Finite Group Databasebeta

← C₃²×C₄₇×C₇₉ #45689175

Subgroups — C₃²×C₄₇×C₇₉ #45689175

Order 33417.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×C₇₉	C₃	1	4	yes	maximal, direct product factor
2	C₄₇×C₇₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₇₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃²×C₄₇	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇₉	C₃×C₄₇	1	4	yes	direct product factor
6	C₃×C₄₇	C₃×C₇₉	1	4	yes	direct product factor
7	C₇₉	C₃²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₄₇	C₃²×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²	C₄₇×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₄₇×C₇₉	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×C₄₇×C₇₉	C₃	direct (N × H)
2. C₄₇×C₇₉	C₃²	direct (N × H)
3. C₃²×C₇₉	C₄₇	direct (N × H)
4. C₃²×C₄₇	C₇₉	direct (N × H)
5. C₃×C₇₉	C₃×C₄₇	direct (N × H)
6. C₃×C₄₇	C₃×C₇₉	direct (N × H)
7. C₇₉	C₃²×C₄₇	direct (N × H)
8. C₄₇	C₃²×C₇₉	direct (N × H)
9. C₃²	C₄₇×C₇₉	direct (N × H)
10. C₃	C₃×C₄₇×C₇₉	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×C₄₇×C₇₉	3
C₃²×C₇₉	47
C₃²×C₄₇	79