Finite Group Databasebeta

← C₁₁×C₁₆×C₇₁ #72190833

Subgroups — C₁₁×C₁₆×C₇₁ #72190833

Order 12496.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×C₇₁	C₄	1	1	yes	characteristic
3	C₂×C₁₁×C₇₁	C₈	1	1	yes	characteristic
4	C₁₆×C₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁×C₇₁	C₁₆	1	1	yes	characteristic, direct product factor, Hall
6	C₈×C₇₁	C₂×C₁₁	1	1	yes	characteristic
7	C₄×C₇₁	C₄×C₁₁	1	1	yes	characteristic
8	C₁₁×C₁₆	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇₁	C₈×C₁₁	1	1	yes	characteristic
10	C₈×C₁₁	C₂×C₇₁	1	1	yes	characteristic
11	C₇₁	C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₁₁	C₄×C₇₁	1	1	yes	characteristic
13	C₂×C₁₁	C₈×C₇₁	1	1	yes	characteristic
14	C₁₆	C₁₁×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₁₁	C₁₆×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₈	C₂×C₁₁×C₇₁	1	1	yes	characteristic
17	C₄	C₄×C₁₁×C₇₁	1	1	yes	characteristic
18	C₂	C₈×C₁₁×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₁×C₇₁
socle, prime radical	C₂×C₁₁×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. C₁₆×C₇₁	C₁₁	direct (N × H)
5. C₁₁×C₇₁	C₁₆	direct (N × H)
8. C₁₁×C₁₆	C₇₁	direct (N × H)
11. C₇₁	C₁₁×C₁₆	direct (N × H)
14. C₁₆	C₁₁×C₇₁	direct (N × H)
15. C₁₁	C₁₆×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×C₁₁×C₇₁	2
C₁₆×C₇₁	11
C₁₁×C₁₆	71