Subgroups — #17992670

Order 4736.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557286	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₃₇	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	D₈	1	1	yes	characteristic
15	C₂×C₄×C₃₇	Q₁₆	1	1	yes	characteristic
16	C₈×C₃₇	—	2	1	no	—
17	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
18	C₈×C₃₇	M₁₆	1	1	yes	characteristic
19	#64436	—	8	2	no	—
20	C₂²×C₃₇	#107	1	1	yes	characteristic
21	C₄×C₃₇	—	2	1	no	—
22	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₃₇	#108	1	1	yes	characteristic
24	C₄×C₃₇	SD₃₂	1	2	yes	—
25	#1372	—	37	1	no	maximal, Sylow
26	C₂×C₃₇	#335	1	1	yes	characteristic
27	C₂×C₃₇	#367	1	1	yes	characteristic
28	C₂×C₃₇	#368	1	1	yes	characteristic
29	C₄×C₁₆	D₃₇	1	1	yes	characteristic
30	#335	—	37	2	no	—
31	C₃₇	#1372	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
33	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
34	C₄⋊C₈	—	74	2	no	—
35	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
36	C₂×C₈	—	148	2	no	—
37	C₂×C₈	Dic₇₄	1	1	yes	characteristic
38	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
39	C₄²	D₁₄₈	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	#64436	1	2	yes	complemented
42	C₂×C₄	D₂₉₆	1	1	yes	characteristic
43	C₂×C₄	Dic₁₄₈	1	1	yes	characteristic
44	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	296	2	no	—
47	C₈	C₂×#64436	1	1	yes	characteristic
48	C₈	#10596934	1	1	yes	characteristic
49	C₂²	#11924470	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	C₄⋊#64436	1	1	yes	characteristic
52	C₄	#11924472	1	1	yes	characteristic
53	C₄	#11924481	1	2	yes	—
54	C₂	#14557286	1	1	yes	characteristic
55	C₂	#14557361	1	1	yes	characteristic
56	C₂	#14557363	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₉₆
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₄×C₁₆×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	#107
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	C₄×C₁₆	D₃₇
hypocenter	C₃₇	#1372
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₃₇	C₈	semidirect
31. C₃₇	#1372	semidirect
41. C₁₆	#64436	semidirect

Maximal subgroups

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

subgroup	index
#14557286	2
C₄×C₁₆×C₃₇	2
#1372	37