Group #35313442 — subgroups

Subgroups — #35313442

Order 21248.

260 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 131 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	#24909260	C₂	1	2	yes	maximal
2	#24905745	C₂	1	1	yes	maximal, characteristic
3	#24905382	C₂	1	2	yes	maximal, complemented
4	C₈×C₈₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₃×#1311	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127752	C₄	1	2	yes	—
7	C₄×C₈×D₈₃	C₂²	1	1	yes	characteristic
8	Dic₈₃⋊C₁₆	C₄	1	4	yes	—
9	(C₂×D₈₃)⋊C₁₆	C₄	1	4	yes	—
10	C₄×C₈₃⋊C₁₆	C₂²	1	2	yes	—
11	#19127423	C₄	1	2	yes	—
12	C₈×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₁₆×C₈₃	C₂²	1	2	yes	—
14	C₈²×C₈₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₈₃	C₂×C₄	1	2	yes	—
16	C₄²×D₈₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈₃⋊C₁₆	C₂×C₄	1	4	yes	—
18	Dic₈₃⋊C₈	C₈	1	4	yes	—
19	(C₂×D₈₃)⋊C₈	C₈	1	4	yes	—
20	C₄×C₈₃⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈₃⋊C₈	C₂×C₄	1	2	yes	—
22	C₈×Dic₈₃	C₂×C₄	1	2	yes	—
23	C₂×C₁₆×C₈₃	C₂×C₄	1	4	yes	—
24	C₄×C₈×C₈₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×D₈₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×D₈₃	C₂×C₈	1	2	yes	—
28	C₂×C₈₃⋊C₈	C₄²	1	2	yes	—
29	C₂×C₈₃⋊C₈	C₂×C₈	1	4	yes	—
30	C₈×D₈₃	—	2	4	no	—
31	C₄×Dic₈₃	C₄²	1	1	yes	characteristic
32	C₄×Dic₈₃	C₂×C₈	1	2	yes	—
33	C₈₃⋊C₁₆	—	2	4	no	—
34	C₂×C₈×C₈₃	C₂×C₈	1	4	yes	—
35	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
36	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
37	C₁₆×C₈₃	—	2	4	no	—
38	C₂²×D₈₃	C₄×C₈	1	1	yes	characteristic
39	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
41	C₂×Dic₈₃	C₄×C₈	1	2	yes	—
42	C₂×Dic₈₃	C₄×C₈	1	1	yes	characteristic
43	C₄×D₈₃	—	2	2	no	—
44	C₄×D₈₃	—	2	4	no	—
45	C₈×C₈₃	—	2	4	no	—
46	C₈×C₈₃	#131	1	4	yes	—
47	C₈₃⋊C₈	—	2	2	no	—
48	C₈₃⋊C₈	—	2	4	no	—
