Group #35320787 — subgroups

Subgroups — #35320787

Order 21248.

310 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 163 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	#24907627	C₂	1	2	yes	maximal
2	#24905555	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14581726	C₂²	1	4	yes	—
5	C₂×#14581724	—	2	2	no	—
6	#19127567	—	2	2	no	—
7	C₂²×C₁₆×C₈₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
9	C₄×C₁₆×C₈₃	C₄	1	4	yes	complemented
10	C₂×C₄⋊Dic₈₃	—	2	4	no	—
11	#14581726	—	2	8	no	—
12	#14581724	—	4	4	no	—
13	C₈₃⋊#95	—	4	4	no	—
14	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₈₃	D₄	1	1	yes	characteristic
17	C₂×C₁₆×C₈₃	—	2	4	no	—
18	C₂×C₁₆×C₈₃	C₂×C₄	1	4	yes	—
19	C₄×C₈×C₈₃	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₈₃	Q₈	1	2	yes	—
21	C₂²×Dic₈₃	—	4	4	no	—
22	C₄⋊Dic₈₃	—	4	4	no	—
23	C₄⋊Dic₈₃	—	4	4	no	—
24	C₂²×C₄×C₈₃	D₈	1	2	yes	—
25	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
26	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₈₃	SD₁₆	1	4	yes	—
28	C₂×C₈×C₈₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₈×C₈₃	#41	1	4	yes	—
31	C₄²×C₈₃	C₄⋊C₄	1	2	yes	—
32	C₄²×C₈₃	Q₁₆	1	2	yes	—
33	C₁₆×C₈₃	—	2	4	no	—
34	C₂³×C₈₃	C₂×D₈	1	1	yes	characteristic
35	C₂×C₄×C₈₃	—	2	4	no	—
36	C₂×C₄×C₈₃	#107	1	4	yes	—
37	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₈₃	#124	1	2	yes	—
39	C₂×C₄×C₈₃	C₂×SD₁₆	1	2	yes	—
40	C₂×C₄×C₈₃	C₂×Q₁₆	1	1	yes	characteristic
41	C₂×Dic₈₃	—	8	4	no	—
42	C₂×Dic₈₃	—	8	8	no	—
43	C₈×C₈₃	#106	1	4	yes	—
44	C₈×C₈₃	#117	1	2	yes	—
45	C₈×C₈₃	#125	1	2	yes	—
46	C₂²×C₈₃	C₂×#107	1	1	yes	characteristic
47	C₂²×C₈₃	#486	1	2	yes	—
48	C₂²×C₈₃	#508	1	4	yes	—
49	C₄×C₈₃	—	2	4	no	—
50	C₄×C₈₃	#382	1	1	yes	characteristic
51	C₄×C₈₃	C₂×#106	1	1	yes	characteristic
52	C₄×C₈₃	#487	1	2	yes	—
53	Dic₈₃	—	16	4	no	—
54	#12889	—	83	1	no	maximal, Sylow
55	C₂×C₈₃	#1834	1	1	yes	characteristic
56	C₂×C₈₃	#2158	1	2	yes	—
57	C₂×C₈₃	#2242	1	4	yes	—
