Subgroups — C₁₃₁×#7457 #45693341

Order 33536.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1398×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1369×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1368×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	M₆₄×C₁₃₁	C₄	1	1	yes	characteristic
5	M₆₄×C₁₃₁	C₄	1	1	yes	characteristic
6	#364×C₁₃₁	—	2	1	no	—
7	#346×C₁₃₁	C₂²	1	1	yes	characteristic
8	#334×C₁₃₁	—	2	1	no	—
9	M₃₂×C₁₃₁	—	4	1	no	—
10	C₂×C₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₆×C₁₃₁	Q₈	1	1	yes	characteristic
12	C₄⋊C₈×C₁₃₁	—	4	1	no	—
13	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
14	C₃₂×C₁₃₁	—	2	1	no	—
15	C₃₂×C₁₃₁	C₈	1	2	yes	complemented
16	C₂×C₈×C₁₃₁	—	8	1	no	—
17	C₂×C₈×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃₁	SD₁₆	1	1	yes	characteristic
19	C₄²×C₁₃₁	SD₁₆	1	1	yes	characteristic
20	C₁₆×C₁₃₁	—	2	1	no	—
21	C₁₆×C₁₃₁	—	8	1	no	—
22	C₁₆×C₁₃₁	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₁₃₁	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₃₁	—	2	1	no	—
25	C₂×C₄×C₁₃₁	#106	1	1	yes	characteristic
26	C₈×C₁₃₁	—	2	1	no	—
27	C₈×C₁₃₁	—	16	1	no	—
28	C₈×C₁₃₁	C₄⋊C₈	1	1	yes	characteristic
29	C₈×C₁₃₁	#108	1	1	yes	characteristic
30	C₂²×C₁₃₁	#365	1	1	yes	characteristic
31	C₄×C₁₃₁	—	4	1	no	—
32	C₄×C₁₃₁	#334	1	1	yes	characteristic
33	C₄×C₁₃₁	#365	1	1	yes	characteristic
34	C₂×C₁₃₁	—	2	1	no	—
35	C₂×C₁₃₁	#1368	1	1	yes	characteristic
36	#7457	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₁₃₁	#7457	1	1	yes	characteristic, direct product factor, Sylow
38	#1398	C₂×C₁₃₁	1	1	yes	characteristic
39	#1369	C₂×C₁₃₁	1	1	yes	characteristic
40	#1368	C₂×C₁₃₁	1	1	yes	characteristic
41	M₆₄	C₄×C₁₃₁	1	1	yes	characteristic
42	M₆₄	C₄×C₁₃₁	1	1	yes	characteristic
43	#364	—	2	1	no	—
44	#346	C₂²×C₁₃₁	1	1	yes	characteristic
45	#334	—	2	1	no	—
46	M₃₂	—	4	1	no	—
47	C₂×C₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
48	C₂×C₁₆	Q₈×C₁₃₁	1	1	yes	characteristic
49	C₄⋊C₈	—	4	1	no	—
50	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
51	C₃₂	—	2	1	no	—
52	C₃₂	C₈×C₁₃₁	1	2	yes	complemented
53	C₂×C₈	—	8	1	no	—
54	C₂×C₈	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
55	C₂×C₈	SD₁₆×C₁₃₁	1	1	yes	characteristic
56	C₄²	SD₁₆×C₁₃₁	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	8	1	no	—
59	C₁₆	C₂×C₈×C₁₃₁	1	1	yes	characteristic
60	C₁₆	M₁₆×C₁₃₁	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#106×C₁₃₁	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	16	1	no	—
65	C₈	C₄⋊C₈×C₁₃₁	1	1	yes	characteristic
66	C₈	#108×C₁₃₁	1	1	yes	characteristic
67	C₂²	#365×C₁₃₁	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#334×C₁₃₁	1	1	yes	characteristic
70	C₄	#365×C₁₃₁	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#1368×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₁	#1368
commutator	C₁₆	C₂×C₈×C₁₃₁
Frattini, cosocle	#346	C₂²×C₁₃₁
prime radical	C₂²×C₁₃₁	#365
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₂×C₄×C₁₃₁ ◁ C₄×C₈×C₁₃₁ ◁ #346×C₁₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
15. C₃₂×C₁₃₁	C₈	semidirect
36. #7457	C₁₃₁	direct (N × H)
37. C₁₃₁	#7457	direct (N × H)
52. C₃₂	C₈×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#1398×C₁₃₁	2
#1369×C₁₃₁	2
#1368×C₁₃₁	2
#7457	131

Subgroups — C131×#7457 #45693341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7457 #45693341