Subgroups — C₁₃₁×#7456 #45693340

Order 33536.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1422×C₁₃₁	C₂	1	2	yes	maximal
2	#1311×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₁₃₁	—	2	2	no	—
4	C₄×C₁₆×C₁₃₁	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
6	C₈²×C₁₃₁	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₃₁	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₃₁	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₁₃₁	D₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₃₁	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₃₁	—	2	1	no	—
12	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₁₃₁	—	4	2	no	—
14	C₂×C₈×C₁₃₁	—	2	2	no	—
15	C₂×C₈×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃₁	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₁₃₁	M₁₆	1	1	yes	characteristic
18	C₁₆×C₁₃₁	—	2	1	no	—
19	C₁₆×C₁₃₁	—	2	1	no	—
20	C₁₆×C₁₃₁	C₁₆	1	2	yes	—
21	C₁₆×C₁₃₁	SD₁₆	1	2	yes	—
22	C₂×C₄×C₁₃₁	—	2	1	no	—
23	C₂×C₄×C₁₃₁	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₁₃₁	—	4	2	no	—
25	C₈×C₁₃₁	#106	1	1	yes	characteristic
26	C₈×C₁₃₁	#108	1	1	yes	characteristic
27	C₈×C₁₃₁	C₂×C₁₆	1	1	yes	characteristic
28	C₈×C₁₃₁	M₃₂	1	1	yes	characteristic
29	C₂²×C₁₃₁	#364	1	1	yes	characteristic
30	C₄×C₁₃₁	—	2	2	no	—
31	C₄×C₁₃₁	#334	1	1	yes	characteristic
32	C₄×C₁₃₁	C₄⋊C₁₆	1	1	yes	characteristic
33	C₂×C₁₃₁	—	2	1	no	—
34	C₂×C₁₃₁	#1367	1	1	yes	characteristic
35	#7456	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₁₃₁	#7456	1	1	yes	characteristic, direct product factor, Sylow
37	#1422	C₂×C₁₃₁	1	2	yes	—
38	#1311	C₂×C₁₃₁	1	1	yes	characteristic
39	M₆₄	—	2	2	no	—
40	C₄×C₁₆	C₄×C₁₃₁	1	1	yes	characteristic
41	C₄×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
42	C₈²	C₄×C₁₃₁	1	1	yes	characteristic
43	C₂×C₁₆	C₈×C₁₃₁	1	1	yes	characteristic
44	C₂×C₁₆	C₈×C₁₃₁	1	1	yes	characteristic
45	C₂×C₁₆	D₄×C₁₃₁	1	1	yes	characteristic
46	C₂×C₁₆	Q₈×C₁₃₁	1	1	yes	characteristic
47	C₄×C₈	—	2	1	no	—
48	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
49	C₃₂	—	4	2	no	—
50	C₂×C₈	—	2	2	no	—
51	C₂×C₈	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
52	C₂×C₈	C₂×C₈×C₁₃₁	1	1	yes	characteristic
53	C₄²	M₁₆×C₁₃₁	1	1	yes	characteristic
54	C₁₆	—	2	1	no	—
55	C₁₆	—	2	1	no	—
56	C₁₆	C₁₆×C₁₃₁	1	2	yes	—
57	C₁₆	SD₁₆×C₁₃₁	1	2	yes	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₄⋊C₈×C₁₃₁	1	1	yes	characteristic
60	C₈	—	4	2	no	—
61	C₈	#106×C₁₃₁	1	1	yes	characteristic
62	C₈	#108×C₁₃₁	1	1	yes	characteristic
63	C₈	C₂×C₁₆×C₁₃₁	1	1	yes	characteristic
64	C₈	M₃₂×C₁₃₁	1	1	yes	characteristic
65	C₂²	#364×C₁₃₁	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	#334×C₁₃₁	1	1	yes	characteristic
68	C₄	C₄⋊C₁₆×C₁₃₁	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#1367×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₃₁	#106
commutator	C₈	C₂×C₁₆×C₁₃₁
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃₁
socle	C₂×C₁₃₁	#1367
prime radical	C₂²×C₁₃₁	#364
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃₁ ◁ C₂×C₁₆×C₁₃₁ ◁ C₄×C₁₆×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
35. #7456	C₁₃₁	direct (N × H)
36. C₁₃₁	#7456	direct (N × H)

Maximal subgroups

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

subgroup	index
#1422×C₁₃₁	2
#1311×C₁₃₁	2
#7456	131

Subgroups — C131×#7456 #45693340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7456 #45693340