Group #45693129 — subgroups

Subgroups — C₁₃₁×#7245 #45693129

Order 33536.

200 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 98 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	#2150×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1567×C₁₃₁	C₂	1	2	yes	maximal
3	C₂×M₃₂×C₁₃₁	C₄	1	2	yes	—
4	#423×C₁₃₁	—	2	2	no	—
5	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
6	C₄⋊C₁₆×C₁₃₁	—	2	2	no	—
7	#335×C₁₃₁	—	2	2	no	—
8	#335×C₁₃₁	C₄	1	4	yes	—
9	C₂×M₁₆×C₁₃₁	—	4	2	no	—
10	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₃₁	Q₈	1	1	yes	characteristic
12	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
13	M₃₂×C₁₃₁	—	4	2	no	—
14	C₂×C₁₆×C₁₃₁	—	2	2	no	—
15	C₄⋊C₈×C₁₃₁	—	2	4	no	—
16	C₄⋊C₈×C₁₃₁	—	4	2	no	—
17	C₄×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
19	C₂²×C₄×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₃₁	SD₁₆	1	2	yes	—
21	M₁₆×C₁₃₁	—	8	4	no	—
22	C₂×C₈×C₁₃₁	—	2	1	no	—
23	C₂×C₈×C₁₃₁	—	2	1	no	—
24	C₂×C₈×C₁₃₁	—	4	1	no	—
25	C₂×C₈×C₁₃₁	—	4	4	no	—
26	C₂×C₈×C₁₃₁	C₄²	1	1	yes	characteristic
27	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃₁	C₄⋊C₄	1	2	yes	—
29	C₄²×C₁₃₁	C₂²⋊C₄	1	2	yes	—
30	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
31	C₄²×C₁₃₁	Q₁₆	1	1	yes	characteristic
32	C₁₆×C₁₃₁	—	4	2	no	—
33	C₂³×C₁₃₁	#106	1	1	yes	characteristic
34	C₂×C₄×C₁₃₁	—	2	1	no	—
35	C₂×C₄×C₁₃₁	—	2	1	no	—
36	C₂×C₄×C₁₃₁	—	2	2	no	—
37	C₂×C₄×C₁₃₁	—	2	2	no	—
38	C₂×C₄×C₁₃₁	#95	1	1	yes	characteristic
39	C₂×C₄×C₁₃₁	#102	1	2	yes	—
40	C₂×C₄×C₁₃₁	#103	1	2	yes	—
41	C₂×C₄×C₁₃₁	#107	1	1	yes	characteristic
42	C₈×C₁₃₁	—	2	2	no	—
43	C₈×C₁₃₁	—	2	1	no	—
44	C₈×C₁₃₁	—	8	4	no	—
45	C₈×C₁₃₁	#100	1	1	yes	characteristic
46	C₈×C₁₃₁	#101	1	1	yes	characteristic
47	C₂²×C₁₃₁	—	2	1	no	—
48	C₂²×C₁₃₁	—	2	2	no	—
49	C₂²×C₁₃₁	#340	1	1	yes	characteristic
50	C₄×C₁₃₁	—	2	1	no	—
51	C₄×C₁₃₁	—	2	2	no	—
52	C₄×C₁₃₁	#338	1	1	yes	characteristic
53	C₄×C₁₃₁	#343	1	1	yes	characteristic
54	C₄×C₁₃₁	#361	1	2	yes	—
55	C₄×C₁₃₁	#362	1	2	yes	—
56	C₂×C₁₃₁	—	4	1	no	—
57	C₂×C₁₃₁	#1292	1	1	yes	characteristic