58	C₂×C₄×C₁₆	D₈₃	1	1	yes	characteristic
59	#1846	—	83	2	no	—
60	#1380	—	83	4	no	—
61	C₈₃	#12889	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₁₆	C₂×D₈₃	1	2	yes	—
63	C₂×#107	—	83	4	no	—
64	C₂×#106	—	166	2	no	—
65	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
66	#382	—	166	2	no	—
67	C₄×C₁₆	Dic₈₃	1	4	yes	complemented
68	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
69	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
70	C₂×C₄⋊C₄	—	166	4	no	—
71	C₂×C₄²	D₃₃₂	1	1	yes	characteristic
72	C₂×C₁₆	—	2	4	no	—
73	C₂×C₁₆	C₂×Dic₈₃	1	4	yes	—
74	#107	—	166	8	no	—
75	#106	—	332	4	no	—
76	C₄×C₈	Dic₁₆₆	1	2	yes	—
77	C₄×C₈	C₂×Dic₈₃	1	2	yes	—
78	#95	—	332	4	no	—
79	C₂²×C₄	—	332	4	no	—
80	C₂²×C₄	D₆₆₄	1	2	yes	—
81	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
82	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
83	C₂×C₈	#13050579	1	4	yes	—
84	C₂×C₈	C₂²×Dic₈₃	1	1	yes	characteristic
85	C₂×C₈	C₂×Dic₁₆₆	1	1	yes	characteristic
86	C₂×C₈	#13050590	1	4	yes	—
87	C₄⋊C₄	—	332	4	no	—
88	C₄⋊C₄	—	332	4	no	—
89	C₄²	C₄⋊Dic₈₃	1	2	yes	—
90	C₄²	Dic₃₃₂	1	2	yes	—
91	C₁₆	—	2	4	no	—
92	C₂³	C₂×D₆₆₄	1	1	yes	characteristic
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	664	8	no	—
95	C₂×C₄	—	664	4	no	—
96	C₂×C₄	#14581726	1	4	yes	—
97	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
98	C₂×C₄	#14581780	1	2	yes	—
99	C₂×C₄	C₂×#13050579	1	2	yes	—
100	C₂×C₄	C₂×Dic₃₃₂	1	1	yes	characteristic
101	C₈	#14581724	1	4	yes	—
102	C₈	#14581751	1	2	yes	—
103	C₈	#14581784	1	2	yes	—
104	C₂²	C₂×#14581726	1	1	yes	characteristic
105	C₂²	#19128048	1	2	yes	—
106	C₂²	#19128133	1	4	yes	—
107	C₄	—	2	4	no	—
108	C₄	—	1328	4	no	—
109	C₄	#19127567	1	1	yes	characteristic
110	C₄	C₂×#14581724	1	1	yes	characteristic
111	C₄	#19128052	1	2	yes	—
112	C₂	#24907591	1	1	yes	characteristic
113	C₂	#24909247	1	2	yes	—
114	C₂	#24909695	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#24907627

