Group #45696244 — subgroups

Subgroups — C₁₃₁×#10360 #45696244

Order 33536.

476 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 106 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	#2845×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#1961×C₁₃₁	C₂	1	3	yes	maximal
3	#1295×C₁₃₁	C₂	1	3	yes	maximal, complemented
4	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
5	C₂×#102×C₁₃₁	—	2	6	no	—
6	C₂×#97×C₁₃₁	C₂²	1	3	yes	—
7	#398×C₁₃₁	—	2	6	no	—
8	#382×C₁₃₁	C₂²	1	3	yes	—
9	C₂²×D₄×C₁₃₁	—	2	3	no	—
10	C₂²×C₈×C₁₃₁	—	2	3	no	—
11	#127×C₁₃₁	—	2	3	no	—
12	#127×C₁₃₁	Q₈	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₃₁	—	2	6	no	—
14	C₂×C₄⋊C₄×C₁₃₁	D₄	1	6	yes	—
15	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
16	#102×C₁₃₁	—	4	12	no	—
17	#97×C₁₃₁	—	2	6	no	—
18	#95×C₁₃₁	—	2	2	no	—
19	#95×C₁₃₁	—	2	6	no	—
20	C₂⁴×C₁₃₁	—	4	1	no	—
21	C₂×D₄×C₁₃₁	—	2	6	no	—
22	C₂×D₄×C₁₃₁	—	4	6	no	—
23	C₂×D₄×C₁₃₁	—	4	6	no	—
24	C₂×D₄×C₁₃₁	—	4	3	no	—
25	C₂²×C₄×C₁₃₁	—	2	6	no	—
26	C₂²×C₄×C₁₃₁	C₂×D₄	1	3	yes	—
27	C₂×C₈×C₁₃₁	—	2	6	no	—
28	C₂×C₈×C₁₃₁	—	4	3	no	—
29	C₂×C₈×C₁₃₁	—	4	3	no	—
30	C₄⋊C₄×C₁₃₁	—	4	6	no	—
31	C₄⋊C₄×C₁₃₁	—	8	6	no	—
32	C₄²×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
33	C₄²×C₁₃₁	#41	1	3	yes	—
34	C₂³×C₁₃₁	—	4	2	no	—
35	C₂³×C₁₃₁	—	8	3	no	—
36	C₂³×C₁₃₁	—	8	3	no	—
37	C₂³×C₁₃₁	#120	1	1	yes	characteristic
38	D₄×C₁₃₁	—	4	12	no	—
39	D₄×C₁₃₁	—	8	6	no	—
40	C₂×C₄×C₁₃₁	—	2	3	no	—
41	C₂×C₄×C₁₃₁	—	2	3	no	—
42	C₂×C₄×C₁₃₁	—	4	6	no	—
43	C₂×C₄×C₁₃₁	—	4	6	no	—
44	C₂×C₄×C₁₃₁	—	4	6	no	—
45	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	3	yes	—
46	C₂×C₄×C₁₃₁	#124	1	3	yes	—
47	C₈×C₁₃₁	—	4	6	no	—
48	C₂²×C₁₃₁	—	8	6	no	—
49	C₂²×C₁₃₁	—	16	3	no	—
50	C₂²×C₁₃₁	—	16	1	no	—
51	C₂²×C₁₃₁	#393	1	1	yes	characteristic
52	C₂²×C₁₃₁	#453	1	3	yes	—
53	C₂²×C₁₃₁	#454	1	3	yes	—
54	C₄×C₁₃₁	—	2	3	no	—
55	C₄×C₁₃₁	—	2	3	no	—
56	C₄×C₁₃₁	—	8	6	no	—
57	C₂×C₁₃₁	—	16	2	no	—
58	C₂×C₁₃₁	#1656	1	3	yes	—
59	C₂×C₁₃₁	#1658	1	1	yes	characteristic
60	C₂×C₁₃₁	#2027	1	3	yes	—
61	#10360	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₁₃₁	#10360	1	1	yes	characteristic, direct product factor, Sylow
63	#2845	C₂×C₁₃₁	1	1	yes	characteristic, complemented
64	#1961	C₂×C₁₃₁	1	3	yes	—
65	#1295	C₂×C₁₃₁	1	3	yes	complemented
66	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
67	C₂×#102	—	2	6	no	—
68	C₂×#97	C₂²×C₁₃₁	1	3	yes	—
69	#398	—	2	6	no	—
70	#382	C₂²×C₁₃₁	1	3	yes	—
71	C₂²×D₄	—	2	3	no	—
72	C₂²×C₈	—	2	3	no	—
73	#127	—	2	3	no	—
74	#127	Q₈×C₁₃₁	1	2	yes	—
75	C₂×C₄⋊C₄	—	2	6	no	—
76	C₂×C₄⋊C₄	D₄×C₁₃₁	1	6	yes	—
77	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
78	#102	—	4	12	no	—
79	#97	—	2	6	no	—
80	#95	—	2	2	no	—
81	#95	—	2	6	no	—
82	C₂⁴	—	4	1	no	—
83	C₂×D₄	—	2	6	no	—
84	C₂×D₄	—	4	6	no	—
85	C₂×D₄	—	4	6	no	—
86	C₂×D₄	—	4	3	no	—
87	C₂²×C₄	—	2	6	no	—
88	C₂²×C₄	C₂×D₄×C₁₃₁	1	3	yes	—
89	C₂×C₈	—	2	6	no	—
90	C₂×C₈	—	4	3	no	—
91	C₂×C₈	—	4	3	no	—
92	C₄⋊C₄	—	4	6	no	—
93	C₄⋊C₄	—	8	6	no	—
94	C₄²	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
95	C₄²	#41×C₁₃₁	1	3	yes	—
96	C₂³	—	4	2	no	—
97	C₂³	—	8	3	no	—
98	C₂³	—	8	3	no	—
99	C₂³	#120×C₁₃₁	1	1	yes	characteristic
100	D₄	—	4	12	no	—
101	D₄	—	8	6	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	4	6	no	—
105	C₂×C₄	—	4	6	no	—
106	C₂×C₄	—	4	6	no	—
107	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	3	yes	—
108	C₂×C₄	#124×C₁₃₁	1	3	yes	—
109	C₈	—	4	6	no	—
110	C₂²	—	8	6	no	—
111	C₂²	—	16	3	no	—
112	C₂²	—	16	1	no	—
113	C₂²	#393×C₁₃₁	1	1	yes	characteristic
114	C₂²	#453×C₁₃₁	1	3	yes	—
115	C₂²	#454×C₁₃₁	1	3	yes	—
116	C₄	—	2	3	no	—
117	C₄	—	2	3	no	—
118	C₄	—	8	6	no	—
119	C₂	—	16	2	no	—
120	C₂	#1656×C₁₃₁	1	3	yes	—
121	C₂	#1658×C₁₃₁	1	1	yes	characteristic
122	C₂	#2027×C₁₃₁	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#2845×C₁₃₁