58	C₂×C₁₃₁	#1387	1	2	yes	—
59	#7245	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₁₃₁	#7245	1	1	yes	characteristic, direct product factor, Sylow
61	#2150	C₂×C₁₃₁	1	1	yes	characteristic
62	#1567	C₂×C₁₃₁	1	2	yes	—
63	C₂×M₃₂	C₄×C₁₃₁	1	2	yes	—
64	#423	—	2	2	no	—
65	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
66	C₄⋊C₁₆	—	2	2	no	—
67	#335	—	2	2	no	—
68	#335	C₄×C₁₃₁	1	4	yes	—
69	C₂×M₁₆	—	4	2	no	—
70	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
71	C₂²×C₈	Q₈×C₁₃₁	1	1	yes	characteristic
72	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
73	M₃₂	—	4	2	no	—
74	C₂×C₁₆	—	2	2	no	—
75	C₄⋊C₈	—	2	4	no	—
76	C₄⋊C₈	—	4	2	no	—
77	C₄×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
78	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
79	C₂²×C₄	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
80	C₂²×C₄	SD₁₆×C₁₃₁	1	2	yes	—
81	M₁₆	—	8	4	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	4	1	no	—
85	C₂×C₈	—	4	4	no	—
86	C₂×C₈	C₄²×C₁₃₁	1	1	yes	characteristic
87	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
88	C₂×C₈	C₄⋊C₄×C₁₃₁	1	2	yes	—
89	C₄²	C₂²⋊C₄×C₁₃₁	1	2	yes	—
90	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
91	C₄²	Q₁₆×C₁₃₁	1	1	yes	characteristic
92	C₁₆	—	4	2	no	—
93	C₂³	#106×C₁₃₁	1	1	yes	characteristic
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	#95×C₁₃₁	1	1	yes	characteristic
99	C₂×C₄	#102×C₁₃₁	1	2	yes	—
100	C₂×C₄	#103×C₁₃₁	1	2	yes	—
101	C₂×C₄	#107×C₁₃₁	1	1	yes	characteristic
102	C₈	—	2	2	no	—
103	C₈	—	2	1	no	—
104	C₈	—	8	4	no	—
105	C₈	#100×C₁₃₁	1	1	yes	characteristic
106	C₈	#101×C₁₃₁	1	1	yes	characteristic
107	C₂²	—	2	1	no	—
108	C₂²	—	2	2	no	—
109	C₂²	#340×C₁₃₁	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	2	2	no	—
112	C₄	#338×C₁₃₁	1	1	yes	characteristic
113	C₄	#343×C₁₃₁	1	1	yes	characteristic
114	C₄	#361×C₁₃₁	1	2	yes	—
115	C₄	#362×C₁₃₁	1	2	yes	—
116	C₂	—	4	1	no	—
117	C₂	#1292×C₁₃₁	1	1	yes	characteristic
118	C₂	#1387×C₁₃₁	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#2150×C₁₃₁

