Subgroups — C₃₇×#3573 #17992391

Order 4736.

1424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#585	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#568	C₂	1	15	yes	maximal, complemented
3	C₂×#131×C₃₇	C₂	1	15	yes	maximal, complemented
4	2₋¹⁺⁴×C₃₇	C₄	1	6	yes	—
5	H(5,𝔽₂)×C₃₇	C₄	1	10	yes	—
6	C₂×#41×C₃₇	C₂²	1	15	yes	—
7	#131×C₃₇	C₂²	1	20	yes	complemented
8	#131×C₃₇	C₂²	1	60	yes	complemented
9	C₂×M₁₆×C₃₇	C₂²	1	45	yes	complemented
10	C₂²×C₈×C₃₇	C₂²	1	15	yes	complemented
11	#41×C₃₇	C₂×C₄	1	60	yes	—
12	#41×C₃₇	C₂³	1	20	yes	—
13	C₂×Q₈×C₃₇	C₂×C₄	1	15	yes	—
14	C₂×D₄×C₃₇	C₂×C₄	1	45	yes	—
15	C₂²×C₄×C₃₇	C₂³	1	15	yes	—
16	M₁₆×C₃₇	C₂³	1	60	yes	—
17	C₂×C₈×C₃₇	C₂³	1	45	yes	—
18	C₂×C₈×C₃₇	C₂³	1	15	yes	—
19	C₂³×C₃₇	C₂²×C₄	1	15	yes	—
20	Q₈×C₃₇	C₂²×C₄	1	20	yes	—
21	D₄×C₃₇	C₂²×C₄	1	60	yes	—
22	C₂×C₄×C₃₇	C₂²×C₄	1	45	yes	—
23	C₂×C₄×C₃₇	C₂⁴	1	15	yes	—
24	C₈×C₃₇	C₂⁴	1	15	yes	—
25	C₈×C₃₇	C₂⁴	1	1	yes	characteristic
26	C₂²×C₃₇	—	4	15	no	—
27	C₂²×C₃₇	C₂³×C₄	1	15	yes	—
28	C₄×C₃₇	C₂³×C₄	1	15	yes	—
29	C₄×C₃₇	C₂⁵	1	1	yes	characteristic
30	#3573	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₃₇	—	2	15	no	—
32	C₂×C₃₇	C₂⁴×C₄	1	1	yes	characteristic
33	#585	C₂×C₃₇	1	1	yes	characteristic
34	#568	C₂×C₃₇	1	15	yes	complemented
35	C₂×#131	C₂×C₃₇	1	15	yes	complemented
36	C₃₇	#3573	1	1	yes	characteristic, direct product factor, Sylow
37	2₋¹⁺⁴	C₄×C₃₇	1	6	yes	—
38	H(5,𝔽₂)	C₄×C₃₇	1	10	yes	—
39	C₂×#41	C₂²×C₃₇	1	15	yes	—
40	#131	C₂²×C₃₇	1	20	yes	complemented
41	#131	C₂²×C₃₇	1	60	yes	complemented
42	C₂×M₁₆	C₂²×C₃₇	1	45	yes	complemented
43	C₂²×C₈	C₂²×C₃₇	1	15	yes	complemented
44	#41	C₂×C₄×C₃₇	1	60	yes	—
45	#41	C₂³×C₃₇	1	20	yes	—
46	C₂×Q₈	C₂×C₄×C₃₇	1	15	yes	—
47	C₂×D₄	C₂×C₄×C₃₇	1	45	yes	—
48	C₂²×C₄	C₂³×C₃₇	1	15	yes	—
49	M₁₆	C₂³×C₃₇	1	60	yes	—
50	C₂×C₈	C₂³×C₃₇	1	15	yes	—
51	C₂×C₈	C₂³×C₃₇	1	45	yes	—
52	C₂³	C₂²×C₄×C₃₇	1	15	yes	—
53	Q₈	C₂²×C₄×C₃₇	1	20	yes	—
54	D₄	C₂²×C₄×C₃₇	1	60	yes	—
55	C₂×C₄	C₂²×C₄×C₃₇	1	45	yes	—
56	C₂×C₄	C₂⁴×C₃₇	1	15	yes	—
57	C₈	C₂⁴×C₃₇	1	1	yes	characteristic
58	C₈	C₂⁴×C₃₇	1	15	yes	—
59	C₂²	—	4	15	no	—
60	C₂²	C₂³×C₄×C₃₇	1	15	yes	—
61	C₄	C₂³×C₄×C₃₇	1	15	yes	—
62	C₄	C₂⁵×C₃₇	1	1	yes	characteristic
63	C₂	—	2	15	no	—
64	C₂	C₂⁴×C₄×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₃₇	C₂⁴
commutator	C₂	C₂⁴×C₄×C₃₇
Frattini, cosocle	C₄	C₂⁵×C₃₇
socle	C₂×C₃₇	C₂⁴×C₄
prime radical	C₃₇×#585	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#568	C₂	semidirect
3. C₂×#131×C₃₇	C₂	semidirect
7. #131×C₃₇	C₂²	semidirect
8. #131×C₃₇	C₂²	semidirect
9. C₂×M₁₆×C₃₇	C₂²	semidirect
10. C₂²×C₈×C₃₇	C₂²	semidirect
30. #3573	C₃₇	direct (N × H)
34. #568	C₂×C₃₇	semidirect
35. C₂×#131	C₂×C₃₇	semidirect
36. C₃₇	#3573	direct (N × H)
40. #131	C₂²×C₃₇	semidirect
41. #131	C₂²×C₃₇	semidirect
42. C₂×M₁₆	C₂²×C₃₇	semidirect
43. C₂²×C₈	C₂²×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#585	2
C₃₇×#568	2
C₂×#131×C₃₇	2
#3573	37

Subgroups — C37×#3573 #17992391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#3573 #17992391