49	C₂²×C₈₃	C₂×C₄×C₈	1	1	yes	characteristic
50	C₂×D₈₃	—	2	2	no	—
51	C₂×D₈₃	—	2	1	no	—
52	C₄×C₈₃	#405	1	2	yes	—
53	C₄×C₈₃	#504	1	4	yes	—
54	Dic₈₃	—	2	2	no	—
55	Dic₈₃	—	2	1	no	—
56	#11412	—	83	1	no	maximal, Sylow
57	C₂×C₈₃	#1450	1	1	yes	characteristic
58	C₂×C₈₃	#2108	1	2	yes	—
59	D₈₃	—	4	1	no	—
60	#2162	—	83	2	no	—
61	#1450	—	83	1	no	—
62	#1312	—	83	2	no	—
63	#1311	D₈₃	1	1	yes	characteristic, complemented
64	C₈×C₁₆	—	83	1	no	—
65	C₈₃	#11412	1	1	yes	characteristic, complemented, Sylow
66	#431	—	83	2	no	—
67	C₂×C₄×C₈	—	83	1	no	—
68	C₄⋊C₁₆	—	83	4	no	—
69	C₂²⋊C₁₆	—	83	4	no	—
70	C₄×C₁₆	—	83	2	no	—
71	C₄×C₁₆	C₂×D₈₃	1	2	yes	—
72	#322	—	83	2	no	—
73	C₈²	—	83	1	no	—
74	C₈²	C₂×D₈₃	1	1	yes	characteristic
75	C₂²×C₈	—	83	2	no	—
76	C₂×C₄²	—	83	1	no	—
77	C₂×C₁₆	—	83	4	no	—
78	C₂×C₁₆	C₄×D₈₃	1	4	yes	—
79	C₄⋊C₈	—	83	4	no	—
80	C₂²⋊C₈	—	83	4	no	—
81	C₄×C₈	—	83	2	no	—
82	C₄×C₈	—	83	2	no	—
83	C₄×C₈	—	83	1	no	—
84	C₄×C₈	C₄×D₈₃	1	2	yes	—
85	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
86	C₂²×C₄	—	83	2	no	—
87	C₂²×C₄	—	83	1	no	—
88	C₂×C₈	—	83	4	no	—
89	C₂×C₈	—	83	2	no	—
90	C₂×C₈	—	166	4	no	—
91	C₂×C₈	C₈×D₈₃	1	4	yes	—
92	C₂×C₈	C₂×C₄×D₈₃	1	2	yes	—
93	C₄²	—	83	2	no	—
94	C₄²	—	83	1	no	—
95	C₄²	C₂×C₄×D₈₃	1	1	yes	characteristic
96	C₁₆	—	2	4	no	—
97	C₁₆	—	166	4	no	—
98	C₂³	—	83	1	no	—
99	C₂×C₄	—	83	2	no	—
100	C₂×C₄	—	83	1	no	—
101	C₂×C₄	—	166	4	no	—
102	C₂×C₄	—	166	2	no	—
103	C₂×C₄	C₄²×D₈₃	1	1	yes	characteristic
104	C₂×C₄	C₂×C₈×D₈₃	1	2	yes	—
105	C₈	—	2	4	no	—
106	C₈	—	166	4	no	—
107	C₈	—	166	2	no	—
108	C₈	#14581798	1	4	yes	—
109	C₂²	—	166	2	no	—
110	C₂²	—	166	1	no	—
111	C₂²	C₄×C₈×D₈₃	1	1	yes	characteristic
112	C₄	—	166	2	no	—
113	C₄	—	166	1	no	—
114	C₄	#19127655	1	2	yes	—
115	C₄	#19128119	1	4	yes	—
116	C₂	—	332	1	no	—
117	C₂	#24905745	1	1	yes	characteristic
118	C₂	#24909061	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#24909260

