Subgroups — C₁₆×C₂₇×C₂₉ #72190865

Order 12528.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₂₇×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₁₆×C₂₉	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂₇×C₂₉	C₄	1	1	yes	characteristic
4	C₈×C₉×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₂×C₂₇×C₂₉	C₈	1	1	yes	characteristic
6	C₃×C₁₆×C₂₉	C₉	1	1	yes	characteristic
7	C₄×C₉×C₂₉	C₃×C₄	1	1	yes	characteristic
8	C₂₇×C₂₉	C₁₆	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₈×C₂₉	C₂×C₉	1	1	yes	characteristic
10	C₂×C₉×C₂₉	C₃×C₈	1	1	yes	characteristic
11	C₁₆×C₂₉	C₂₇	1	1	yes	characteristic, direct product factor, Hall
12	C₁₆×C₂₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₄×C₂₉	C₄×C₉	1	1	yes	characteristic
14	C₉×C₂₉	C₃×C₁₆	1	1	yes	characteristic
15	C₈×C₂₉	C₂×C₂₇	1	1	yes	characteristic
16	C₈×C₂₇	C₂×C₂₉	1	1	yes	characteristic
17	C₂×C₃×C₂₉	C₈×C₉	1	1	yes	characteristic
18	C₉×C₁₆	C₃×C₂₉	1	1	yes	characteristic
19	C₄×C₂₉	C₄×C₂₇	1	1	yes	characteristic
20	C₄×C₂₇	C₄×C₂₉	1	1	yes	characteristic
21	C₃×C₂₉	C₉×C₁₆	1	1	yes	characteristic
22	C₈×C₉	C₂×C₃×C₂₉	1	1	yes	characteristic
23	C₂×C₂₉	C₈×C₂₇	1	1	yes	characteristic
24	C₂×C₂₇	C₈×C₂₉	1	1	yes	characteristic
25	C₃×C₁₆	C₉×C₂₉	1	1	yes	characteristic
26	C₄×C₉	C₃×C₄×C₂₉	1	1	yes	characteristic
27	C₂₉	C₁₆×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂₇	C₁₆×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₈	C₂×C₉×C₂₉	1	1	yes	characteristic
30	C₂×C₉	C₃×C₈×C₂₉	1	1	yes	characteristic
31	C₁₆	C₂₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₃×C₄	C₄×C₉×C₂₉	1	1	yes	characteristic
33	C₉	C₃×C₁₆×C₂₉	1	1	yes	characteristic
34	C₈	C₂×C₂₇×C₂₉	1	1	yes	characteristic
35	C₂×C₃	C₈×C₉×C₂₉	1	1	yes	characteristic
36	C₄	C₄×C₂₇×C₂₉	1	1	yes	characteristic
37	C₃	C₉×C₁₆×C₂₉	1	1	yes	characteristic
38	C₂	C₈×C₂₇×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₉	C₂×C₃×C₂₉
socle, prime radical	C₂×C₃×C₂₉	C₈×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂₇×C₂₉	C₁₆	direct (N × H)
11. C₁₆×C₂₉	C₂₇	direct (N × H)
12. C₁₆×C₂₇	C₂₉	direct (N × H)
27. C₂₉	C₁₆×C₂₇	direct (N × H)
28. C₂₇	C₁₆×C₂₉	direct (N × H)
31. C₁₆	C₂₇×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
C₈×C₂₇×C₂₉	2
C₉×C₁₆×C₂₉	3
C₁₆×C₂₇	29

Subgroups — C16×C27×C29 #72190865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×C₂₇×C₂₉ #72190865