Finite Group Databasebeta

← C₁₁×C₁₆×C₁₃₇ #72201402

Subgroups — C₁₁×C₁₆×C₁₃₇ #72201402

Order 24112.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₁×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×C₁₃₇	C₄	1	1	yes	characteristic
3	C₂×C₁₁×C₁₃₇	C₈	1	1	yes	characteristic
4	C₁₆×C₁₃₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁×C₁₃₇	C₁₆	1	1	yes	characteristic, direct product factor, Hall
6	C₈×C₁₃₇	C₂×C₁₁	1	1	yes	characteristic
7	C₄×C₁₃₇	C₄×C₁₁	1	1	yes	characteristic
8	C₂×C₁₃₇	C₈×C₁₁	1	1	yes	characteristic
9	C₁₁×C₁₆	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₃₇	C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
11	C₈×C₁₁	C₂×C₁₃₇	1	1	yes	characteristic
12	C₄×C₁₁	C₄×C₁₃₇	1	1	yes	characteristic
13	C₂×C₁₁	C₈×C₁₃₇	1	1	yes	characteristic
14	C₁₆	C₁₁×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₁₁	C₁₆×C₁₃₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₈	C₂×C₁₁×C₁₃₇	1	1	yes	characteristic
17	C₄	C₄×C₁₁×C₁₃₇	1	1	yes	characteristic
18	C₂	C₈×C₁₁×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₁×C₁₃₇
socle, prime radical	C₂×C₁₁×C₁₃₇	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×C₁₃₇	C₁₁	direct (N × H)
5. C₁₁×C₁₃₇	C₁₆	direct (N × H)
9. C₁₁×C₁₆	C₁₃₇	direct (N × H)
10. C₁₃₇	C₁₁×C₁₆	direct (N × H)
14. C₁₆	C₁₁×C₁₃₇	direct (N × H)
15. C₁₁	C₁₆×C₁₃₇	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×C₁₃₇	2
C₁₆×C₁₃₇	11
C₁₁×C₁₆	137