Group #35307258 — subgroups

Subgroups — #35307258

Order 21248.

538 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19128052	C₂	1	3	yes	maximal
2	#24908424	C₂	1	3	yes	maximal
3	C₈₃×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#14581792	C₂²	1	3	yes	—
5	#19128052	—	2	6	no	—
6	#19128052	—	2	6	no	—
7	C₂×#14581717	—	2	6	no	—
8	#19127571	C₂²	1	1	yes	characteristic
9	#19127464	—	2	6	no	—
10	C₂×C₄×C₈×C₈₃	C₂²	1	3	yes	—
11	C₂²×Dic₁₆₆	—	2	3	no	—
12	#14581792	—	2	3	no	—
13	#14581792	—	2	3	no	—
14	#14581792	—	2	3	no	—
15	#14581792	D₄	1	6	yes	—
16	C₂×C₄⋊Dic₈₃	—	2	3	no	—
17	C₂×C₄⋊Dic₈₃	—	2	3	no	—
18	C₂×C₄⋊Dic₈₃	—	2	3	no	—
19	#14581717	—	2	24	no	—
20	C₂²×C₈×C₈₃	D₄	1	6	yes	—
21	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
22	C₄×C₈×C₈₃	—	2	3	no	—
23	C₄×C₈×C₈₃	—	2	3	no	—
24	C₂×Dic₁₆₆	—	2	6	no	—
25	C₂×Dic₁₆₆	—	4	6	no	—
26	C₂×Dic₁₆₆	—	4	6	no	—
27	C₂×Dic₁₆₆	—	4	3	no	—
28	C₂²×Dic₈₃	—	4	3	no	—
29	C₂²×Dic₈₃	—	4	1	no	—
30	C₄⋊Dic₈₃	—	2	6	no	—
31	C₄⋊Dic₈₃	—	2	6	no	—
32	C₄⋊Dic₈₃	—	4	3	no	—
33	C₄⋊Dic₈₃	—	4	3	no	—
34	C₄⋊Dic₈₃	—	4	6	no	—
35	C₂²×C₄×C₈₃	C₂×D₄	1	3	yes	—
36	C₂×C₈×C₈₃	—	2	6	no	—
37	C₂×C₈×C₈₃	—	2	6	no	—
38	C₂×C₈×C₈₃	—	2	6	no	—
39	C₄²×C₈₃	C₂×D₄	1	3	yes	—
40	C₄²×C₈₃	#41	1	1	yes	characteristic
41	C₂³×C₈₃	#127	1	1	yes	characteristic
42	C₂×C₄×C₈₃	#120	1	3	yes	—
43	C₂×C₄×C₈₃	#121	1	3	yes	—
44	C₂×C₄×C₈₃	#135	1	6	yes	—
45	C₂×C₄×C₈₃	#137	1	6	yes	—
46	C₂×Dic₈₃	—	4	6	no	—
47	C₂×Dic₈₃	—	8	3	no	—
48	C₂×Dic₈₃	—	8	3	no	—
49	C₂×Dic₈₃	—	8	3	no	—
50	Dic₁₆₆	—	4	12	no	—
51	Dic₁₆₆	—	8	6	no	—
52	C₈×C₈₃	—	4	6	no	—
53	C₂²×C₈₃	#392	1	1	yes	characteristic
54	C₂²×C₈₃	#495	1	3	yes	—
55	C₂²×C₈₃	#497	1	3	yes	—
56	C₄×C₈₃	#452	1	6	yes	—
57	C₄×C₈₃	#464	1	6	yes	—
58	Dic₈₃	—	8	6	no	—
59	Dic₈₃	—	16	1	no	—
60	#10319	—	83	1	no	maximal, Sylow
61	C₂×C₈₃	#1711	1	1	yes	characteristic
62	C₂×C₈₃	#1718	1	3	yes	—
63	C₂×C₈₃	#2015	1	3	yes	—
64	C₂×#487	—	83	3	no	—
65	#1990	—	83	3	no	—
66	#1273	D₈₃	1	1	yes	characteristic
67	C₈₃	#10319	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₄⋊Q₈	—	83	3	no	—
69	#487	—	166	6	no	—
70	#487	—	166	6	no	—
71	C₂×#103	—	166	6	no	—
72	C₂×C₄×C₈	C₂×D₈₃	1	3	yes	—
73	#384	—	83	1	no	—
74	#340	—	166	6	no	—
75	C₂²×Q₈	—	166	3	no	—
76	C₂²×C₈	D₃₃₂	1	6	yes	—
77	C₄⋊Q₈	—	83	6	no	—
78	C₄⋊Q₈	—	166	3	no	—
79	C₄⋊Q₈	—	166	3	no	—
80	C₄⋊Q₈	—	166	3	no	—
81	C₂×C₄⋊C₄	—	166	3	no	—
82	C₂×C₄⋊C₄	—	166	3	no	—
83	C₂×C₄⋊C₄	—	166	3	no	—
84	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
85	#103	—	166	24	no	—
86	C₄×C₈	—	2	3	no	—
87	C₄×C₈	—	2	3	no	—
88	C₂×Q₈	—	332	3	no	—
89	C₂×Q₈	—	332	6	no	—
90	C₂×Q₈	—	332	6	no	—
91	C₂×Q₈	—	166	6	no	—
92	C₂²×C₄	—	332	3	no	—
93	C₂²×C₄	—	332	1	no	—
94	C₂²×C₄	C₂×D₃₃₂	1	3	yes	—
95	C₂×C₈	—	2	6	no	—
96	C₂×C₈	—	2	6	no	—
97	C₂×C₈	—	2	6	no	—
98	C₄⋊C₄	—	332	3	no	—
99	C₄⋊C₄	—	332	3	no	—
100	C₄⋊C₄	—	332	6	no	—
101	C₄⋊C₄	—	166	6	no	—
102	C₄⋊C₄	—	166	6	no	—
103	C₄²	D₄×D₈₃	1	3	yes	—
104	C₄²	#13050591	1	1	yes	characteristic
105	C₂³	#14581789	1	1	yes	characteristic
106	Q₈	—	332	12	no	—
107	Q₈	—	664	6	no	—
108	C₂×C₄	—	332	6	no	—
109	C₂×C₄	—	664	3	no	—
110	C₂×C₄	—	664	3	no	—
111	C₂×C₄	—	664	3	no	—
112	C₂×C₄	#14581762	1	3	yes	—
113	C₂×C₄	#14581767	1	3	yes	—
114	C₂×C₄	#14581814	1	6	yes	—
115	C₂×C₄	#14581825	1	6	yes	—
116	C₈	—	4	6	no	—
117	C₂²	#19127611	1	1	yes	characteristic
118	C₂²	#19128085	1	3	yes	—
119	C₂²	#19128095	1	3	yes	—
120	C₄	—	1328	1	no	—
121	C₄	—	664	6	no	—
122	C₄	#19127865	1	6	yes	—
123	C₄	#19127924	1	6	yes	—
124	C₂	#24907075	1	1	yes	characteristic
125	C₂	#24907109	1	3	yes	—
126	C₂	#24908560	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19128052

