Finite Group Databasebeta

← C₁₆×C₂₃×C₇₁ #72203289

Subgroups — C₁₆×C₂₃×C₇₁ #72203289

Order 26128.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₂₃×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×C₇₁	C₄	1	1	yes	characteristic
3	C₂×C₂₃×C₇₁	C₈	1	1	yes	characteristic
4	C₂₃×C₇₁	C₁₆	1	1	yes	characteristic, direct product factor, Hall
5	C₁₆×C₇₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₈×C₇₁	C₂×C₂₃	1	1	yes	characteristic
7	C₁₆×C₂₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₄×C₇₁	C₄×C₂₃	1	1	yes	characteristic
9	C₈×C₂₃	C₂×C₇₁	1	1	yes	characteristic
10	C₂×C₇₁	C₈×C₂₃	1	1	yes	characteristic
11	C₄×C₂₃	C₄×C₇₁	1	1	yes	characteristic
12	C₇₁	C₁₆×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₂₃	C₈×C₇₁	1	1	yes	characteristic
14	C₂₃	C₁₆×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₁₆	C₂₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₈	C₂×C₂₃×C₇₁	1	1	yes	characteristic
17	C₄	C₄×C₂₃×C₇₁	1	1	yes	characteristic
18	C₂	C₈×C₂₃×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₂₃×C₇₁
socle, prime radical	C₂×C₂₃×C₇₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×C₇₁	C₁₆	direct (N × H)
5. C₁₆×C₇₁	C₂₃	direct (N × H)
7. C₁₆×C₂₃	C₇₁	direct (N × H)
12. C₇₁	C₁₆×C₂₃	direct (N × H)
14. C₂₃	C₁₆×C₇₁	direct (N × H)
15. C₁₆	C₂₃×C₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₂₃×C₇₁	2
C₁₆×C₇₁	23
C₁₆×C₂₃	71