Subgroups — C₂×C₃₂×D₃₇ #17996884

Order 4736.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₃₇
commutator, hypocenter	C₃₇	C₂²×C₃₂
Frattini	C₁₆	C₂²×D₃₇
Fitting	C₂×C₃₂×C₃₇	C₂
socle	C₂²×C₃₇	C₂×C₁₆
prime radical	C₂²×D₃₇	C₁₆
cosocle	C₁₆×C₃₇	C₂³
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×#11924442	C₂	semidirect
3. C₃₂×D₃₇	C₂	direct (N × H)
4. C₂×C₃₂×C₃₇	C₂	semidirect
9. #11924442	C₂²	semidirect
11. C₃₂×C₃₇	C₂²	semidirect
29. C₂×D₃₇	C₃₂	direct (N × H)
35. C₂×C₃₇	C₂×C₃₂	semidirect
37. D₃₇	C₂×C₃₂	direct (N × H)
41. C₂×C₃₂	D₃₇	direct (N × H)
42. C₃₇	C₂²×C₃₂	semidirect
49. C₃₂	C₂×D₃₇	direct (N × H)
73. C₂	C₃₂×D₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₃₇	2
C₂×#11924442	2
C₃₂×D₃₇	2
C₂×C₃₂×C₃₇	2
C₂²×C₃₂	37

Subgroups — C2×C32×D37 #17996884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₂×D₃₇ #17996884