Subgroups — #17992799

Order 4736.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924442	C₂	1	1	yes	maximal, characteristic
2	#14557363	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#368	C₂	1	1	yes	maximal, characteristic
4	#11924472	—	2	1	no	—
5	#11924442	C₄	1	2	yes	—
6	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
7	#108×C₃₇	—	2	1	no	—
8	M₁₆×C₃₇	—	4	1	no	—
9	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
10	#10596934	—	4	1	no	—
11	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₃₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
14	C₈×C₃₇	—	8	1	no	—
15	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
17	#64436	—	8	1	no	—
18	C₂²×C₃₇	Q₃₂	1	1	yes	characteristic
19	C₄×C₃₇	#107	1	1	yes	characteristic
20	C₄×C₃₇	D₁₆	1	1	yes	characteristic
21	#1425	—	37	1	no	maximal, Sylow
22	C₂×C₃₇	—	2	1	no	—
23	C₂×C₃₇	#366	1	1	yes	characteristic
24	C₂×C₃₂	—	37	1	no	—
25	#368	—	37	1	no	—
26	#368	D₃₇	1	1	yes	characteristic
27	C₃₇	#1425	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	74	1	no	—
31	C₃₂	—	37	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	148	1	no	—
34	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
35	C₁₆	Dic₇₄	1	1	yes	characteristic
36	C₁₆	C₄×D₃₇	1	1	yes	characteristic
37	C₂×C₄	#10596939	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	296	1	no	—
40	C₈	#10596936	1	1	yes	characteristic
41	C₈	#10596942	1	1	yes	characteristic
42	C₂²	#11924482	1	1	yes	characteristic
43	C₄	#11924469	1	1	yes	characteristic
44	C₄	#11924477	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#14557358	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924477
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₃₇×#368	C₂
socle	C₂×C₃₇	#366
prime radical	C₂²×C₃₇	Q₃₂
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	#368	D₃₇
hypocenter	C₃₇	#1425
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
27. C₃₇	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924442	2
#14557363	2
C₃₇×#368	2
#1425	37