526

—

C₄⋊C₄

—

526

—

C₄²

C₂²⋊D₂₆₃

yes

characteristic

C₄²

C₂²⋊D₂₆₃

yes

characteristic

C₄²

D₁₀₅₂

yes

—

C₂³

C₂×C₄×D₂₆₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

526

—

C₂×C₄

—

1052

—

C₂×C₄

(C₂×D₂₆₃)⋊C₄

yes

—

C₂×C₄

(C₂×D₂₆₃)⋊C₄

yes

—

C₂×C₄

C₂×C₂²⋊D₂₆₃

yes

characteristic

C₂×C₄

C₂×D₁₀₅₂

yes

characteristic

C₂×C₄

C₂×Dic₅₂₆

yes

—

C₂×C₄

#16862376

yes

—

C₈

—

C₈

—

1052

—

C₂²

—

100

C₂²

C₂×(C₂×D₂₆₃)⋊C₄

yes

characteristic

101

C₂²

C₄×Dic₅₂₆

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

1052

—

105

C₄

#22554449

yes

—

106

C₄

#22554458

yes

characteristic

107

C₄

#22554470

yes

characteristic

108

C₂

—

109

C₂

#30681844

yes

characteristic

110

C₂

#30681920

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₂₆₃)⋊C₄
commutator, prime radical	C₂³×C₂₆₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₆₃
Fitting	C₄×M₁₆×C₂₆₃	C₂
socle	C₂²×C₂₆₃	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₂₆₃	C₂³
hypercenter	C₄×M₁₆	D₂₆₃
hypocenter	C₂₆₃	#1998
LCS	G ▷ C₂³×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂×(C₂×D₂₆₃)⋊C₄

commutator, prime radical

C₂³×C₂₆₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₆₃

Fitting

C₄×M₁₆×C₂₆₃

C₂

socle

C₂²×C₂₆₃

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₂₆₃

C₂³

hypercenter

C₄×M₁₆

D₂₆₃

hypocenter

C₂₆₃

#1998

LCS

G ▷ C₂³×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
55. C₂₆₃	#1998	semidirect

H ≅ G/N

type

55. C₂₆₃

#1998

semidirect

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

subgroup	index
C₂×#22554462	2
#30681962	2
#30681706	2
C₄×M₁₆×C₂₆₃	2
#1998	263

subgroup

index

C₄×M₁₆×C₂₆₃

263

Subgroups — #46783740

Conjugacy classes of subgroups

Complements

Maximal subgroups