Subgroups — C₃×C₉×C₁₆×C₂₉ #72190866

Order 12528.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₆×C₂₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₆×C₂₉	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₄×C₉×C₂₉	C₄	1	1	yes	characteristic
5	C₃²×C₈×C₂₉	C₂×C₃	1	1	yes	characteristic
6	C₈×C₉×C₂₉	C₂×C₃	1	3	yes	—
7	C₂×C₃×C₉×C₂₉	C₈	1	1	yes	characteristic
8	C₃×C₁₆×C₂₉	C₉	1	3	yes	direct product factor
9	C₃×C₁₆×C₂₉	C₃²	1	1	yes	characteristic
10	C₃²×C₄×C₂₉	C₃×C₄	1	1	yes	characteristic
11	C₄×C₉×C₂₉	C₃×C₄	1	3	yes	—
12	C₃×C₉×C₂₉	C₁₆	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₈×C₂₉	C₂×C₉	1	3	yes	—
14	C₃×C₈×C₂₉	C₂×C₃²	1	1	yes	characteristic
15	C₂×C₃²×C₂₉	C₃×C₈	1	1	yes	characteristic
16	C₂×C₉×C₂₉	C₃×C₈	1	3	yes	—
17	C₁₆×C₂₉	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₉×C₁₆	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃×C₄×C₂₉	C₄×C₉	1	3	yes	—
20	C₃×C₄×C₂₉	C₃²×C₄	1	1	yes	characteristic
21	C₃²×C₂₉	C₃×C₁₆	1	1	yes	characteristic
22	C₉×C₂₉	C₃×C₁₆	1	3	yes	direct product factor
23	C₈×C₂₉	C₂×C₃×C₉	1	1	yes	characteristic
24	C₃×C₈×C₉	C₂×C₂₉	1	1	yes	characteristic
25	C₂×C₃×C₂₉	C₈×C₉	1	3	yes	—
26	C₂×C₃×C₂₉	C₃²×C₈	1	1	yes	characteristic
27	C₃²×C₁₆	C₃×C₂₉	1	1	yes	characteristic
28	C₉×C₁₆	C₃×C₂₉	1	3	yes	direct product factor
29	C₄×C₂₉	C₃×C₄×C₉	1	1	yes	characteristic
30	C₃×C₄×C₉	C₄×C₂₉	1	1	yes	characteristic
31	C₃×C₂₉	C₉×C₁₆	1	3	yes	direct product factor
32	C₃×C₂₉	C₃²×C₁₆	1	1	yes	characteristic
33	C₃²×C₈	C₂×C₃×C₂₉	1	1	yes	characteristic
34	C₈×C₉	C₂×C₃×C₂₉	1	3	yes	—
35	C₂×C₂₉	C₃×C₈×C₉	1	1	yes	characteristic
36	C₂×C₃×C₉	C₈×C₂₉	1	1	yes	characteristic
37	C₃×C₁₆	C₉×C₂₉	1	3	yes	direct product factor
38	C₃×C₁₆	C₃²×C₂₉	1	1	yes	characteristic
39	C₃²×C₄	C₃×C₄×C₂₉	1	1	yes	characteristic
40	C₄×C₉	C₃×C₄×C₂₉	1	3	yes	—
41	C₂₉	C₃×C₉×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₉	C₁₆×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₃×C₈	C₂×C₉×C₂₉	1	3	yes	—
44	C₃×C₈	C₂×C₃²×C₂₉	1	1	yes	characteristic
45	C₂×C₃²	C₃×C₈×C₂₉	1	1	yes	characteristic
46	C₂×C₉	C₃×C₈×C₂₉	1	3	yes	—
47	C₁₆	C₃×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₃×C₄	C₄×C₉×C₂₉	1	3	yes	—
49	C₃×C₄	C₃²×C₄×C₂₉	1	1	yes	characteristic
50	C₃²	C₃×C₁₆×C₂₉	1	1	yes	characteristic
51	C₉	C₃×C₁₆×C₂₉	1	3	yes	direct product factor
52	C₈	C₂×C₃×C₉×C₂₉	1	1	yes	characteristic
53	C₂×C₃	C₈×C₉×C₂₉	1	3	yes	—
54	C₂×C₃	C₃²×C₈×C₂₉	1	1	yes	characteristic
55	C₄	C₃×C₄×C₉×C₂₉	1	1	yes	characteristic
56	C₃	C₉×C₁₆×C₂₉	1	3	yes	direct product factor
57	C₃	C₃²×C₁₆×C₂₉	1	1	yes	characteristic
58	C₂	C₃×C₈×C₉×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂×C₃²×C₂₉
socle, prime radical	C₂×C₃²×C₂₉	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₆×C₂₉	C₃	direct (N × H)
8. C₃×C₁₆×C₂₉	C₉	direct (N × H)
12. C₃×C₉×C₂₉	C₁₆	direct (N × H)
17. C₁₆×C₂₉	C₃×C₉	direct (N × H)
18. C₃×C₉×C₁₆	C₂₉	direct (N × H)
22. C₉×C₂₉	C₃×C₁₆	direct (N × H)
28. C₉×C₁₆	C₃×C₂₉	direct (N × H)
31. C₃×C₂₉	C₉×C₁₆	direct (N × H)
37. C₃×C₁₆	C₉×C₂₉	direct (N × H)
41. C₂₉	C₃×C₉×C₁₆	direct (N × H)
42. C₃×C₉	C₁₆×C₂₉	direct (N × H)
47. C₁₆	C₃×C₉×C₂₉	direct (N × H)
51. C₉	C₃×C₁₆×C₂₉	direct (N × H)
56. C₃	C₉×C₁₆×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₈×C₉×C₂₉	2
C₃²×C₁₆×C₂₉	3
C₉×C₁₆×C₂₉	3
C₃×C₉×C₁₆	29

Subgroups — C3×C9×C16×C29 #72190866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×C₁₆×C₂₉ #72190866