Subgroups — C₃×C₃₂×C₁₂₁ #72190047

Order 11616.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₆×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	C₃₂×C₁₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₈×C₁₂₁	C₄	1	1	yes	characteristic
4	C₁₆×C₁₂₁	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₂₁	C₈	1	1	yes	characteristic
6	C₃×C₁₁×C₃₂	C₁₁	1	1	yes	maximal, characteristic
7	C₈×C₁₂₁	C₃×C₄	1	1	yes	characteristic
8	C₂×C₃×C₁₂₁	C₁₆	1	1	yes	characteristic
9	C₃×C₁₁×C₁₆	C₂×C₁₁	1	1	yes	characteristic
10	C₄×C₁₂₁	C₃×C₈	1	1	yes	characteristic
11	C₃×C₁₂₁	C₃₂	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁×C₃₂	C₃×C₁₁	1	1	yes	characteristic
13	C₃×C₈×C₁₁	C₄×C₁₁	1	1	yes	characteristic
14	C₂×C₁₂₁	C₃×C₁₆	1	1	yes	characteristic
15	C₁₁×C₁₆	C₂×C₃×C₁₁	1	1	yes	characteristic
16	C₃×C₄×C₁₁	C₈×C₁₁	1	1	yes	characteristic
17	C₁₂₁	C₃×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₃₂	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
19	C₈×C₁₁	C₃×C₄×C₁₁	1	1	yes	characteristic
20	C₂×C₃×C₁₁	C₁₁×C₁₆	1	1	yes	characteristic
21	C₃×C₁₆	C₂×C₁₂₁	1	1	yes	characteristic
22	C₄×C₁₁	C₃×C₈×C₁₁	1	1	yes	characteristic
23	C₃×C₁₁	C₁₁×C₃₂	1	1	yes	characteristic
24	C₃₂	C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₈	C₄×C₁₂₁	1	1	yes	characteristic
26	C₂×C₁₁	C₃×C₁₁×C₁₆	1	1	yes	characteristic
27	C₁₆	C₂×C₃×C₁₂₁	1	1	yes	characteristic
28	C₃×C₄	C₈×C₁₂₁	1	1	yes	characteristic
29	C₁₁	C₃×C₁₁×C₃₂	1	1	yes	characteristic
30	C₈	C₃×C₄×C₁₂₁	1	1	yes	characteristic
31	C₂×C₃	C₁₆×C₁₂₁	1	1	yes	characteristic
32	C₄	C₃×C₈×C₁₂₁	1	1	yes	characteristic
33	C₃	C₃₂×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₁₆×C₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₁×C₁₆	C₂×C₃×C₁₁
socle, prime radical	C₂×C₃×C₁₁	C₁₁×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×C₁₂₁	C₃	direct (N × H)
11. C₃×C₁₂₁	C₃₂	direct (N × H)
17. C₁₂₁	C₃×C₃₂	direct (N × H)
18. C₃×C₃₂	C₁₂₁	direct (N × H)
24. C₃₂	C₃×C₁₂₁	direct (N × H)
33. C₃	C₃₂×C₁₂₁	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×C₁₆×C₁₂₁	2
C₃₂×C₁₂₁	3
C₃×C₁₁×C₃₂	11

Subgroups — C3×C32×C121 #72190047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₂×C₁₂₁ #72190047