C₂

yes

maximal, characteristic

#1567×C₁₃₁

C₂

yes

maximal

C₂×M₃₂×C₁₃₁

C₄

yes

—

#423×C₁₃₁

—

C₂×C₄×C₈×C₁₃₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₁₃₁

—

#335×C₁₃₁

—

#335×C₁₃₁

C₄

yes

—

C₂×M₁₆×C₁₃₁

—

C₂²×C₈×C₁₃₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃₁

Q₈

yes

characteristic

C₂×C₄²×C₁₃₁

D₄

yes

characteristic

M₃₂×C₁₃₁

—

C₂×C₁₆×C₁₃₁

—

C₄⋊C₈×C₁₃₁

—

C₄⋊C₈×C₁₃₁

—

C₄×C₈×C₁₃₁

C₂×C₄

yes

—

C₄×C₈×C₁₃₁

D₄

yes

—

C₂²×C₄×C₁₃₁

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₃₁

SD₁₆

yes

—

M₁₆×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

C₄²

yes

characteristic

C₂×C₈×C₁₃₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃₁

C₄⋊C₄

yes

—

C₄²×C₁₃₁

C₂²⋊C₄

yes

—

C₄²×C₁₃₁

D₈

yes

characteristic

C₄²×C₁₃₁

Q₁₆

yes

characteristic

C₁₆×C₁₃₁

—

C₂³×C₁₃₁

#106

yes

characteristic

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

#95

yes

characteristic

C₂×C₄×C₁₃₁

#102

yes

—

C₂×C₄×C₁₃₁

#103

yes

—

C₂×C₄×C₁₃₁

#107

yes

characteristic

C₈×C₁₃₁

—

C₈×C₁₃₁

—

C₈×C₁₃₁

—

C₈×C₁₃₁

yes

C₈×C₁₃₁

yes

C₂²×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

#340

yes

characteristic

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

yes

C₄×C₁₃₁

yes

C₄×C₁₃₁

yes

—

C₄×C₁₃₁

#362

yes

—

C₂×C₁₃₁

—

C₂×C₁₃₁

#1292

yes

characteristic

C₂×C₁₃₁

#1387

yes

—

#7245

C₁₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₁₃₁

#7245

yes

characteristic, direct product factor, Sylow

#2150

C₂×C₁₃₁

yes

characteristic

#1567

C₂×C₁₃₁

yes

—

C₂×M₃₂

C₄×C₁₃₁

yes

—

#423

—

C₂×C₄×C₈

C₂²×C₁₃₁

yes

characteristic

C₄⋊C₁₆

—

#335

—

#335

C₄×C₁₃₁

yes

—

C₂×M₁₆

—

C₂²×C₈

C₂×C₄×C₁₃₁

yes

characteristic

C₂²×C₈

Q₈×C₁₃₁

yes

characteristic

C₂×C₄²

D₄×C₁₃₁

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₁₃₁

yes

—

C₄×C₈

D₄×C₁₃₁

yes

—

C₂²×C₄

C₄⋊C₄×C₁₃₁

yes

characteristic

C₂²×C₄

SD₁₆×C₁₃₁

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₁₃₁

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₃₁

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₃₁

yes

—

C₄²

C₂²⋊C₄×C₁₃₁

yes

—

C₄²

D₈×C₁₃₁

yes

characteristic

C₄²

Q₁₆×C₁₃₁

yes

characteristic

C₁₆

—

C₂³

#106×C₁₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#95×C₁₃₁

yes

characteristic

C₂×C₄

#102×C₁₃₁

yes

—

100

C₂×C₄

#103×C₁₃₁

yes

—

101

C₂×C₄

#107×C₁₃₁

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

#100×C₁₃₁

yes

characteristic

106

C₈

#101×C₁₃₁

yes

characteristic

107

C₂²

—

108

C₂²

—

109

C₂²

#340×C₁₃₁

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

#338×C₁₃₁

yes

characteristic

113

C₄

#343×C₁₃₁

yes

characteristic

114

C₄

#361×C₁₃₁

yes

—

115

C₄

#362×C₁₃₁

yes

—

116

C₂

—

117

C₂

#1292×C₁₃₁

yes

characteristic

118

C₂

#1387×C₁₃₁

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	#340
commutator	C₂×C₈	C₄²×C₁₃₁
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₃₁
prime radical	C₂³×C₁₃₁	#106
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ C₂×C₄×C₈×C₁₃₁ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃₁

#340

commutator

C₂×C₈

C₄²×C₁₃₁

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₁₃₁

prime radical

C₂³×C₁₃₁

#106

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ C₂×C₄×C₈×C₁₃₁ ◁ G

N	H ≅ G/N	type
59. #7245	C₁₃₁	direct (N × H)
60. C₁₃₁	#7245	direct (N × H)

H ≅ G/N

type

59. #7245

C₁₃₁

direct (N × H)

60. C₁₃₁

#7245

direct (N × H)

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

subgroup	index
#2150×C₁₃₁	2
#1567×C₁₃₁	2
#7245	131

subgroup

index

#2150×C₁₃₁

#1567×C₁₃₁

#7245

131

Subgroups — C₁₃₁×#7245 #45693129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C131×#7245 #45693129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7245 #45693129