Group #45706676 — subgroups

Subgroups — C₁₃₁×#20792 #45706676

Order 33536.

1118 conjugacy classes of subgroups; only the 622 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 622 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×#423×C₁₃₁	C₂	1	6	yes	maximal
2	C₂×#376×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1843×C₁₃₁	C₂	1	8	yes	maximal, complemented
4	C₂²×M₁₆×C₁₃₁	C₂²	1	4	yes	—
5	C₂²×C₄²×C₁₃₁	C₂²	1	3	yes	—
6	#423×C₁₃₁	—	2	24	no	—
7	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	24	yes	—
8	#376×C₁₃₁	C₄	1	4	yes	—
9	#376×C₁₃₁	C₂²	1	4	yes	—
10	C₂×#95×C₁₃₁	C₄	1	4	yes	—
11	C₂³×C₄×C₁₃₁	C₂×C₄	1	6	yes	—
12	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
13	C₂×M₁₆×C₁₃₁	—	2	24	no	—
14	C₂²×C₈×C₁₃₁	C₂³	1	8	yes	—
15	C₂×C₄²×C₁₃₁	C₂×C₄	1	6	yes	—
16	C₂×C₄²×C₁₃₁	D₄	1	12	yes	—
17	C₂×C₄²×C₁₃₁	Q₈	1	12	yes	—
18	C₂×C₄²×C₁₃₁	C₂³	1	6	yes	—
19	C₄⋊C₈×C₁₃₁	—	2	48	no	—
20	#95×C₁₃₁	C₂×C₄	1	16	yes	—
21	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₃₁	—	4	12	no	—
23	C₂²×C₄×C₁₃₁	C₄⋊C₄	1	24	yes	—
24	C₂²×C₄×C₁₃₁	C₂²×C₄	1	12	yes	—
25	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₃₁	C₂×D₄	1	6	yes	—
27	C₂²×C₄×C₁₃₁	C₂×Q₈	1	6	yes	—
28	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
29	M₁₆×C₁₃₁	—	4	16	no	—
30	C₂×C₈×C₁₃₁	—	2	24	no	—
31	C₄²×C₁₃₁	C₄⋊C₄	1	24	yes	—
32	C₄²×C₁₃₁	C₂×D₄	1	12	yes	—
33	C₄²×C₁₃₁	C₂×Q₈	1	12	yes	—
34	C₂³×C₁₃₁	—	2	4	no	—
35	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	6	yes	—
36	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃₁	—	2	24	no	—
38	C₂×C₄×C₁₃₁	—	4	24	no	—
39	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	24	yes	—
40	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	6	yes	—
41	C₂×C₄×C₁₃₁	#127	1	4	yes	—
42	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	12	yes	—
43	C₂×C₄×C₁₃₁	C₂²×D₄	1	3	yes	—
44	C₂×C₄×C₁₃₁	C₂²×Q₈	1	3	yes	—
45	C₈×C₁₃₁	—	4	8	no	—
46	C₂²×C₁₃₁	—	2	12	no	—
47	C₂²×C₁₃₁	#384	1	4	yes	—
48	C₂²×C₁₃₁	C₂²×C₄⋊C₄	1	3	yes	—
49	C₂²×C₁₃₁	#568	1	4	yes	—
50	C₄×C₁₃₁	—	2	24	no	—
51	C₄×C₁₃₁	#384	1	4	yes	—
52	C₄×C₁₃₁	C₂×#127	1	1	yes	characteristic
53	C₄×C₁₃₁	C₂×C₄⋊Q₈	1	3	yes	—
54	C₂×C₁₃₁	—	2	4	no	—
55	C₂×C₁₃₁	C₂×#384	1	1	yes	characteristic
56	C₂×C₁₃₁	#2905	1	6	yes	—
57	#20792	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₁₃₁	#20792	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×#423	C₂×C₁₃₁	1	6	yes	—
60	C₂×#376	C₂×C₁₃₁	1	1	yes	characteristic
61	#1843	C₂×C₁₃₁	1	8	yes	complemented
62	C₂²×M₁₆	C₂²×C₁₃₁	1	4	yes	—
63	C₂²×C₄²	C₂²×C₁₃₁	1	3	yes	—
64	#423	—	2	24	no	—
65	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	24	yes	—
66	#376	C₄×C₁₃₁	1	4	yes	—
67	#376	C₂²×C₁₃₁	1	4	yes	—
68	C₂×#95	C₄×C₁₃₁	1	4	yes	—
69	C₂³×C₄	C₂×C₄×C₁₃₁	1	6	yes	—
70	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
71	C₂×M₁₆	—	2	24	no	—
72	C₂²×C₈	C₂³×C₁₃₁	1	8	yes	—
73	C₂×C₄²	C₂×C₄×C₁₃₁	1	6	yes	—
74	C₂×C₄²	D₄×C₁₃₁	1	12	yes	—
75	C₂×C₄²	Q₈×C₁₃₁	1	12	yes	—
76	C₂×C₄²	C₂³×C₁₃₁	1	6	yes	—
77	C₄⋊C₈	—	2	48	no	—
78	#95	C₂×C₄×C₁₃₁	1	16	yes	—
79	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
80	C₂²×C₄	—	4	12	no	—
81	C₂²×C₄	C₄⋊C₄×C₁₃₁	1	24	yes	—
82	C₂²×C₄	C₂²×C₄×C₁₃₁	1	12	yes	—
83	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
84	C₂²×C₄	C₂×D₄×C₁₃₁	1	6	yes	—
85	C₂²×C₄	C₂×Q₈×C₁₃₁	1	6	yes	—
86	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
87	M₁₆	—	4	16	no	—
88	C₂×C₈	—	2	24	no	—
89	C₄²	C₄⋊C₄×C₁₃₁	1	24	yes	—
90	C₄²	C₂×D₄×C₁₃₁	1	12	yes	—
91	C₄²	C₂×Q₈×C₁₃₁	1	12	yes	—
92	C₂³	—	2	4	no	—
93	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	6	yes	—
94	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
95	C₂×C₄	—	2	24	no	—
96	C₂×C₄	—	4	24	no	—
97	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	24	yes	—
98	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	6	yes	—
99	C₂×C₄	#127×C₁₃₁	1	4	yes	—
100	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	12	yes	—
101	C₂×C₄	C₂²×D₄×C₁₃₁	1	3	yes	—
102	C₂×C₄	C₂²×Q₈×C₁₃₁	1	3	yes	—
103	C₈	—	4	8	no	—
104	C₂²	—	2	12	no	—
105	C₂²	#384×C₁₃₁	1	4	yes	—
106	C₂²	C₂²×C₄⋊C₄×C₁₃₁	1	3	yes	—
107	C₂²	#568×C₁₃₁	1	4	yes	—
108	C₄	—	2	24	no	—
109	C₄	#384×C₁₃₁	1	4	yes	—
110	C₄	C₂×#127×C₁₃₁	1	1	yes	characteristic
111	C₄	C₂×C₄⋊Q₈×C₁₃₁	1	3	yes	—
112	C₂	—	2	4	no	—
113	C₂	C₂×#384×C₁₃₁	1	1	yes	characteristic
114	C₂	#2905×C₁₃₁	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#423×C₁₃₁

