Subgroups — C₁₃₇×#7462 #46856848

Order 35072.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1373×C₁₃₇	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₁₃₇	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₁₃₇	C₄	1	1	yes	characteristic
5	#364×C₁₃₇	—	2	2	no	—
6	C₄×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
7	M₃₂×C₁₃₇	—	4	2	no	—
8	C₂×C₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₃₇	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₁₃₇	D₄	1	1	yes	characteristic
11	C₃₂×C₁₃₇	—	2	1	no	—
12	C₃₂×C₁₃₇	C₈	1	2	yes	—
13	C₂×C₈×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₃₇	D₈	1	1	yes	characteristic
15	C₄²×C₁₃₇	Q₁₆	1	1	yes	characteristic
16	C₁₆×C₁₃₇	—	2	1	no	—
17	C₁₆×C₁₃₇	—	8	2	no	—
18	C₁₆×C₁₃₇	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₁₃₇	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₃₇	—	2	1	no	—
21	C₂×C₄×C₁₃₇	#107	1	1	yes	characteristic
22	C₈×C₁₃₇	C₄⋊C₈	1	1	yes	characteristic
23	C₈×C₁₃₇	#108	1	1	yes	characteristic
24	C₈×C₁₃₇	D₁₆	1	1	yes	characteristic
25	C₈×C₁₃₇	Q₃₂	1	1	yes	characteristic
26	C₂²×C₁₃₇	#368	1	1	yes	characteristic
27	C₄×C₁₃₇	—	2	2	no	—
28	C₄×C₁₃₇	#335	1	1	yes	characteristic
29	C₄×C₁₃₇	#366	1	1	yes	characteristic
30	C₂×C₁₃₇	—	2	1	no	—
31	C₂×C₁₃₇	#1371	1	1	yes	characteristic
32	#7462	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₁₃₇	#7462	1	1	yes	characteristic, direct product factor, Sylow
34	C₄×C₃₂	C₂×C₁₃₇	1	1	yes	characteristic
35	#1373	C₂×C₁₃₇	1	2	yes	—
36	C₂×C₃₂	C₄×C₁₃₇	1	1	yes	characteristic
37	C₂×C₃₂	C₄×C₁₃₇	1	1	yes	characteristic
38	#364	—	2	2	no	—
39	C₄×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
40	M₃₂	—	4	2	no	—
41	C₂×C₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
42	C₂×C₁₆	Q₈×C₁₃₇	1	1	yes	characteristic
43	C₄×C₈	D₄×C₁₃₇	1	1	yes	characteristic
44	C₃₂	—	2	1	no	—
45	C₃₂	C₈×C₁₃₇	1	2	yes	—
46	C₂×C₈	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
47	C₂×C₈	D₈×C₁₃₇	1	1	yes	characteristic
48	C₄²	Q₁₆×C₁₃₇	1	1	yes	characteristic
49	C₁₆	—	2	1	no	—
50	C₁₆	—	8	2	no	—
51	C₁₆	C₂×C₈×C₁₃₇	1	1	yes	characteristic
52	C₁₆	M₁₆×C₁₃₇	1	1	yes	characteristic
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	#107×C₁₃₇	1	1	yes	characteristic
55	C₈	C₄⋊C₈×C₁₃₇	1	1	yes	characteristic
56	C₈	#108×C₁₃₇	1	1	yes	characteristic
57	C₈	D₁₆×C₁₃₇	1	1	yes	characteristic
58	C₈	Q₃₂×C₁₃₇	1	1	yes	characteristic
59	C₂²	#368×C₁₃₇	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	#335×C₁₃₇	1	1	yes	characteristic
62	C₄	#366×C₁₃₇	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#1371×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₃₇	D₁₆
commutator	C₁₆	C₂×C₈×C₁₃₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃₇
socle	C₂×C₁₃₇	#1371
prime radical	C₂²×C₁₃₇	#368
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃₇ ◁ C₂×C₈×C₁₃₇ ◁ C₄×C₈×C₁₃₇ ◁ C₄×C₁₆×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
32. #7462	C₁₃₇	direct (N × H)
33. C₁₃₇	#7462	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₃₂×C₁₃₇	2
#1373×C₁₃₇	2
#7462	137

Subgroups — C137×#7462 #46856848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#7462 #46856848