Subgroups — #18009706

Order 4736.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558466	C₂	1	1	yes	maximal, characteristic
2	#14558420	C₂	1	1	yes	maximal, characteristic
3	#14557366	C₂	1	1	yes	maximal, characteristic
4	D₃₇⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×#3866	C₄	1	1	yes	characteristic
6	#11924586	C₄	1	2	yes	complemented
7	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
8	#11924442	C₄	1	1	yes	characteristic, complemented
9	C₃₂×C₃₇	C₄	1	1	yes	characteristic, complemented
10	C₄×#3866	C₈	1	1	yes	characteristic
11	D₃₇⋊C₈	C₈	1	1	yes	characteristic
12	C₈×D₃₇	C₂×C₄	1	1	yes	characteristic
13	#10596927	C₈	1	2	yes	—
14	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
15	#10596925	C₂×C₄	1	1	yes	characteristic
16	C₂×#3866	—	2	1	no	—
17	C₄×D₃₇	C₂×C₈	1	1	yes	characteristic
18	#64438	—	2	1	no	—
19	C₈×C₃₇	C₄²	1	1	yes	characteristic
20	#64436	C₂×C₈	1	1	yes	characteristic
21	C₂×D₃₇	M₃₂	1	1	yes	characteristic
22	#3866	—	4	1	no	—
23	C₄×C₃₇	C₄×C₈	1	1	yes	characteristic
24	Dic₃₇	M₃₂	1	1	yes	characteristic
25	#1398	—	37	1	no	maximal, Sylow
26	C₂×C₃₇	#346	1	1	yes	characteristic
27	D₃₇	—	2	1	no	—
28	M₆₄	—	37	1	no	—
29	M₆₄	—	37	1	no	—
30	#346	—	37	1	no	—
31	C₃₇	#1398	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₆	—	37	1	no	—
33	C₂×C₁₆	—	37	1	no	—
34	C₄×C₈	—	37	1	no	—
35	C₃₂	—	37	2	no	—
36	C₃₂	—	37	1	no	—
37	C₃₂	#3866	1	1	yes	characteristic, complemented
38	C₂×C₈	—	37	1	no	—
39	C₂×C₈	—	37	1	no	—
40	C₄²	—	37	1	no	—
41	C₁₆	—	37	2	no	—
42	C₁₆	—	37	1	no	—
43	C₁₆	C₂×#3866	1	1	yes	characteristic
44	C₂×C₄	—	37	1	no	—
45	C₂×C₄	—	74	1	no	—
46	C₈	—	37	1	no	—
47	C₈	—	74	1	no	—
48	C₈	C₄×#3866	1	1	yes	characteristic
49	C₂²	—	37	1	no	—
50	C₄	—	37	1	no	—
51	C₄	—	148	1	no	—
52	C₄	C₈×#3866	1	1	yes	characteristic
53	C₂	—	74	1	no	—
54	C₂	#14558420	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#3866
commutator	C₄×C₃₇	C₄×C₈
Frattini	C₁₆	C₂×#3866
Fitting	C₃₂×C₃₇	C₄
socle	C₂×C₃₇	#346
prime radical	C₂×D₃₇	M₃₂
cosocle	C₁₆×D₃₇	C₂²
hypercenter	C₃₂	#3866
hypocenter	C₃₇	#1398
LCS	G ▷ C₄×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. #11924586	C₄	semidirect
8. #11924442	C₄	semidirect
9. C₃₂×C₃₇	C₄	semidirect
31. C₃₇	#1398	semidirect
37. C₃₂	#3866	semidirect

Maximal subgroups

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

subgroup	index
#14558466	2
#14558420	2
#14557366	2
#1398	37