Subgroups — C₁₃₁×#7541 #45693425

Order 33536.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	M₁₂₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#1425×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₁₃₁	—	2	1	no	—
5	D₃₂×C₁₃₁	—	2	1	no	—
6	D₃₂×C₁₃₁	C₄	1	2	yes	—
7	C₂×C₃₂×C₁₃₁	C₂²	1	1	yes	characteristic
8	#368×C₁₃₁	—	2	1	no	—
9	C₆₄×C₁₃₁	—	2	1	no	—
10	C₂×D₈×C₁₃₁	—	4	1	no	—
11	D₁₆×C₁₃₁	—	2	2	no	—
12	D₁₆×C₁₃₁	—	4	1	no	—
13	C₂×C₁₆×C₁₃₁	D₄	1	1	yes	characteristic
14	#108×C₁₃₁	—	4	1	no	—
15	C₃₂×C₁₃₁	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₁₃₁	D₄	1	1	yes	characteristic
17	C₂×D₄×C₁₃₁	—	8	1	no	—
18	D₈×C₁₃₁	—	4	2	no	—
19	D₈×C₁₃₁	—	8	1	no	—
20	M₁₆×C₁₃₁	—	8	1	no	—
21	C₂×C₈×C₁₃₁	D₈	1	1	yes	characteristic
22	C₁₆×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₃₁	SD₁₆	1	1	yes	characteristic
24	C₂³×C₁₃₁	—	16	1	no	—
25	D₄×C₁₃₁	—	8	2	no	—
26	D₄×C₁₃₁	—	16	1	no	—
27	C₂×C₄×C₁₃₁	D₁₆	1	1	yes	characteristic
28	C₈×C₁₃₁	—	16	1	no	—
29	C₈×C₁₃₁	#102	1	1	yes	characteristic
30	C₈×C₁₃₁	SD₃₂	1	1	yes	characteristic
31	C₂²×C₁₃₁	—	16	2	no	—
32	C₂²×C₁₃₁	—	32	2	no	—
33	C₂²×C₁₃₁	SD₆₄	1	1	yes	characteristic
34	C₄×C₁₃₁	#357	1	1	yes	characteristic
35	C₄×C₁₃₁	D₃₂	1	1	yes	characteristic
36	C₂×C₁₃₁	—	2	1	no	—
37	C₂×C₁₃₁	—	32	2	no	—
38	C₂×C₁₃₁	#1415	1	1	yes	characteristic
39	#7541	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₁₃₁	#7541	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×D₃₂	C₂×C₁₃₁	1	1	yes	characteristic
42	M₁₂₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
43	#1425	C₂×C₁₃₁	1	1	yes	characteristic, complemented
44	C₂×D₁₆	—	2	1	no	—
45	D₃₂	—	2	1	no	—
46	D₃₂	C₄×C₁₃₁	1	2	yes	—
47	C₂×C₃₂	C₂²×C₁₃₁	1	1	yes	characteristic
48	#368	—	2	1	no	—
49	C₆₄	—	2	1	no	—
50	C₂×D₈	—	4	1	no	—
51	D₁₆	—	2	2	no	—
52	D₁₆	—	4	1	no	—
53	C₂×C₁₆	D₄×C₁₃₁	1	1	yes	characteristic
54	#108	—	4	1	no	—
55	C₃₂	C₂×C₄×C₁₃₁	1	1	yes	characteristic
56	C₃₂	D₄×C₁₃₁	1	1	yes	characteristic
57	C₂×D₄	—	8	1	no	—
58	D₈	—	4	2	no	—
59	D₈	—	8	1	no	—
60	M₁₆	—	8	1	no	—
61	C₂×C₈	D₈×C₁₃₁	1	1	yes	characteristic
62	C₁₆	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
63	C₁₆	SD₁₆×C₁₃₁	1	1	yes	characteristic
64	C₂³	—	16	1	no	—
65	D₄	—	8	2	no	—
66	D₄	—	16	1	no	—
67	C₂×C₄	D₁₆×C₁₃₁	1	1	yes	characteristic
68	C₈	—	16	1	no	—
69	C₈	#102×C₁₃₁	1	1	yes	characteristic
70	C₈	SD₃₂×C₁₃₁	1	1	yes	characteristic
71	C₂²	—	16	2	no	—
72	C₂²	—	32	2	no	—
73	C₂²	SD₆₄×C₁₃₁	1	1	yes	characteristic
74	C₄	#357×C₁₃₁	1	1	yes	characteristic
75	C₄	D₃₂×C₁₃₁	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	32	2	no	—
78	C₂	#1415×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₁	#1415
commutator	C₃₂	C₂×C₄×C₁₃₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₃₁
prime radical	C₂×D₃₂×C₁₃₁	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₈×C₁₃₁ ◁ C₂×C₁₆×C₁₃₁ ◁ C₂×C₃₂×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. M₁₂₈×C₁₃₁	C₂	semidirect
3. #1425×C₁₃₁	C₂	semidirect
39. #7541	C₁₃₁	direct (N × H)
40. C₁₃₁	#7541	direct (N × H)
42. M₁₂₈	C₂×C₁₃₁	semidirect
43. #1425	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₂×C₁₃₁	2
M₁₂₈×C₁₃₁	2
#1425×C₁₃₁	2
#7541	131

Subgroups — C131×#7541 #45693425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7541 #45693425