Subgroups — C₁₃₁×#7531 #45693415

Order 33536.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1709×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1411×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#494×C₁₃₁	C₂²	1	1	yes	characteristic
4	#493×C₁₃₁	C₄	1	1	yes	characteristic
5	#486×C₁₃₁	—	2	2	no	—
6	#356×C₁₃₁	—	2	2	no	—
7	C₈²×C₁₃₁	C₄	1	1	yes	characteristic
8	C₂×Q₁₆×C₁₃₁	—	4	1	no	—
9	C₂×D₈×C₁₃₁	—	4	1	no	—
10	C₄⋊Q₈×C₁₃₁	D₄	1	2	yes	—
11	#127×C₁₃₁	—	2	1	no	—
12	#102×C₁₃₁	—	4	4	no	—
13	#101×C₁₃₁	—	4	2	no	—
14	C₄×C₈×C₁₃₁	—	2	1	no	—
15	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Q₈×C₁₃₁	—	2	2	no	—
17	C₂×D₄×C₁₃₁	—	4	2	no	—
18	C₂×D₄×C₁₃₁	—	4	1	no	—
19	Q₁₆×C₁₃₁	—	8	2	no	—
20	D₈×C₁₃₁	—	8	2	no	—
21	M₁₆×C₁₃₁	—	8	2	no	—
22	C₂×C₈×C₁₃₁	—	2	1	no	—
23	C₂×C₈×C₁₃₁	—	2	2	no	—
24	C₄⋊C₄×C₁₃₁	—	4	2	no	—
25	C₄²×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂³×C₁₃₁	—	8	1	no	—
27	Q₈×C₁₃₁	—	8	2	no	—
28	D₄×C₁₃₁	—	8	2	no	—
29	D₄×C₁₃₁	—	8	4	no	—
30	C₂×C₄×C₁₃₁	—	2	1	no	—
31	C₂×C₄×C₁₃₁	—	4	2	no	—
32	C₂×C₄×C₁₃₁	#99	1	1	yes	characteristic
33	C₈×C₁₃₁	—	2	2	no	—
34	C₈×C₁₃₁	—	4	2	no	—
35	C₈×C₁₃₁	—	16	2	no	—
36	C₂²×C₁₃₁	—	16	2	no	—
37	C₂²×C₁₃₁	—	16	1	no	—
38	C₂²×C₁₃₁	#353	1	1	yes	characteristic
39	C₄×C₁₃₁	—	2	2	no	—
40	C₄×C₁₃₁	—	2	1	no	—
41	C₄×C₁₃₁	—	8	2	no	—
42	C₂×C₁₃₁	—	2	1	no	—
43	C₂×C₁₃₁	—	32	1	no	—
44	C₂×C₁₃₁	#1408	1	1	yes	characteristic
45	#7531	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₁₃₁	#7531	1	1	yes	characteristic, direct product factor, Sylow
47	#1709	C₂×C₁₃₁	1	1	yes	characteristic
48	#1411	C₂×C₁₃₁	1	2	yes	complemented
49	#494	C₂²×C₁₃₁	1	1	yes	characteristic
50	#493	C₄×C₁₃₁	1	1	yes	characteristic
51	#486	—	2	2	no	—
52	#356	—	2	2	no	—
53	C₈²	C₄×C₁₃₁	1	1	yes	characteristic
54	C₂×Q₁₆	—	4	1	no	—
55	C₂×D₈	—	4	1	no	—
56	C₄⋊Q₈	D₄×C₁₃₁	1	2	yes	—
57	#127	—	2	1	no	—
58	#102	—	4	4	no	—
59	#101	—	4	2	no	—
60	C₄×C₈	—	2	1	no	—
61	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
62	C₂×Q₈	—	2	2	no	—
63	C₂×D₄	—	4	2	no	—
64	C₂×D₄	—	4	1	no	—
65	Q₁₆	—	8	2	no	—
66	D₈	—	8	2	no	—
67	M₁₆	—	8	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₄⋊C₄	—	4	2	no	—
71	C₄²	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	8	2	no	—
74	D₄	—	8	2	no	—
75	D₄	—	8	4	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	2	no	—
78	C₂×C₄	#99×C₁₃₁	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	4	2	no	—
81	C₈	—	16	2	no	—
82	C₂²	—	16	2	no	—
83	C₂²	—	16	1	no	—
84	C₂²	#353×C₁₃₁	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	2	1	no	—
87	C₄	—	8	2	no	—
88	C₂	—	2	1	no	—
89	C₂	—	32	1	no	—
90	C₂	#1408×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₁	#1408
commutator	C₄×C₈	C₂×C₄×C₁₃₁
Frattini, cosocle	#494	C₂²×C₁₃₁
prime radical	#493×C₁₃₁	C₄
LCS	G ▷ C₄×C₈ ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄×C₁₃₁ ◁ C₄²×C₁₃₁ ◁ #494×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #1411×C₁₃₁	C₂	semidirect
45. #7531	C₁₃₁	direct (N × H)
46. C₁₃₁	#7531	direct (N × H)
48. #1411	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#1709×C₁₃₁	2
#1411×C₁₃₁	2
#7531	131

Subgroups — C131×#7531 #45693415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7531 #45693415