Subgroups — C₃₇⋊#564 #14558288

Order 2368.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924528	C₂	1	2	yes	maximal
2	#11924527	C₂	1	4	yes	maximal
3	#11924526	C₂	1	4	yes	maximal
4	#11924526	C₂	1	4	yes	maximal
5	#125×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
7	C₄⋊C₄×C₃₇	C₂²	1	4	yes	—
8	C₄²×C₃₇	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₃₇	C₂²	1	2	yes	—
10	C₄⋊Dic₃₇	C₂²	1	4	yes	—
11	C₄⋊Dic₃₇	C₂²	1	2	yes	—
12	#10596936	C₂²	1	4	yes	—
13	#10596936	C₂²	1	4	yes	—
14	#10596936	C₂²	1	4	yes	—
15	#10596936	C₂²	1	4	yes	—
16	C₄×Dic₃₇	C₂²	1	4	yes	—
17	C₂×C₄×C₃₇	C₂³	1	4	yes	—
18	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₂³	1	2	yes	—
20	C₂×Dic₃₇	C₂³	1	4	yes	—
21	C₂×Dic₃₇	C₂³	1	4	yes	—
22	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
23	C₄×C₃₇	—	2	4	no	—
24	C₄×C₃₇	—	2	2	no	—
25	C₄×C₃₇	—	2	1	no	—
26	Dic₃₇	—	2	4	no	—
27	Dic₃₇	—	2	4	no	—
28	C₂×C₃₇	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
30	#564	—	37	1	no	maximal, Sylow
31	C₃₇	#564	1	1	yes	characteristic, complemented, Sylow
32	#125	—	37	4	no	—
33	#125	—	37	4	no	—
34	#125	—	37	4	no	—
35	#125	—	37	2	no	—
36	#125	D₃₇	1	1	yes	characteristic
37	C₄⋊C₄	—	37	4	no	—
38	C₄⋊C₄	—	37	4	no	—
39	C₄⋊C₄	—	37	4	no	—
40	C₄⋊C₄	—	37	4	no	—
41	C₄⋊C₄	—	37	4	no	—
42	C₄⋊C₄	—	37	2	no	—
43	C₄⋊C₄	—	37	2	no	—
44	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
45	C₄⋊C₄	C₂×D₃₇	1	4	yes	—
46	C₄²	—	37	4	no	—
47	C₄²	C₂×D₃₇	1	1	yes	characteristic
48	C₂×C₄	—	37	4	no	—
49	C₂×C₄	—	37	4	no	—
50	C₂×C₄	C₂²×D₃₇	1	4	yes	—
51	C₂×C₄	C₂²×D₃₇	1	2	yes	—
52	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
53	C₂²	C₂³×D₃₇	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	74	4	no	—
58	C₄	—	74	4	no	—
59	C₂	#11924583	1	2	yes	—
60	C₂	#11924584	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₇
commutator, socle, prime radical, cosocle	C₂²×C₃₇	C₂⁴
Fitting	#125×C₃₇	C₂
hypercenter	#125	D₃₇
hypocenter	C₃₇	#564
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
31. C₃₇	#564	semidirect

Maximal subgroups

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

subgroup	index
#11924528	2
#11924527	2
#11924526	2
#125×C₃₇	2
#564	37

Subgroups — C37⋊#564 #14558288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇⋊#564 #14558288