Subgroups — Q₆₄×D₃₇ #17996899

Order 4736.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₃₇	C₂	1	2	yes	maximal
2	Dic₅₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#14557373	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₃₇	—	2	2	no	—
7	Dic₂₉₆	C₂²	1	2	yes	—
8	#11924482	—	2	2	no	—
9	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
10	#11924442	C₂²	1	1	yes	characteristic
11	Q₃₂×C₃₇	C₂²	1	2	yes	—
12	C₃₂×C₃₇	C₂²	1	1	yes	characteristic
13	Q₈×D₃₇	—	4	2	no	—
14	Q₁₆×C₃₇	—	2	2	no	—
15	#10596942	—	4	2	no	—
16	Dic₁₄₈	—	2	2	no	—
17	C₈×D₃₇	D₄	1	1	yes	characteristic
18	C₁₆×C₃₇	C₂³	1	1	yes	characteristic
19	#10596925	D₄	1	1	yes	characteristic
20	Q₈×C₃₇	—	4	2	no	—
21	C₄×D₃₇	—	8	2	no	—
22	C₄×D₃₇	D₈	1	1	yes	characteristic
23	Dic₇₄	—	4	2	no	—
24	Dic₇₄	—	8	2	no	—
25	C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
26	#64436	D₈	1	1	yes	characteristic
27	C₂×D₃₇	D₁₆	1	1	yes	characteristic
28	C₄×C₃₇	—	8	2	no	—
29	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
30	Dic₃₇	—	8	2	no	—
31	Dic₃₇	D₁₆	1	1	yes	characteristic
32	C₂×Q₆₄	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	C₂×D₁₆	1	1	yes	characteristic
34	D₃₇	Q₆₄	1	2	yes	direct product factor
35	C₂×Q₃₂	—	37	2	no	—
36	Q₆₄	—	37	2	no	—
37	Q₆₄	—	37	1	no	—
38	Q₆₄	D₃₇	1	1	yes	characteristic, direct product factor
39	C₂×C₃₂	—	37	1	no	—
40	C₃₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₁₆	—	74	2	no	—
42	Q₃₂	—	37	2	no	—
43	Q₃₂	—	74	2	no	—
44	Q₃₂	C₂×D₃₇	1	2	yes	—
45	C₂×C₁₆	—	37	1	no	—
46	C₃₂	—	37	1	no	—
47	C₃₂	C₂×D₃₇	1	1	yes	characteristic
48	C₂×Q₈	—	148	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	74	2	no	—
51	Q₁₆	—	148	2	no	—
52	C₂×C₈	—	37	1	no	—
53	C₁₆	—	37	1	no	—
54	C₁₆	C₂²×D₃₇	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	296	2	no	—
57	Q₈	—	148	2	no	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	296	2	no	—
60	C₈	—	37	1	no	—
61	C₈	D₄×D₃₇	1	1	yes	characteristic
62	C₂²	—	37	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	37	1	no	—
65	C₄	—	296	2	no	—
66	C₄	D₈×D₃₇	1	1	yes	characteristic
67	C₂	—	37	2	no	—
68	C₂	D₁₆×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₃₇
commutator, cosocle	C₁₆×C₃₇	C₂³
Frattini	C₁₆	C₂²×D₃₇
Fitting	C₃₇×Q₆₄	C₂
socle	C₂×C₃₇	C₂×D₁₆
prime radical	C₂×D₃₇	D₁₆
hypercenter	Q₆₄	D₃₇
hypocenter	C₃₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₅₉₂	C₂	semidirect
3. #14557373	C₂	semidirect
5. C₃₇×Q₆₄	C₂	semidirect
34. D₃₇	Q₆₄	direct (N × H)
38. Q₆₄	D₃₇	direct (N × H)
40. C₃₇	C₂×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
Q₃₂×D₃₇	2
Dic₅₉₂	2
#14557373	2
C₃₂×D₃₇	2
C₃₇×Q₆₄	2
C₂×Q₆₄	37

Subgroups — Q64×D37 #17996899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₆₄×D₃₇ #17996899