Subgroups — C₁₃₇×#7548 #46856934

Order 35072.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₂₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1425×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1424×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
5	#368×C₁₃₇	—	2	1	no	—
6	#366×C₁₃₇	—	2	1	no	—
7	C₆₄×C₁₃₇	C₄	1	2	yes	complemented
8	C₂×C₁₆×C₁₃₇	D₄	1	1	yes	characteristic
9	#108×C₁₃₇	—	4	1	no	—
10	#107×C₁₃₇	—	4	1	no	—
11	C₃₂×C₁₃₇	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₁₃₇	Q₈	1	1	yes	characteristic
13	M₁₆×C₁₃₇	—	8	1	no	—
14	C₂×C₈×C₁₃₇	D₈	1	1	yes	characteristic
15	C₄⋊C₄×C₁₃₇	—	8	1	no	—
16	C₁₆×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₁₃₇	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₁₃₇	—	16	1	no	—
19	C₂×C₄×C₁₃₇	D₁₆	1	1	yes	characteristic
20	C₈×C₁₃₇	—	16	1	no	—
21	C₈×C₁₃₇	#107	1	1	yes	characteristic
22	C₈×C₁₃₇	Q₃₂	1	1	yes	characteristic
23	C₂²×C₁₃₇	SD₆₄	1	1	yes	characteristic
24	C₄×C₁₃₇	—	32	1	no	—
25	C₄×C₁₃₇	#366	1	1	yes	characteristic
26	C₄×C₁₃₇	SD₆₄	1	1	yes	characteristic
27	C₂×C₁₃₇	—	2	1	no	—
28	C₂×C₁₃₇	#1424	1	1	yes	characteristic
29	#7548	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₁₃₇	#7548	1	1	yes	characteristic, direct product factor, Sylow
31	M₁₂₈	C₂×C₁₃₇	1	1	yes	characteristic
32	#1425	C₂×C₁₃₇	1	1	yes	characteristic
33	#1424	C₂×C₁₃₇	1	1	yes	characteristic
34	C₂×C₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
35	#368	—	2	1	no	—
36	#366	—	2	1	no	—
37	C₆₄	C₄×C₁₃₇	1	2	yes	complemented
38	C₂×C₁₆	D₄×C₁₃₇	1	1	yes	characteristic
39	#108	—	4	1	no	—
40	#107	—	4	1	no	—
41	C₃₂	C₂×C₄×C₁₃₇	1	1	yes	characteristic
42	C₃₂	Q₈×C₁₃₇	1	1	yes	characteristic
43	M₁₆	—	8	1	no	—
44	C₂×C₈	D₈×C₁₃₇	1	1	yes	characteristic
45	C₄⋊C₄	—	8	1	no	—
46	C₁₆	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
47	C₁₆	Q₁₆×C₁₃₇	1	1	yes	characteristic
48	C₂×C₄	—	16	1	no	—
49	C₂×C₄	D₁₆×C₁₃₇	1	1	yes	characteristic
50	C₈	—	16	1	no	—
51	C₈	#107×C₁₃₇	1	1	yes	characteristic
52	C₈	Q₃₂×C₁₃₇	1	1	yes	characteristic
53	C₂²	SD₆₄×C₁₃₇	1	1	yes	characteristic
54	C₄	—	32	1	no	—
55	C₄	#366×C₁₃₇	1	1	yes	characteristic
56	C₄	SD₆₄×C₁₃₇	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#1424×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₇	#1424
commutator	C₃₂	C₂×C₄×C₁₃₇
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₃₇
prime radical	C₂²×C₁₃₇	SD₆₄
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₇ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₈×C₁₃₇ ◁ C₂×C₁₆×C₁₃₇ ◁ C₂×C₃₂×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₆₄×C₁₃₇	C₄	semidirect
29. #7548	C₁₃₇	direct (N × H)
30. C₁₃₇	#7548	direct (N × H)
37. C₆₄	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
M₁₂₈×C₁₃₇	2
#1425×C₁₃₇	2
#1424×C₁₃₇	2
#7548	137

Subgroups — C137×#7548 #46856934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#7548 #46856934