Group #35307243 — subgroups

Subgroups — #35307243

Order 21248.

586 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 169 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×#19128099	C₂	1	3	yes	maximal
2	#24908265	C₂	1	3	yes	maximal
3	C₈₃×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#14581792	C₂²	1	3	yes	—
5	#19128099	—	2	12	no	—
6	C₂×#14581724	—	2	6	no	—
7	C₂×#14581717	—	2	6	no	—
8	#19127571	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₈₃	C₂²	1	3	yes	—
10	C₂²×Dic₁₆₆	—	2	3	no	—
11	#14581792	—	2	6	no	—
12	#14581792	—	2	3	no	—
13	#14581792	D₄	1	6	yes	—
14	C₂×C₄⋊Dic₈₃	—	2	6	no	—
15	C₂×C₄⋊Dic₈₃	—	2	3	no	—
16	#14581724	—	2	24	no	—
17	#14581717	—	4	12	no	—
18	C₂²×C₈×C₈₃	D₄	1	6	yes	—
19	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
20	C₄×C₈×C₈₃	—	2	6	no	—
21	C₂×Dic₁₆₆	—	2	6	no	—
22	C₂×Dic₁₆₆	—	4	6	no	—
23	C₂×Dic₁₆₆	—	4	6	no	—
24	C₂×Dic₁₆₆	—	4	3	no	—
25	C₂²×Dic₈₃	—	4	3	no	—
26	C₂²×Dic₈₃	—	4	1	no	—
27	C₄⋊Dic₈₃	—	2	12	no	—
28	C₄⋊Dic₈₃	—	4	6	no	—
29	C₄⋊Dic₈₃	—	4	6	no	—
30	C₂²×C₄×C₈₃	C₂×D₄	1	3	yes	—
31	C₂×C₈×C₈₃	—	2	6	no	—
32	C₂×C₈×C₈₃	—	2	6	no	—
33	C₂×C₈×C₈₃	SD₁₆	1	12	yes	—
34	C₄²×C₈₃	C₂×D₄	1	3	yes	—
35	C₄²×C₈₃	#41	1	1	yes	characteristic
36	C₂³×C₈₃	#127	1	1	yes	characteristic
37	C₂×C₄×C₈₃	#120	1	3	yes	—
38	C₂×C₄×C₈₃	#121	1	3	yes	—
39	C₂×C₄×C₈₃	C₂×SD₁₆	1	6	yes	—
40	C₂×C₄×C₈₃	#137	1	6	yes	—
41	C₂×Dic₈₃	—	4	6	no	—
42	C₂×Dic₈₃	—	8	3	no	—
43	C₂×Dic₈₃	—	8	3	no	—
44	C₂×Dic₈₃	—	8	3	no	—
45	Dic₁₆₆	—	4	12	no	—
46	Dic₁₆₆	—	8	6	no	—
47	C₈×C₈₃	—	2	12	no	—
48	C₂²×C₈₃	#392	1	1	yes	characteristic
49	C₂²×C₈₃	#492	1	3	yes	—
50	C₂²×C₈₃	#497	1	3	yes	—
51	C₄×C₈₃	#448	1	6	yes	—
52	C₄×C₈₃	#461	1	6	yes	—
53	Dic₈₃	—	8	6	no	—
54	Dic₈₃	—	16	1	no	—
55	#10316	—	83	1	no	maximal, Sylow
56	C₂×C₈₃	#1705	1	1	yes	characteristic
57	C₂×C₈₃	#1716	1	3	yes	—
58	C₂×C₈₃	#2013	1	3	yes	—
59	C₂×#498	—	83	3	no	—
60	#1956	—	83	3	no	—
61	#1273	D₈₃	1	1	yes	characteristic
62	C₈₃	#10316	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₄⋊Q₈	—	83	3	no	—
64	#498	—	166	12	no	—
65	C₂×#106	—	166	6	no	—
66	C₂×#103	—	166	6	no	—
67	C₂×C₄×C₈	C₂×D₈₃	1	3	yes	—
68	#384	—	83	1	no	—
69	C₂²×Q₈	—	166	3	no	—
70	C₂²×C₈	D₃₃₂	1	6	yes	—
71	C₄⋊Q₈	—	83	6	no	—
72	C₄⋊Q₈	—	166	6	no	—
73	C₄⋊Q₈	—	166	3	no	—
74	C₂×C₄⋊C₄	—	166	3	no	—
75	C₂×C₄⋊C₄	—	166	6	no	—
76	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
77	#106	—	166	24	no	—
78	#103	—	332	12	no	—
79	C₄×C₈	—	2	6	no	—
80	C₂×Q₈	—	332	3	no	—
81	C₂×Q₈	—	332	6	no	—
82	C₂×Q₈	—	332	6	no	—
83	C₂×Q₈	—	166	6	no	—
84	C₂²×C₄	—	332	3	no	—
85	C₂²×C₄	—	332	1	no	—
86	C₂²×C₄	C₂×D₃₃₂	1	3	yes	—
87	C₂×C₈	—	2	6	no	—
88	C₂×C₈	—	2	6	no	—
89	C₂×C₈	#13050579	1	12	yes	—
90	C₄⋊C₄	—	332	6	no	—
91	C₄⋊C₄	—	332	6	no	—
92	C₄⋊C₄	—	166	12	no	—
93	C₄²	D₄×D₈₃	1	3	yes	—
94	C₄²	#13050591	1	1	yes	characteristic
95	C₂³	#14581789	1	1	yes	characteristic
96	Q₈	—	332	12	no	—
97	Q₈	—	664	6	no	—
98	C₂×C₄	—	332	6	no	—
99	C₂×C₄	—	664	3	no	—
100	C₂×C₄	—	664	3	no	—
101	C₂×C₄	—	664	3	no	—
102	C₂×C₄	#14581762	1	3	yes	—
103	C₂×C₄	#14581767	1	3	yes	—
104	C₂×C₄	C₂×#13050579	1	6	yes	—
105	C₂×C₄	#14581825	1	6	yes	—
106	C₈	—	2	12	no	—
107	C₂²	#19127611	1	1	yes	characteristic
108	C₂²	#19128074	1	3	yes	—
109	C₂²	#19128095	1	3	yes	—
110	C₄	—	1328	1	no	—
111	C₄	—	664	6	no	—
112	C₄	#19127842	1	6	yes	—
113	C₄	#19127907	1	6	yes	—
114	C₂	#24907050	1	1	yes	characteristic
115	C₂	#24907096	1	3	yes	—
116	C₂	#24908548	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19128099