C₂

yes

maximal

#24905555

C₂

yes

maximal

C₂×C₄×C₁₆×C₈₃

C₂

yes

maximal, characteristic

C₂×#14581726

C₂²

yes

—

C₂×#14581724

—

#19127567

—

C₂²×C₁₆×C₈₃

C₂²

yes

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₄×C₁₆×C₈₃

C₄

yes

complemented

C₂×C₄⋊Dic₈₃

—

#14581726

—

#14581724

—

C₈₃⋊#95

—

C₂²×C₈×C₈₃

D₄

yes

characteristic

C₂²×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₄²×C₈₃

D₄

yes

characteristic

C₂×C₁₆×C₈₃

—

C₂×C₁₆×C₈₃

C₂×C₄

yes

—

C₄×C₈×C₈₃

C₂×C₄

yes

—

C₄×C₈×C₈₃

Q₈

yes

—

C₂²×Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂²×C₄×C₈₃

D₈

yes

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₈×C₈₃

C₄⋊C₄

yes

—

C₂×C₈×C₈₃

SD₁₆

yes

—

C₂×C₈×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₈₃

#41

yes

—

C₄²×C₈₃

C₄⋊C₄

yes

—

C₄²×C₈₃

Q₁₆

yes

—

C₁₆×C₈₃

—

C₂³×C₈₃

C₂×D₈

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#107

yes

—

C₂×C₄×C₈₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₃

#124

yes

—

C₂×C₄×C₈₃

C₂×SD₁₆

yes

—

C₂×C₄×C₈₃

C₂×Q₁₆

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

#106

yes

—

C₈×C₈₃

#117

yes

—

C₈×C₈₃

#125

yes

—

C₂²×C₈₃

C₂×#107

yes

characteristic

C₂²×C₈₃

#486

yes

—

C₂²×C₈₃

#508

yes

—

C₄×C₈₃

—

C₄×C₈₃

yes

C₄×C₈₃

yes

C₄×C₈₃

yes

—

Dic₈₃

—

—

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₂×C₈₃

#2242

yes

—

C₂×C₄×C₁₆

D₈₃

yes

characteristic

#1846

—

#1380

—

C₈₃

#12889

yes

characteristic, complemented, Sylow

C₂²×C₁₆

C₂×D₈₃

yes

—

C₂×#107

—

C₂×#106

—

166

—

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

#382

—

166

—

C₄×C₁₆

Dic₈₃

yes

complemented

C₂²×C₈

D₃₃₂

yes

characteristic

C₂²×C₈

C₂²×D₈₃

yes

characteristic

C₂×C₄⋊C₄

—

166

—

C₂×C₄²

D₃₃₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₈₃

yes

—

#107

—

166

—

#106

—

332

—

C₄×C₈

Dic₁₆₆

yes

—

C₄×C₈

C₂×Dic₈₃

yes

—

#95

—

332

—

C₂²×C₄

—

332

—

C₂²×C₄

D₆₆₄

yes

—

C₂²×C₄

C₂×D₃₃₂

yes

characteristic

C₂×C₈

C₄⋊Dic₈₃

yes

—

C₂×C₈

#13050579

yes

—

C₂×C₈

C₂²×Dic₈₃

yes

characteristic

C₂×C₈

C₂×Dic₁₆₆

yes

characteristic

C₂×C₈

#13050590

yes

—

C₄⋊C₄

—

332

—

C₄⋊C₄

—

332

—

C₄²

C₄⋊Dic₈₃

yes

—

C₄²

Dic₃₃₂

yes

—

C₁₆

—

C₂³

C₂×D₆₆₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

664

—

C₂×C₄

—

664

—

C₂×C₄

#14581726

yes

—

C₂×C₄

C₂×C₄⋊Dic₈₃

yes

characteristic

C₂×C₄

#14581780

yes

—

C₂×C₄

C₂×#13050579

yes

—

100

C₂×C₄

C₂×Dic₃₃₂

yes

characteristic

101

C₈

#14581724

yes

—

102

C₈

#14581751

yes

—

103

C₈

#14581784

yes

—

104

C₂²

C₂×#14581726

yes

characteristic

105

C₂²

#19128048

yes

—

106

C₂²

#19128133

yes

—

107

C₄

—

108

C₄

—

1328

—

109

C₄

#19127567

yes

characteristic

110

C₄

C₂×#14581724

yes

characteristic

111

C₄

#19128052

yes

—

112

C₂

#24907591

yes

characteristic

113

C₂

#24909247

yes

—

114

C₂

#24909695

yes

—

	subgroup	G/H
center	C₂³	C₂×D₆₆₄
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₂×C₄×C₁₆×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	C₂×D₈
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₈₃
hypocenter	C₈₃	#12889
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₂³

C₂×D₆₆₄

commutator

C₂×C₈×C₈₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₃

Fitting

C₂×C₄×C₁₆×C₈₃

C₂

socle, prime radical

C₂³×C₈₃

C₂×D₈

cosocle

C₂²×C₈×C₈₃

C₂³

hypercenter

C₂×C₄×C₁₆

D₈₃

hypocenter

C₈₃

#12889

LCS

G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
9. C₄×C₁₆×C₈₃	C₄	semidirect
61. C₈₃	#12889	semidirect
67. C₄×C₁₆	Dic₈₃	semidirect

H ≅ G/N

type

9. C₄×C₁₆×C₈₃

C₄

semidirect

61. C₈₃

#12889

semidirect

67. C₄×C₁₆

Dic₈₃

semidirect

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

subgroup	index
#24907627	2
#24905555	2
C₂×C₄×C₁₆×C₈₃	2
#12889	83

subgroup

index

#24907627

#24905555

C₂×C₄×C₁₆×C₈₃

#12889

Subgroups — #35320787

Conjugacy classes of subgroups

Complements

Maximal subgroups