Finite Group Databasebeta

← C₃×C₉×C₁₁² #72183003

Subgroups — C₃×C₉×C₁₁² #72183003

Order 3267.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁²	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₁²	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₁²	C₉	1	3	yes	direct product factor
4	C₃×C₁₁²	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₁₁	C₁₁	1	12	yes	maximal, direct product factor
6	C₁₁²	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₃²×C₁₁	C₃×C₁₁	1	12	yes	—
8	C₉×C₁₁	C₃×C₁₁	1	36	yes	direct product factor
9	C₃×C₁₁	C₉×C₁₁	1	36	yes	direct product factor
10	C₃×C₁₁	C₃²×C₁₁	1	12	yes	—
11	C₃×C₉	C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₁	C₃×C₉×C₁₁	1	12	yes	direct product factor
13	C₃²	C₃×C₁₁²	1	1	yes	characteristic
14	C₉	C₃×C₁₁²	1	3	yes	direct product factor
15	C₃	C₉×C₁₁²	1	3	yes	direct product factor
16	C₃	C₃²×C₁₁²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃²×C₁₁²
socle, prime radical	C₃²×C₁₁²	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₁²	C₃	direct (N × H)
3. C₃×C₁₁²	C₉	direct (N × H)
5. C₃×C₉×C₁₁	C₁₁	direct (N × H)
6. C₁₁²	C₃×C₉	direct (N × H)
8. C₉×C₁₁	C₃×C₁₁	direct (N × H)
9. C₃×C₁₁	C₉×C₁₁	direct (N × H)
11. C₃×C₉	C₁₁²	direct (N × H)
12. C₁₁	C₃×C₉×C₁₁	direct (N × H)
14. C₉	C₃×C₁₁²	direct (N × H)
15. C₃	C₉×C₁₁²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₁²	3
C₉×C₁₁²	3
C₃×C₉×C₁₁	11