Subgroups — C₃³×C₁₆×C₂₉ #72190867

Order 12528.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₆×C₂₉	C₃	1	13	yes	maximal, direct product factor
3	C₃³×C₄×C₂₉	C₄	1	1	yes	characteristic
4	C₃²×C₈×C₂₉	C₂×C₃	1	13	yes	—
5	C₂×C₃³×C₂₉	C₈	1	1	yes	characteristic
6	C₃×C₁₆×C₂₉	C₃²	1	13	yes	direct product factor
7	C₃²×C₄×C₂₉	C₃×C₄	1	13	yes	—
8	C₃³×C₂₉	C₁₆	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₈×C₂₉	C₂×C₃²	1	13	yes	—
10	C₂×C₃²×C₂₉	C₃×C₈	1	13	yes	—
11	C₁₆×C₂₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
12	C₃³×C₁₆	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₄×C₂₉	C₃²×C₄	1	13	yes	—
14	C₃²×C₂₉	C₃×C₁₆	1	13	yes	direct product factor
15	C₈×C₂₉	C₂×C₃³	1	1	yes	characteristic
16	C₃³×C₈	C₂×C₂₉	1	1	yes	characteristic
17	C₂×C₃×C₂₉	C₃²×C₈	1	13	yes	—
18	C₃²×C₁₆	C₃×C₂₉	1	13	yes	direct product factor
19	C₄×C₂₉	C₃³×C₄	1	1	yes	characteristic
20	C₃³×C₄	C₄×C₂₉	1	1	yes	characteristic
21	C₃×C₂₉	C₃²×C₁₆	1	13	yes	direct product factor
22	C₃²×C₈	C₂×C₃×C₂₉	1	13	yes	—
23	C₂×C₂₉	C₃³×C₈	1	1	yes	characteristic
24	C₂×C₃³	C₈×C₂₉	1	1	yes	characteristic
25	C₃×C₁₆	C₃²×C₂₉	1	13	yes	direct product factor
26	C₃²×C₄	C₃×C₄×C₂₉	1	13	yes	—
27	C₂₉	C₃³×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
28	C₃³	C₁₆×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₈	C₂×C₃²×C₂₉	1	13	yes	—
30	C₂×C₃²	C₃×C₈×C₂₉	1	13	yes	—
31	C₁₆	C₃³×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₃×C₄	C₃²×C₄×C₂₉	1	13	yes	—
33	C₃²	C₃×C₁₆×C₂₉	1	13	yes	direct product factor
34	C₈	C₂×C₃³×C₂₉	1	1	yes	characteristic
35	C₂×C₃	C₃²×C₈×C₂₉	1	13	yes	—
36	C₄	C₃³×C₄×C₂₉	1	1	yes	characteristic
37	C₃	C₃²×C₁₆×C₂₉	1	13	yes	direct product factor
38	C₂	C₃³×C₈×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃³×C₂₉
socle, prime radical	C₂×C₃³×C₂₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₆×C₂₉	C₃	direct (N × H)
6. C₃×C₁₆×C₂₉	C₃²	direct (N × H)
8. C₃³×C₂₉	C₁₆	direct (N × H)
11. C₁₆×C₂₉	C₃³	direct (N × H)
12. C₃³×C₁₆	C₂₉	direct (N × H)
14. C₃²×C₂₉	C₃×C₁₆	direct (N × H)
18. C₃²×C₁₆	C₃×C₂₉	direct (N × H)
21. C₃×C₂₉	C₃²×C₁₆	direct (N × H)
25. C₃×C₁₆	C₃²×C₂₉	direct (N × H)
27. C₂₉	C₃³×C₁₆	direct (N × H)
28. C₃³	C₁₆×C₂₉	direct (N × H)
31. C₁₆	C₃³×C₂₉	direct (N × H)
33. C₃²	C₃×C₁₆×C₂₉	direct (N × H)
37. C₃	C₃²×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
C₃³×C₈×C₂₉	2
C₃²×C₁₆×C₂₉	3
C₃³×C₁₆	29

Subgroups — C33×C16×C29 #72190867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₁₆×C₂₉ #72190867