Subgroups — C₃³×C₃₂×C₃₇ #72208686

Order 31968.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₃₂×C₃₇	C₃	1	13	yes	maximal, direct product factor
3	C₃³×C₈×C₃₇	C₄	1	1	yes	characteristic
4	C₃²×C₁₆×C₃₇	C₂×C₃	1	13	yes	—
5	C₃³×C₄×C₃₇	C₈	1	1	yes	characteristic
6	C₃×C₃₂×C₃₇	C₃²	1	13	yes	direct product factor
7	C₃²×C₈×C₃₇	C₃×C₄	1	13	yes	—
8	C₂×C₃³×C₃₇	C₁₆	1	1	yes	characteristic
9	C₃×C₁₆×C₃₇	C₂×C₃²	1	13	yes	—
10	C₃²×C₄×C₃₇	C₃×C₈	1	13	yes	—
11	C₃₂×C₃₇	C₃³	1	1	yes	characteristic, direct product factor, Hall
12	C₃³×C₃₇	C₃₂	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₈×C₃₇	C₃²×C₄	1	13	yes	—
14	C₃³×C₃₂	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃²×C₃₇	C₃×C₁₆	1	13	yes	—
16	C₁₆×C₃₇	C₂×C₃³	1	1	yes	characteristic
17	C₃×C₄×C₃₇	C₃²×C₈	1	13	yes	—
18	C₃³×C₁₆	C₂×C₃₇	1	1	yes	characteristic
19	C₃²×C₃₇	C₃×C₃₂	1	13	yes	direct product factor
20	C₈×C₃₇	C₃³×C₄	1	1	yes	characteristic
21	C₃²×C₃₂	C₃×C₃₇	1	13	yes	direct product factor
22	C₂×C₃×C₃₇	C₃²×C₁₆	1	13	yes	—
23	C₃³×C₈	C₄×C₃₇	1	1	yes	characteristic
24	C₄×C₃₇	C₃³×C₈	1	1	yes	characteristic
25	C₃²×C₁₆	C₂×C₃×C₃₇	1	13	yes	—
26	C₃×C₃₇	C₃²×C₃₂	1	13	yes	direct product factor
27	C₃³×C₄	C₈×C₃₇	1	1	yes	characteristic
28	C₃×C₃₂	C₃²×C₃₇	1	13	yes	direct product factor
29	C₂×C₃₇	C₃³×C₁₆	1	1	yes	characteristic
30	C₃²×C₈	C₃×C₄×C₃₇	1	13	yes	—
31	C₂×C₃³	C₁₆×C₃₇	1	1	yes	characteristic
32	C₃×C₁₆	C₂×C₃²×C₃₇	1	13	yes	—
33	C₃₇	C₃³×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
34	C₃²×C₄	C₃×C₈×C₃₇	1	13	yes	—
35	C₃₂	C₃³×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₃³	C₃₂×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₃×C₈	C₃²×C₄×C₃₇	1	13	yes	—
38	C₂×C₃²	C₃×C₁₆×C₃₇	1	13	yes	—
39	C₁₆	C₂×C₃³×C₃₇	1	1	yes	characteristic
40	C₃×C₄	C₃²×C₈×C₃₇	1	13	yes	—
41	C₃²	C₃×C₃₂×C₃₇	1	13	yes	direct product factor
42	C₈	C₃³×C₄×C₃₇	1	1	yes	characteristic
43	C₂×C₃	C₃²×C₁₆×C₃₇	1	13	yes	—
44	C₄	C₃³×C₈×C₃₇	1	1	yes	characteristic
45	C₃	C₃²×C₃₂×C₃₇	1	13	yes	direct product factor
46	C₂	C₃³×C₁₆×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃³×C₃₇
socle, prime radical	C₂×C₃³×C₃₇	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₃₂×C₃₇	C₃	direct (N × H)
6. C₃×C₃₂×C₃₇	C₃²	direct (N × H)
11. C₃₂×C₃₇	C₃³	direct (N × H)
12. C₃³×C₃₇	C₃₂	direct (N × H)
14. C₃³×C₃₂	C₃₇	direct (N × H)
19. C₃²×C₃₇	C₃×C₃₂	direct (N × H)
21. C₃²×C₃₂	C₃×C₃₇	direct (N × H)
26. C₃×C₃₇	C₃²×C₃₂	direct (N × H)
28. C₃×C₃₂	C₃²×C₃₇	direct (N × H)
33. C₃₇	C₃³×C₃₂	direct (N × H)
35. C₃₂	C₃³×C₃₇	direct (N × H)
36. C₃³	C₃₂×C₃₇	direct (N × H)
41. C₃²	C₃×C₃₂×C₃₇	direct (N × H)
45. C₃	C₃²×C₃₂×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₁₆×C₃₇	2
C₃²×C₃₂×C₃₇	3
C₃³×C₃₂	37

Subgroups — C33×C32×C37 #72208686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₃₂×C₃₇ #72208686