Finite Group Databasebeta

← C₄×C₁₃²×C₄₇ #44540952

Subgroups — C₄×C₁₃²×C₄₇ #44540952

Order 31772.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃²×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×C₄₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₃×C₄₇	C₁₃	1	14	yes	maximal, direct product factor
4	C₂×C₁₃×C₄₇	C₂×C₁₃	1	14	yes	—
5	C₄×C₁₃²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₇	C₄×C₁₃	1	14	yes	direct product factor
7	C₂×C₁₃²	C₂×C₄₇	1	1	yes	characteristic
8	C₄×C₄₇	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₁₃²	C₄×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₄₇	C₂×C₁₃²	1	1	yes	characteristic
11	C₄×C₁₃	C₁₃×C₄₇	1	14	yes	direct product factor
12	C₄₇	C₄×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₁₃	C₂×C₁₃×C₄₇	1	14	yes	—
14	C₁₃	C₄×C₁₃×C₄₇	1	14	yes	direct product factor
15	C₄	C₁₃²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₁₃²×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₃²×C₄₇
socle, prime radical	C₂×C₁₃²×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃²×C₄₇	C₄	direct (N × H)
3. C₄×C₁₃×C₄₇	C₁₃	direct (N × H)
5. C₄×C₁₃²	C₄₇	direct (N × H)
6. C₁₃×C₄₇	C₄×C₁₃	direct (N × H)
8. C₄×C₄₇	C₁₃²	direct (N × H)
9. C₁₃²	C₄×C₄₇	direct (N × H)
11. C₄×C₁₃	C₁₃×C₄₇	direct (N × H)
12. C₄₇	C₄×C₁₃²	direct (N × H)
14. C₁₃	C₄×C₁₃×C₄₇	direct (N × H)
15. C₄	C₁₃²×C₄₇	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×C₁₃²×C₄₇	2
C₄×C₁₃×C₄₇	13
C₄×C₁₃²	47