C₂

yes

maximal

#24908424

C₂

yes

maximal

C₈₃×#1273

C₂

yes

maximal, characteristic

C₂×#14581792

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#19127464

—

C₂×C₄×C₈×C₈₃

C₂²

yes

—

C₂²×Dic₁₆₆

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

C₂×C₄⋊Dic₈₃

—

#14581717

—

C₂²×C₈×C₈₃

D₄

yes

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄×C₈×C₈₃

—

C₄×C₈×C₈₃

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

—

C₂²×Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₄²×C₈₃

C₂×D₄

yes

—

C₄²×C₈₃

yes

C₂³×C₈₃

yes

C₂×C₄×C₈₃

yes

—

C₂×C₄×C₈₃

#121

yes

—

C₂×C₄×C₈₃

#135

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

#495

yes

—

C₂²×C₈₃

#497

yes

—

C₄×C₈₃

#452

yes

—

C₄×C₈₃

#464

yes

—

Dic₈₃

—

Dic₈₃

—

—

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₂×C₈₃

#2015

yes

—

C₂×#487

—

#1990

—

#1273

D₈₃

yes

characteristic

C₈₃

#10319

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

#487

—

166

—

#487

—

166

—

C₂×#103

—

166

—

C₂×C₄×C₈

C₂×D₈₃

yes

—

#384

—

#340

—

166

—

C₂²×Q₈

—

166

—

C₂²×C₈

D₃₃₂

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

166

—

C₄⋊Q₈

—

166

—

C₄⋊Q₈

—

166

—

C₂×C₄⋊C₄

—

166

—

C₂×C₄⋊C₄

—

166

—

C₂×C₄⋊C₄

—

166

—

C₂×C₄²

C₂²×D₈₃

yes

characteristic

#103

—

166

—

C₄×C₈

—

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

—

C₄⋊C₄

—

332

—

C₄⋊C₄

—

332

—

100

C₄⋊C₄

—

332

—

101

C₄⋊C₄

—

166

—

102

C₄⋊C₄

—

166

—

103

C₄²

D₄×D₈₃

yes

—

104

C₄²

#13050591

yes

characteristic

105

C₂³

#14581789

yes

characteristic

106

Q₈

—

332

—

107

Q₈

—

664

—

108

C₂×C₄

—

332

—

109

C₂×C₄

—

664

—

110

C₂×C₄

—

664

—

111

C₂×C₄

—

664

—

112

C₂×C₄

#14581762

yes

—

113

C₂×C₄

#14581767

yes

—

114

C₂×C₄

#14581814

yes

—

115

C₂×C₄

#14581825

yes

—

116

C₈

—

117

C₂²

#19127611

yes

characteristic

118

C₂²

#19128085

yes

—

119

C₂²

#19128095

yes

—

120

C₄

—

1328

—

121

C₄

—

664

—

122

C₄

#19127865

yes

—

123

C₄

#19127924

yes

—

124

C₂

#24907075

yes

characteristic

125

C₂

#24907109

yes

—

126

C₂

#24908560

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	#10319
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
67. C₈₃	#10319	semidirect

H ≅ G/N

type

67. C₈₃

#10319

semidirect

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

subgroup	index
C₂×#19128052	2
#24908424	2
C₈₃×#1273	2
#10319	83

subgroup

index

C₂×#19128052

#24908424

C₈₃×#1273

#10319

Subgroups — #35307258

Conjugacy classes of subgroups

Complements

Maximal subgroups