Subgroups — #17992662

Order 4736.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557284	C₂	1	2	yes	maximal
2	C₃₇×#346	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#64436	—	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	Q₈	1	1	yes	characteristic
9	C₄²×C₃₇	D₄	1	1	yes	characteristic
10	C₂×#64436	—	4	2	no	—
11	C₁₆×C₃₇	—	2	1	no	—
12	C₁₆×C₃₇	C₈	1	2	yes	complemented
13	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₇	SD₁₆	1	2	yes	—
15	C₈×C₃₇	—	2	1	no	—
16	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
17	C₈×C₃₇	M₁₆	1	1	yes	characteristic
18	#64436	—	8	2	no	—
19	C₂²×C₃₇	#106	1	1	yes	characteristic
20	C₄×C₃₇	—	2	2	no	—
21	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₃₇	#108	1	1	yes	characteristic
23	#1368	—	37	1	no	maximal, Sylow
24	C₂×C₃₇	#334	1	1	yes	characteristic
25	C₂×C₃₇	#365	1	2	yes	—
26	#346	D₃₇	1	1	yes	characteristic
27	#334	—	37	2	no	—
28	C₃₇	#1368	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
30	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
31	C₄⋊C₈	—	74	2	no	—
32	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
33	C₂×C₈	—	148	2	no	—
34	C₂×C₈	Dic₇₄	1	1	yes	characteristic
35	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
36	C₄²	D₁₄₈	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	#64436	1	2	yes	complemented
39	C₂×C₄	#10596930	1	2	yes	—
40	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
41	C₈	—	2	1	no	—
42	C₈	—	296	2	no	—
43	C₈	C₂×#64436	1	1	yes	characteristic
44	C₈	#10596934	1	1	yes	characteristic
45	C₂²	#11924468	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊#64436	1	1	yes	characteristic
48	C₄	#11924472	1	1	yes	characteristic
49	C₂	#14557284	1	1	yes	characteristic
50	C₂	#14557356	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924468
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#346	C₂
socle, prime radical	C₂²×C₃₇	#106
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#346	D₃₇
hypocenter	C₃₇	#1368
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₃₇	C₈	semidirect
28. C₃₇	#1368	semidirect
38. C₁₆	#64436	semidirect

Maximal subgroups

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

subgroup	index
#14557284	2
C₃₇×#346	2
#1368	37