C₂

yes

maximal

#24908265

C₂

yes

maximal

C₈₃×#1273

C₂

yes

maximal, characteristic

C₂×#14581792

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₃

C₂²

yes

—

C₂²×Dic₁₆₆

—

#14581792

—

#14581792

—

#14581792

D₄

yes

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

#14581724

—

#14581717

—

C₂²×C₈×C₈₃

D₄

yes

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

SD₁₆

yes

—

C₄²×C₈₃

C₂×D₄

yes

—

C₄²×C₈₃

yes

C₂³×C₈₃

yes

C₂×C₄×C₈₃

yes

—

C₂×C₄×C₈₃

#121

yes

—

C₂×C₄×C₈₃

C₂×SD₁₆

yes

—

C₂×C₄×C₈₃

#137

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₂²×C₈₃

#392

yes

characteristic

C₂²×C₈₃

#492

yes

—

C₂²×C₈₃

#497

yes

—

C₄×C₈₃

#448

yes

—

C₄×C₈₃

#461

yes

—

Dic₈₃

—

Dic₈₃

—

—

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₂×C₈₃

#2013

yes

—

C₂×#498

—

#1956

—

#1273

D₈₃

yes

characteristic

C₈₃

#10316

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

#498

—

166

—

C₂×#106

—

166

—

C₂×#103

—

166

—

C₂×C₄×C₈

C₂×D₈₃

yes

—

#384

—

C₂²×Q₈

—

166

—

C₂²×C₈

D₃₃₂

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

166

—

C₄⋊Q₈

—

166

—

C₂×C₄⋊C₄

—

166

—

C₂×C₄⋊C₄

—

166

—

C₂×C₄²

C₂²×D₈₃

yes

characteristic

#106

—

166

—

#103

—

332

—

C₄×C₈

—

C₂×Q₈

—

332

—

C₂×Q₈

—

332

—

C₂×Q₈

—

332

—

C₂×Q₈

—

166

—

C₂²×C₄

—

332

—

C₂²×C₄

—

332

—

C₂²×C₄

C₂×D₃₃₂

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#13050579

yes

—

C₄⋊C₄

—

332

—

C₄⋊C₄

—

332

—

C₄⋊C₄

—

166

—

C₄²

D₄×D₈₃

yes

—

C₄²

yes

C₂³

yes

Q₈

—

332

—

Q₈

—

664

—

C₂×C₄

—

332

—

C₂×C₄

—

664

—

100

C₂×C₄

—

664

—

101

C₂×C₄

—

664

—

102

C₂×C₄

#14581762

yes

—

103

C₂×C₄

#14581767

yes

—

104

C₂×C₄

C₂×#13050579

yes

—

105

C₂×C₄

#14581825

yes

—

106

C₈

—

107

C₂²

#19127611

yes

characteristic

108

C₂²

#19128074

yes

—

109

C₂²

#19128095

yes

—

110

C₄

—

1328

—

111

C₄

—

664

—

112

C₄

#19127842

yes

—

113

C₄

#19127907

yes

—

114

C₂

#24907050

yes

characteristic

115

C₂

#24907096

yes

—

116

C₂

#24908548

yes

—

	subgroup	G/H
center	C₂³	#14581789
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1273	C₂
socle, prime radical	C₂³×C₈₃	#127
hypercenter	#1273	D₈₃
hypocenter	C₈₃	#10316
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#14581789

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1273

C₂

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
62. C₈₃	#10316	semidirect

H ≅ G/N

type

62. C₈₃

#10316

semidirect

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

subgroup	index
C₂×#19128099	2
#24908265	2
C₈₃×#1273	2
#10316	83

subgroup

index

C₂×#19128099

#24908265

C₈₃×#1273

#10316

Subgroups — #35307243

Conjugacy classes of subgroups

Complements

Maximal subgroups