Finite Group Databasebeta

← C₃²×C₃₁×C₉₇ #41028811

Subgroups — C₃²×C₃₁×C₉₇ #41028811

Order 27063.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₉₇	C₃	1	4	yes	maximal, direct product factor
2	C₃₁×C₉₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₉₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₉₇	C₃×C₃₁	1	4	yes	direct product factor
5	C₃²×C₃₁	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₉₇	C₃²×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₃₁	C₃×C₉₇	1	4	yes	direct product factor
8	C₃₁	C₃²×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²	C₃₁×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₃₁×C₉₇	1	4	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₉₇	C₃	direct (N × H)
2. C₃₁×C₉₇	C₃²	direct (N × H)
3. C₃²×C₉₇	C₃₁	direct (N × H)
4. C₃×C₉₇	C₃×C₃₁	direct (N × H)
5. C₃²×C₃₁	C₉₇	direct (N × H)
6. C₉₇	C₃²×C₃₁	direct (N × H)
7. C₃×C₃₁	C₃×C₉₇	direct (N × H)
8. C₃₁	C₃²×C₉₇	direct (N × H)
9. C₃²	C₃₁×C₉₇	direct (N × H)
10. C₃	C₃×C₃₁×C₉₇	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×C₃₁×C₉₇	3
C₃²×C₉₇	31
C₃²×C₃₁	97