C₂

yes

maximal

#24905745

C₂

yes

maximal, characteristic

#24905382

C₂

yes

maximal, complemented

C₈×C₈₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₈₃×#1311

C₂

yes

maximal, characteristic, complemented

#19127752

C₄

yes

—

C₄×C₈×D₈₃

C₂²

yes

characteristic

Dic₈₃⋊C₁₆

C₄

yes

—

(C₂×D₈₃)⋊C₁₆

C₄

yes

—

C₄×C₈₃⋊C₁₆

C₂²

yes

—

#19127423

C₄

yes

—

C₈×C₈₃⋊C₈

C₂²

yes

characteristic

C₄×C₁₆×C₈₃

C₂²

yes

—

C₈²×C₈₃

C₂²

yes

characteristic

C₂×C₈×D₈₃

C₂×C₄

yes

—

C₄²×D₈₃

C₂×C₄

yes

characteristic

C₂×C₈₃⋊C₁₆

C₂×C₄

yes

—

Dic₈₃⋊C₈

C₈

yes

—

(C₂×D₈₃)⋊C₈

C₈

yes

—

C₄×C₈₃⋊C₈

C₂×C₄

yes

characteristic

C₄×C₈₃⋊C₈

C₂×C₄

yes

—

C₈×Dic₈₃

C₂×C₄

yes

—

C₂×C₁₆×C₈₃

C₂×C₄

yes

—

C₄×C₈×C₈₃

C₂×C₄

yes

—

C₄×C₈×C₈₃

C₂³

yes

characteristic

C₂×C₄×D₈₃

C₄²

yes

characteristic

C₂×C₄×D₈₃

C₂×C₈

yes

—

C₂×C₈₃⋊C₈

C₄²

yes

—

C₂×C₈₃⋊C₈

C₂×C₈

yes

—

C₈×D₈₃

—

C₄×Dic₈₃

C₄²

yes

characteristic

C₄×Dic₈₃

C₂×C₈

yes

—

C₈₃⋊C₁₆

—

C₂×C₈×C₈₃

C₂×C₈

yes

—

C₂×C₈×C₈₃

C₂²×C₄

yes

—

C₄²×C₈₃

C₂²×C₄

yes

characteristic

C₁₆×C₈₃

—

C₂²×D₈₃

C₄×C₈

yes

characteristic

C₂×C₄×C₈₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₈

yes

—

C₂×Dic₈₃

C₄×C₈

yes

—

C₂×Dic₈₃

C₄×C₈

yes

characteristic

C₄×D₈₃

—

C₄×D₈₃

—

C₈×C₈₃

—

C₈×C₈₃

#131

yes

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

C₂×C₄×C₈

yes

characteristic

C₂×D₈₃

—

C₂×D₈₃

—

C₄×C₈₃

#405

yes

—

C₄×C₈₃

#504

yes

—

Dic₈₃

—

Dic₈₃

—

—

C₂×C₈₃

yes

C₂×C₈₃

yes

—

D₈₃

—

—

—

—

D₈₃

yes

characteristic, complemented

C₈×C₁₆

—

C₈₃

#11412

yes

characteristic, complemented, Sylow

#431

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₈₃

yes

—

#322

—

C₈²

—

C₈²

C₂×D₈₃

yes

characteristic

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₈₃

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₈₃

yes

—

C₄×C₈

C₂²×D₈₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

166

—

C₂×C₈

C₈×D₈₃

yes

—

C₂×C₈

C₂×C₄×D₈₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×C₄×D₈₃

yes

characteristic

C₁₆

—

C₁₆

—

166

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

166

—

102

C₂×C₄

—

166

—

103

C₂×C₄

C₄²×D₈₃

yes

characteristic

104

C₂×C₄

C₂×C₈×D₈₃

yes

—

105

C₈

—

106

C₈

—

166

—

107

C₈

—

166

—

108

C₈

#14581798

yes

—

109

C₂²

—

166

—

110

C₂²

—

166

—

111

C₂²

C₄×C₈×D₈₃

yes

characteristic

112

C₄

—

166

—

113

C₄

—

166

—

114

C₄

#19127655

yes

—

115

C₄

#19128119

yes

—

116

C₂

—

332

—

117

C₂

#24905745

yes

characteristic

118

C₂

#24909061

yes

—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₈₃
commutator, socle	C₂²×C₈₃	C₂×C₄×C₈
Fitting	C₈₃×#1311	C₂
prime radical	C₂²×D₈₃	C₄×C₈
cosocle	C₄×C₈×C₈₃	C₂³
hypercenter	#1311	D₈₃
hypocenter	C₈₃	#11412
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄×C₈ ◁ #1311

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₈₃

commutator, socle

C₂²×C₈₃

C₂×C₄×C₈

Fitting

C₈₃×#1311

C₂

prime radical

C₂²×D₈₃

C₄×C₈

cosocle

C₄×C₈×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂²×C₈₃ ▷ C₈₃

C₁ ◁ C₄×C₈ ◁ #1311

N	H ≅ G/N	type
3. #24905382	C₂	semidirect
4. C₈×C₈₃⋊C₁₆	C₂	semidirect
5. C₈₃×#1311	C₂	semidirect
63. #1311	D₈₃	semidirect
65. C₈₃	#11412	semidirect

H ≅ G/N

type

3. #24905382

C₂

semidirect

4. C₈×C₈₃⋊C₁₆

C₂

semidirect

5. C₈₃×#1311

C₂

semidirect

63. #1311

D₈₃

semidirect

65. C₈₃

#11412

semidirect

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

subgroup	index
#24909260	2
#24905745	2
#24905382	2
C₈×C₈₃⋊C₁₆	2
C₈₃×#1311	2
#11412	83

subgroup

index

#24909260

#24905745

#24905382

C₈×C₈₃⋊C₁₆

C₈₃×#1311

#11412

Subgroups — #35313442

Conjugacy classes of subgroups

Complements

Maximal subgroups