Subgroups — C₁₃₁×#7463 #45693347

Order 33536.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1397×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1372×C₁₃₁	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₁₃₁	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₁₃₁	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
6	#335×C₁₃₁	—	2	2	no	—
7	C₂×C₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₁₃₁	Q₈	1	1	yes	characteristic
9	C₄⋊C₈×C₁₃₁	—	4	2	no	—
10	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
11	C₃₂×C₁₃₁	—	2	1	no	—
12	C₃₂×C₁₃₁	C₈	1	2	yes	complemented
13	C₂×C₈×C₁₃₁	—	8	2	no	—
14	C₂×C₈×C₁₃₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃₁	Q₁₆	1	1	yes	characteristic
16	C₄²×C₁₃₁	D₈	1	1	yes	characteristic
17	C₁₆×C₁₃₁	—	2	1	no	—
18	C₁₆×C₁₃₁	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₁₃₁	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₃₁	#107	1	1	yes	characteristic
21	C₂×C₄×C₁₃₁	SD₃₂	1	2	yes	—
22	C₈×C₁₃₁	—	2	1	no	—
23	C₈×C₁₃₁	—	16	2	no	—
24	C₈×C₁₃₁	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₁₃₁	#108	1	1	yes	characteristic
26	C₂²×C₁₃₁	#367	1	1	yes	characteristic
27	C₄×C₁₃₁	—	2	2	no	—
28	C₄×C₁₃₁	#335	1	1	yes	characteristic
29	C₄×C₁₃₁	#368	1	1	yes	characteristic
30	C₂×C₁₃₁	#1372	1	1	yes	characteristic
31	C₂×C₁₃₁	#1426	1	2	yes	—
32	#7463	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₁₃₁	#7463	1	1	yes	characteristic, direct product factor, Sylow
34	#1397	C₂×C₁₃₁	1	1	yes	characteristic
35	#1372	C₂×C₁₃₁	1	2	yes	—
36	C₂×C₃₂	C₄×C₁₃₁	1	1	yes	characteristic
37	C₂×C₃₂	C₄×C₁₃₁	1	1	yes	characteristic
38	C₄×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
39	#335	—	2	2	no	—
40	C₂×C₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
41	C₂×C₁₆	Q₈×C₁₃₁	1	1	yes	characteristic
42	C₄⋊C₈	—	4	2	no	—
43	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
44	C₃₂	—	2	1	no	—
45	C₃₂	C₈×C₁₃₁	1	2	yes	complemented
46	C₂×C₈	—	8	2	no	—
47	C₂×C₈	C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
48	C₂×C₈	Q₁₆×C₁₃₁	1	1	yes	characteristic
49	C₄²	D₈×C₁₃₁	1	1	yes	characteristic
50	C₁₆	—	2	1	no	—
51	C₁₆	C₂×C₈×C₁₃₁	1	1	yes	characteristic
52	C₁₆	M₁₆×C₁₃₁	1	1	yes	characteristic
53	C₂×C₄	#107×C₁₃₁	1	1	yes	characteristic
54	C₂×C₄	SD₃₂×C₁₃₁	1	2	yes	—
55	C₈	—	2	1	no	—
56	C₈	—	16	2	no	—
57	C₈	C₄⋊C₈×C₁₃₁	1	1	yes	characteristic
58	C₈	#108×C₁₃₁	1	1	yes	characteristic
59	C₂²	#367×C₁₃₁	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	#335×C₁₃₁	1	1	yes	characteristic
62	C₄	#368×C₁₃₁	1	1	yes	characteristic
63	C₂	#1372×C₁₃₁	1	1	yes	characteristic
64	C₂	#1426×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃₁	#367
commutator	C₁₆	C₂×C₈×C₁₃₁
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃₁
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₄²×C₁₃₁ ◁ C₄×C₈×C₁₃₁ ◁ C₄×C₁₆×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₃₂×C₁₃₁	C₈	semidirect
32. #7463	C₁₃₁	direct (N × H)
33. C₁₃₁	#7463	direct (N × H)
45. 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
#1397×C₁₃₁	2
#1372×C₁₃₁	2
#7463	131

Subgroups — C131×#7463 #45693347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7463 #45693347