Subgroups — #17992664

Order 4736.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557354	C₂	1	2	yes	maximal
2	C₃₇×#346	C₂	1	1	yes	maximal, characteristic
3	#11924476	—	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	D₄	1	1	yes	characteristic
9	C₄²×C₃₇	Q₈	1	1	yes	characteristic
10	C₁₆×C₃₇	—	2	1	no	—
11	C₁₆×C₃₇	C₈	1	2	yes	—
12	#10596925	—	4	2	no	—
13	C₂×C₄×C₃₇	—	2	1	no	—
14	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
16	C₈×C₃₇	M₁₆	1	1	yes	characteristic
17	C₈×C₃₇	SD₁₆	1	2	yes	—
18	C₂²×C₃₇	#108	1	1	yes	characteristic
19	C₄×C₃₇	—	4	1	no	—
20	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₃₇	#106	1	1	yes	characteristic
22	#1369	—	37	1	no	maximal, Sylow
23	C₂×C₃₇	—	2	1	no	—
24	C₂×C₃₇	#334	1	1	yes	characteristic
25	#364	—	37	2	no	—
26	#346	D₃₇	1	1	yes	characteristic
27	C₃₇	#1369	1	1	yes	characteristic, complemented, Sylow
28	M₃₂	—	74	2	no	—
29	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
30	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
31	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
32	C₂×C₈	D₁₄₈	1	1	yes	characteristic
33	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
34	C₄²	Dic₇₄	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	—	148	2	no	—
37	C₁₆	#64436	1	2	yes	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
40	C₈	#10596930	1	2	yes	—
41	C₈	C₂×#64436	1	1	yes	characteristic
42	C₈	#10596934	1	1	yes	characteristic
43	C₂²	#11924472	1	1	yes	characteristic
44	C₄	—	4	1	no	—
45	C₄	C₄⋊#64436	1	1	yes	characteristic
46	C₄	#11924468	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#14557284	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924468
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#346	C₂
socle	C₂×C₃₇	#334
prime radical	C₂²×C₃₇	#108
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#346	D₃₇
hypocenter	C₃₇	#1369
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
27. C₃₇	#1369	semidirect

Maximal subgroups

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

subgroup	index
#14557354	2
C₃₇×#346	2
#1369	37