Finite Group Databasebeta

← C₃²×C₄×C₁₁ #87684

Subgroups — C₃²×C₄×C₁₁ #87684

Order 396.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₁	C₂×C₃	1	4	yes	—
5	C₄×C₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁	C₃×C₄	1	4	yes	direct product factor
8	C₂×C₁₁	C₂×C₃²	1	1	yes	characteristic
9	C₂×C₃²	C₂×C₁₁	1	1	yes	characteristic
10	C₃×C₄	C₃×C₁₁	1	4	yes	direct product factor
11	C₁₁	C₃²×C₄	1	1	yes	characteristic, direct product factor, Sylow
12	C₃²	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃	C₂×C₃×C₁₁	1	4	yes	—
14	C₄	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₃×C₄×C₁₁	1	4	yes	direct product factor
16	C₂	C₂×C₃²×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃²×C₁₁
socle, prime radical	C₂×C₃²×C₁₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₁₁	C₃	direct (N × H)
3. C₃²×C₁₁	C₄	direct (N × H)
5. C₄×C₁₁	C₃²	direct (N × H)
6. C₃²×C₄	C₁₁	direct (N × H)
7. C₃×C₁₁	C₃×C₄	direct (N × H)
10. C₃×C₄	C₃×C₁₁	direct (N × H)
11. C₁₁	C₃²×C₄	direct (N × H)
12. C₃²	C₄×C₁₁	direct (N × H)
14. C₄	C₃²×C₁₁	direct (N × H)
15. C₃	C₃×C₄×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₁	2
C₃×C₄×C₁₁	3
C₃²×C₄	11