C₂

yes

maximal, characteristic, complemented

#1961×C₁₃₁

C₂

yes

maximal

#1295×C₁₃₁

C₂

yes

maximal, complemented

C₂×#127×C₁₃₁

C₂²

yes

characteristic

C₂×#102×C₁₃₁

—

C₂×#97×C₁₃₁

C₂²

yes

—

#398×C₁₃₁

—

#382×C₁₃₁

C₂²

yes

—

C₂²×D₄×C₁₃₁

—

C₂²×C₈×C₁₃₁

—

#127×C₁₃₁

—

#127×C₁₃₁

Q₈

yes

—

C₂×C₄⋊C₄×C₁₃₁

—

C₂×C₄⋊C₄×C₁₃₁

D₄

yes

—

C₂×C₄²×C₁₃₁

C₂³

yes

characteristic

#102×C₁₃₁

—

#97×C₁₃₁

—

#95×C₁₃₁

—

#95×C₁₃₁

—

C₂⁴×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂×D₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

C₂×D₄

yes

—

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄⋊C₄×C₁₃₁

—

C₄²×C₁₃₁

C₂×Q₈

yes

characteristic

C₄²×C₁₃₁

#41

yes

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

#120

yes

characteristic

D₄×C₁₃₁

—

D₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃₁

#124

yes

—

C₈×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

#393

yes

characteristic

C₂²×C₁₃₁

#453

yes

—

C₂²×C₁₃₁

#454

yes

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₄×C₁₃₁

—

C₂×C₁₃₁

—

C₂×C₁₃₁

#1656

yes

—

C₂×C₁₃₁

#1658

yes

characteristic

C₂×C₁₃₁

#2027

yes

—

#10360

C₁₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₁₃₁

#10360

yes

characteristic, direct product factor, Sylow

#2845

C₂×C₁₃₁

yes

characteristic, complemented

#1961

C₂×C₁₃₁

yes

—

#1295

C₂×C₁₃₁

yes

complemented

C₂×#127

C₂²×C₁₃₁

yes

characteristic

C₂×#102

—

C₂×#97

C₂²×C₁₃₁

yes

—

#398

—

#382

C₂²×C₁₃₁

yes

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

Q₈×C₁₃₁

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₃₁

yes

—

C₂×C₄²

C₂³×C₁₃₁

yes

—

—

—

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Q₈×C₁₃₁

yes

characteristic

C₄²

#41×C₁₃₁

yes

—

C₂³

—

C₂³

—

C₂³

—

C₂³

#120×C₁₃₁

yes

characteristic

100

D₄

—

101

D₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₂²⋊Q₈×C₁₃₁

yes

—

108

C₂×C₄

#124×C₁₃₁

yes

—

109

C₈

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

#393×C₁₃₁

yes

characteristic

114

C₂²

#453×C₁₃₁

yes

—

115

C₂²

#454×C₁₃₁

yes

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₂

—

120

C₂

#1656×C₁₃₁

yes

—

121

C₂

#1658×C₁₃₁

yes

characteristic

122

C₂

#2027×C₁₃₁

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₁
prime radical	C₂×#127×C₁₃₁	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃₁

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃₁

prime radical

C₂×#127×C₁₃₁

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

N	H ≅ G/N	type
1. #2845×C₁₃₁	C₂	semidirect
3. #1295×C₁₃₁	C₂	semidirect
61. #10360	C₁₃₁	direct (N × H)
62. C₁₃₁	#10360	direct (N × H)
63. #2845	C₂×C₁₃₁	semidirect
65. #1295	C₂×C₁₃₁	semidirect

H ≅ G/N

type

1. #2845×C₁₃₁

C₂

semidirect

3. #1295×C₁₃₁

C₂

semidirect

61. #10360

C₁₃₁

direct (N × H)

62. C₁₃₁

#10360

direct (N × H)

63. #2845

C₂×C₁₃₁

semidirect

65. #1295

C₂×C₁₃₁

semidirect

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

subgroup	index
#2845×C₁₃₁	2
#1961×C₁₃₁	2
#1295×C₁₃₁	2
#10360	131

subgroup

index

#2845×C₁₃₁

#1961×C₁₃₁

#1295×C₁₃₁

#10360

131

Subgroups — C₁₃₁×#10360 #45696244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C131×#10360 #45696244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#10360 #45696244