Subgroups — #17994352

Order 4736.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557491	C₂	1	3	yes	maximal
2	#14557290	C₂	1	3	yes	maximal
3	C₃₇×#338	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64436	C₂²	1	1	yes	characteristic
5	#11924495	C₂²	1	3	yes	—
6	#11924446	C₄	1	6	yes	complemented
7	C₈×Dic₃₇	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₃₇	C₂²	1	3	yes	—
9	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
10	M₁₆×C₃₇	—	2	6	no	—
11	C₂×C₈×C₃₇	C₂×C₄	1	6	yes	—
12	C₂²⋊Dic₃₇	—	2	3	no	—
13	C₄⋊Dic₃₇	—	2	3	no	—
14	C₄×Dic₃₇	C₂×C₄	1	6	yes	—
15	C₂×#64436	C₂×C₄	1	3	yes	—
16	C₂×#64436	C₂×C₄	1	3	yes	—
17	C₂³×C₃₇	#41	1	1	yes	characteristic
18	C₂×C₄×C₃₇	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₃₇	#41	1	3	yes	—
20	C₂×Dic₃₇	—	2	6	no	—
21	C₈×C₃₇	—	2	6	no	—
22	#64436	C₄²	1	1	yes	characteristic
23	#64436	C₄²	1	3	yes	—
24	C₂²×C₃₇	—	4	1	no	—
25	C₂²×C₃₇	#117	1	3	yes	—
26	C₄×C₃₇	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₃₇	#117	1	3	yes	—
28	Dic₃₇	—	4	6	no	—
29	#1747	—	37	1	no	maximal, Sylow
30	C₂×C₃₇	—	2	3	no	—
31	C₂×C₃₇	#376	1	1	yes	characteristic
32	#405	—	37	3	no	—
33	#338	D₃₇	1	1	yes	characteristic
34	H(3,ℤ/4)	—	37	3	no	—
35	C₃₇	#1747	1	1	yes	characteristic, complemented, Sylow
36	C₂×M₁₆	C₂×D₃₇	1	3	yes	—
37	C₂²×C₈	—	37	1	no	—
38	#117	—	37	3	no	—
39	#97	—	37	6	no	—
40	C₄×C₈	—	37	6	no	—
41	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	37	3	no	—
44	C₂×C₈	—	37	3	no	—
45	C₂×C₈	C₄×D₃₇	1	6	yes	—
46	C₄⋊C₄	—	74	3	no	—
47	C₂²⋊C₄	—	74	3	no	—
48	C₄²	—	37	6	no	—
49	C₂³	#10596966	1	1	yes	characteristic
50	C₂×C₄	—	74	6	no	—
51	C₂×C₄	C₂×C₄×D₃₇	1	3	yes	—
52	C₂×C₄	#10596964	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	37	1	no	—
55	C₈	—	37	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#11924494	1	3	yes	—
58	C₄	—	148	6	no	—
59	C₄	C₄²×D₃₇	1	1	yes	characteristic
60	C₄	#11924492	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#14557378	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₃₇
commutator	C₄×C₃₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#338	C₂
socle	C₂×C₃₇	#376
prime radical	C₂³×C₃₇	#41
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#338	D₃₇
hypocenter	C₃₇	#1747
LCS	G ▷ C₄×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #11924446	C₄	semidirect
7. C₈×Dic₃₇	C₄	semidirect
35. C₃₇	#1747	semidirect

Maximal subgroups

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

subgroup	index
#14557491	2
#14557290	2
C₃₇×#338	2
#1747	37