C₂

yes

maximal

C₂×#376×C₁₃₁

C₂

yes

maximal, characteristic

#1843×C₁₃₁

C₂

yes

maximal, complemented

C₂²×M₁₆×C₁₃₁

C₂²

yes

—

C₂²×C₄²×C₁₃₁

C₂²

yes

—

#423×C₁₃₁

—

C₂×C₄⋊C₈×C₁₃₁

C₂²

yes

—

#376×C₁₃₁

C₄

yes

—

#376×C₁₃₁

C₂²

yes

—

C₂×#95×C₁₃₁

C₄

yes

—

C₂³×C₄×C₁₃₁

C₂×C₄

yes

—

C₂³×C₄×C₁₃₁

C₂³

yes

characteristic

C₂×M₁₆×C₁₃₁

—

C₂²×C₈×C₁₃₁

C₂³

yes

—

C₂×C₄²×C₁₃₁

C₂×C₄

yes

—

C₂×C₄²×C₁₃₁

D₄

yes

—

C₂×C₄²×C₁₃₁

Q₈

yes

—

C₂×C₄²×C₁₃₁

C₂³

yes

—

C₄⋊C₈×C₁₃₁

—

#95×C₁₃₁

C₂×C₄

yes

—

C₂⁴×C₁₃₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃₁

—

C₂²×C₄×C₁₃₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₃₁

C₂²×C₄

yes

—

C₂²×C₄×C₁₃₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃₁

C₂×D₄

yes

—

C₂²×C₄×C₁₃₁

C₂×Q₈

yes

—

C₂²×C₄×C₁₃₁

C₂⁴

yes

characteristic

M₁₆×C₁₃₁

—

C₂×C₈×C₁₃₁

—

C₄²×C₁₃₁

C₄⋊C₄

yes

—

C₄²×C₁₃₁

C₂×D₄

yes

—

C₄²×C₁₃₁

C₂×Q₈

yes

—

C₂³×C₁₃₁

—

C₂³×C₁₃₁

C₂×C₄⋊C₄

yes

—

C₂³×C₁₃₁

C₂³×C₄

yes

characteristic

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

—

C₂×C₄×C₁₃₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃₁

#127

yes

—

C₂×C₄×C₁₃₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₃₁

C₂²×D₄

yes

—

C₂×C₄×C₁₃₁

C₂²×Q₈

yes

—

C₈×C₁₃₁

—

C₂²×C₁₃₁

—

C₂²×C₁₃₁

#384

yes

—

C₂²×C₁₃₁

C₂²×C₄⋊C₄

yes

—

C₂²×C₁₃₁

#568

yes

—

C₄×C₁₃₁

—

C₄×C₁₃₁

#384

yes

—

C₄×C₁₃₁

C₂×#127

yes

characteristic

C₄×C₁₃₁

C₂×C₄⋊Q₈

yes

—

C₂×C₁₃₁

—

C₂×C₁₃₁

C₂×#384

yes

characteristic

C₂×C₁₃₁

#2905

yes

—

#20792

C₁₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₁₃₁

#20792

yes

characteristic, direct product factor, Sylow

C₂×#423

C₂×C₁₃₁

yes

—

C₂×#376

C₂×C₁₃₁

yes

characteristic

#1843

C₂×C₁₃₁

yes

complemented

C₂²×M₁₆

C₂²×C₁₃₁

yes

—

C₂²×C₄²

C₂²×C₁₃₁

yes

—

#423

—

C₂×C₄⋊C₈

C₂²×C₁₃₁

yes

—

#376

C₄×C₁₃₁

yes

—

#376

C₂²×C₁₃₁

yes

—

C₂×#95

C₄×C₁₃₁

yes

—

C₂³×C₄

C₂×C₄×C₁₃₁

yes

—

C₂³×C₄

C₂³×C₁₃₁

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂³×C₁₃₁

yes

—

C₂×C₄²

C₂×C₄×C₁₃₁

yes

—

C₂×C₄²

