Subgroups — C₃×C₂₉×C₂₅₆ #72199697

Order 22272.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₉×C₆₄	C₄	1	1	yes	characteristic
3	C₃×C₂₉×C₃₂	C₈	1	1	yes	characteristic
4	C₂₉×C₂₅₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₉×C₁₂₈	C₂×C₃	1	1	yes	characteristic
6	C₂₉×C₆₄	C₃×C₄	1	1	yes	characteristic
7	C₃×C₁₆×C₂₉	C₁₆	1	1	yes	characteristic
8	C₂₉×C₃₂	C₃×C₈	1	1	yes	characteristic
9	C₃×C₂₅₆	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₈×C₂₉	C₃₂	1	1	yes	characteristic
11	C₁₆×C₂₉	C₃×C₁₆	1	1	yes	characteristic
12	C₃×C₁₂₈	C₂×C₂₉	1	1	yes	characteristic
13	C₃×C₄×C₂₉	C₆₄	1	1	yes	characteristic
14	C₂₅₆	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₈×C₂₉	C₃×C₃₂	1	1	yes	characteristic
16	C₃×C₆₄	C₄×C₂₉	1	1	yes	characteristic
17	C₂×C₃×C₂₉	C₁₂₈	1	1	yes	characteristic
18	C₁₂₈	C₂×C₃×C₂₉	1	1	yes	characteristic
19	C₄×C₂₉	C₃×C₆₄	1	1	yes	characteristic
20	C₃×C₃₂	C₈×C₂₉	1	1	yes	characteristic
21	C₃×C₂₉	C₂₅₆	1	1	yes	characteristic, direct product factor, Hall
22	C₆₄	C₃×C₄×C₂₉	1	1	yes	characteristic
23	C₂×C₂₉	C₃×C₁₂₈	1	1	yes	characteristic
24	C₃×C₁₆	C₁₆×C₂₉	1	1	yes	characteristic
25	C₃₂	C₃×C₈×C₂₉	1	1	yes	characteristic
26	C₂₉	C₃×C₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×C₈	C₂₉×C₃₂	1	1	yes	characteristic
28	C₁₆	C₃×C₁₆×C₂₉	1	1	yes	characteristic
29	C₃×C₄	C₂₉×C₆₄	1	1	yes	characteristic
30	C₈	C₃×C₂₉×C₃₂	1	1	yes	characteristic
31	C₂×C₃	C₂₉×C₁₂₈	1	1	yes	characteristic
32	C₄	C₃×C₂₉×C₆₄	1	1	yes	characteristic
33	C₃	C₂₉×C₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₂₉×C₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₂₈	C₂×C₃×C₂₉
socle, prime radical	C₂×C₃×C₂₉	C₁₂₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×C₂₅₆	C₃	direct (N × H)
9. C₃×C₂₅₆	C₂₉	direct (N × H)
14. C₂₅₆	C₃×C₂₉	direct (N × H)
21. C₃×C₂₉	C₂₅₆	direct (N × H)
26. C₂₉	C₃×C₂₅₆	direct (N × H)
33. C₃	C₂₉×C₂₅₆	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×C₂₉×C₁₂₈	2
C₂₉×C₂₅₆	3
C₃×C₂₅₆	29

Subgroups — C3×C29×C256 #72199697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₉×C₂₅₆ #72199697