Subgroups — C₃³×C₁₃×C₃₂ #72189708

Order 11232.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×C₃₂	C₃	1	13	yes	maximal, direct product factor
3	C₃³×C₈×C₁₃	C₄	1	1	yes	characteristic
4	C₃²×C₁₃×C₁₆	C₂×C₃	1	13	yes	—
5	C₃³×C₄×C₁₃	C₈	1	1	yes	characteristic
6	C₃×C₁₃×C₃₂	C₃²	1	13	yes	direct product factor
7	C₃²×C₈×C₁₃	C₃×C₄	1	13	yes	—
8	C₃³×C₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃³×C₁₃	C₁₆	1	1	yes	characteristic
10	C₃×C₁₃×C₁₆	C₂×C₃²	1	13	yes	—
11	C₃²×C₄×C₁₃	C₃×C₈	1	13	yes	—
12	C₃³×C₁₆	C₂×C₁₃	1	1	yes	characteristic
13	C₁₃×C₃₂	C₃³	1	1	yes	characteristic, direct product factor, Hall
14	C₃³×C₁₃	C₃₂	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₈×C₁₃	C₃²×C₄	1	13	yes	—
16	C₃²×C₃₂	C₃×C₁₃	1	13	yes	direct product factor
17	C₂×C₃²×C₁₃	C₃×C₁₆	1	13	yes	—
18	C₃³×C₈	C₄×C₁₃	1	1	yes	characteristic
19	C₁₃×C₁₆	C₂×C₃³	1	1	yes	characteristic
20	C₃×C₄×C₁₃	C₃²×C₈	1	13	yes	—
21	C₃²×C₁₆	C₂×C₃×C₁₃	1	13	yes	—
22	C₃²×C₁₃	C₃×C₃₂	1	13	yes	direct product factor
23	C₃³×C₄	C₈×C₁₃	1	1	yes	characteristic
24	C₈×C₁₃	C₃³×C₄	1	1	yes	characteristic
25	C₃×C₃₂	C₃²×C₁₃	1	13	yes	direct product factor
26	C₂×C₃×C₁₃	C₃²×C₁₆	1	13	yes	—
27	C₃²×C₈	C₃×C₄×C₁₃	1	13	yes	—
28	C₂×C₃³	C₁₃×C₁₆	1	1	yes	characteristic
29	C₄×C₁₃	C₃³×C₈	1	1	yes	characteristic
30	C₃×C₁₆	C₂×C₃²×C₁₃	1	13	yes	—
31	C₃×C₁₃	C₃²×C₃₂	1	13	yes	direct product factor
32	C₃²×C₄	C₃×C₈×C₁₃	1	13	yes	—
33	C₃₂	C₃³×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₃³	C₁₃×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₁₃	C₃³×C₁₆	1	1	yes	characteristic
36	C₃×C₈	C₃²×C₄×C₁₃	1	13	yes	—
37	C₂×C₃²	C₃×C₁₃×C₁₆	1	13	yes	—
38	C₁₆	C₂×C₃³×C₁₃	1	1	yes	characteristic
39	C₁₃	C₃³×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	C₃²×C₈×C₁₃	1	13	yes	—
41	C₃²	C₃×C₁₃×C₃₂	1	13	yes	direct product factor
42	C₈	C₃³×C₄×C₁₃	1	1	yes	characteristic
43	C₂×C₃	C₃²×C₁₃×C₁₆	1	13	yes	—
44	C₄	C₃³×C₈×C₁₃	1	1	yes	characteristic
45	C₃	C₃²×C₁₃×C₃₂	1	13	yes	direct product factor
46	C₂	C₃³×C₁₃×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃³×C₁₃
socle, prime radical	C₂×C₃³×C₁₃	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×C₁₃×C₃₂	C₃	direct (N × H)
6. C₃×C₁₃×C₃₂	C₃²	direct (N × H)
8. C₃³×C₃₂	C₁₃	direct (N × H)
13. C₁₃×C₃₂	C₃³	direct (N × H)
14. C₃³×C₁₃	C₃₂	direct (N × H)
16. C₃²×C₃₂	C₃×C₁₃	direct (N × H)
22. C₃²×C₁₃	C₃×C₃₂	direct (N × H)
25. C₃×C₃₂	C₃²×C₁₃	direct (N × H)
31. C₃×C₁₃	C₃²×C₃₂	direct (N × H)
33. C₃₂	C₃³×C₁₃	direct (N × H)
34. C₃³	C₁₃×C₃₂	direct (N × H)
39. C₁₃	C₃³×C₃₂	direct (N × H)
41. C₃²	C₃×C₁₃×C₃₂	direct (N × H)
45. C₃	C₃²×C₁₃×C₃₂	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×C₁₃×C₁₆	2
C₃²×C₁₃×C₃₂	3
C₃³×C₃₂	13

Subgroups — C33×C13×C32 #72189708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₁₃×C₃₂ #72189708