Subgroups — C₃₇×#1373 #17990191

Order 4736.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#364	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₃₇	—	2	2	no	—
4	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
6	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
9	C₄²×C₃₇	Q₈	1	1	yes	characteristic
10	C₁₆×C₃₇	—	2	1	no	—
11	C₁₆×C₃₇	—	4	2	no	—
12	C₁₆×C₃₇	C₈	1	2	yes	—
13	C₂×C₄×C₃₇	—	2	1	no	—
14	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
16	C₈×C₃₇	M₁₆	1	1	yes	characteristic
17	C₈×C₃₇	D₈	1	1	yes	characteristic
18	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
19	C₂²×C₃₇	#108	1	1	yes	characteristic
20	C₄×C₃₇	—	2	2	no	—
21	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₃₇	#107	1	1	yes	characteristic
23	#1373	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×C₃₇	—	2	1	no	—
25	C₂×C₃₇	#335	1	1	yes	characteristic
26	#364	C₂×C₃₇	1	2	yes	—
27	C₄×C₁₆	C₂×C₃₇	1	1	yes	characteristic
28	C₃₇	#1373	1	1	yes	characteristic, direct product factor, Sylow
29	M₃₂	—	2	2	no	—
30	C₂×C₁₆	C₄×C₃₇	1	1	yes	characteristic
31	C₂×C₁₆	C₄×C₃₇	1	1	yes	characteristic
32	C₄×C₈	C₂²×C₃₇	1	1	yes	characteristic
33	C₂×C₈	C₂×C₄×C₃₇	1	1	yes	characteristic
34	C₂×C₈	D₄×C₃₇	1	1	yes	characteristic
35	C₄²	Q₈×C₃₇	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	4	2	no	—
38	C₁₆	C₈×C₃₇	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊C₄×C₃₇	1	1	yes	characteristic
41	C₈	C₂×C₈×C₃₇	1	1	yes	characteristic
42	C₈	M₁₆×C₃₇	1	1	yes	characteristic
43	C₈	D₈×C₃₇	1	1	yes	characteristic
44	C₈	Q₁₆×C₃₇	1	1	yes	characteristic
45	C₂²	#108×C₃₇	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊C₈×C₃₇	1	1	yes	characteristic
48	C₄	#107×C₃₇	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	C₃₇×#335	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₃₇	D₈
commutator	C₈	C₂×C₈×C₃₇
Frattini, cosocle	C₄×C₈	C₂²×C₃₇
socle	C₂×C₃₇	#335
prime radical	C₂²×C₃₇	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₇ ◁ C₂×C₈×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
23. #1373	C₃₇	direct (N × H)
28. C₃₇	#1373	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#364	2
C₄×C₁₆×C₃₇	2
#1373	37

Subgroups — C37×#1373 #17990191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#1373 #17990191