D₄×C₁₃₁

yes

—

C₂×C₄²

Q₈×C₁₃₁

yes

—

C₂×C₄²

C₂³×C₁₃₁

yes

—

C₄⋊C₈

—

#95

C₂×C₄×C₁₃₁

yes

—

C₂⁴

C₂²×C₄×C₁₃₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄⋊C₄×C₁₃₁

yes

—

C₂²×C₄

C₂²×C₄×C₁₃₁

yes

—

C₂²×C₄

C₂²×C₄×C₁₃₁

yes

characteristic

C₂²×C₄

C₂×D₄×C₁₃₁

yes

—

C₂²×C₄

C₂×Q₈×C₁₃₁

yes

—

C₂²×C₄

C₂⁴×C₁₃₁

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄²

C₄⋊C₄×C₁₃₁

yes

—

C₄²

C₂×D₄×C₁₃₁

yes

—

C₄²

C₂×Q₈×C₁₃₁

yes

—

C₂³

—

C₂³

C₂×C₄⋊C₄×C₁₃₁

yes

—

C₂³

C₂³×C₄×C₁₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄⋊C₄×C₁₃₁

yes

—

C₂×C₄

C₂×C₄⋊C₄×C₁₃₁

yes

—

C₂×C₄

#127×C₁₃₁

yes

—

100

C₂×C₄

C₄⋊Q₈×C₁₃₁

yes

—

101

C₂×C₄

C₂²×D₄×C₁₃₁

yes

—

102

C₂×C₄

C₂²×Q₈×C₁₃₁

yes

—

103

C₈

—

104

C₂²

—

105

C₂²

#384×C₁₃₁

yes

—

106

C₂²

C₂²×C₄⋊C₄×C₁₃₁

yes

—

107

C₂²

#568×C₁₃₁

yes

—

108

C₄

—

109

C₄

#384×C₁₃₁

yes

—

110

C₄

C₂×#127×C₁₃₁

yes

characteristic

111

C₄

C₂×C₄⋊Q₈×C₁₃₁

yes

—

112

C₂

—

113

C₂

C₂×#384×C₁₃₁

yes

characteristic

114

C₂

#2905×C₁₃₁

yes

—

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂³×C₁₃₁	C₂³×C₄
prime radical	C₂⁴×C₁₃₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

subgroup

G/H

center

C₂²×C₄×C₁₃₁

C₂⁴

commutator

C₂³

C₂³×C₄×C₁₃₁

Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₃₁

socle

C₂³×C₁₃₁

C₂³×C₄

prime radical

C₂⁴×C₁₃₁

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

N	H ≅ G/N	type
3. #1843×C₁₃₁	C₂	semidirect
57. #20792	C₁₃₁	direct (N × H)
58. C₁₃₁	#20792	direct (N × H)
61. #1843	C₂×C₁₃₁	semidirect

H ≅ G/N

type

3. #1843×C₁₃₁

C₂

semidirect

57. #20792

C₁₃₁

direct (N × H)

58. C₁₃₁

#20792

direct (N × H)

61. #1843

C₂×C₁₃₁

semidirect

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

subgroup	index
C₂×#423×C₁₃₁	2
C₂×#376×C₁₃₁	2
#1843×C₁₃₁	2
#20792	131

subgroup

index

C₂×#423×C₁₃₁

C₂×#376×C₁₃₁

#1843×C₁₃₁

#20792

131

Subgroups — C₁₃₁×#20792 #45706676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C131×#20792 #45706676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#20792 #45706676