Finite Group Databasebeta

← C₁₆×C₂₉×C₃₇ #72195046

Subgroups — C₁₆×C₂₉×C₃₇ #72195046

Order 17168.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₂₉×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₉×C₃₇	C₄	1	1	yes	characteristic
3	C₂×C₂₉×C₃₇	C₈	1	1	yes	characteristic
4	C₂₉×C₃₇	C₁₆	1	1	yes	characteristic, direct product factor, Hall
5	C₁₆×C₃₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₆×C₂₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₈×C₃₇	C₂×C₂₉	1	1	yes	characteristic
8	C₈×C₂₉	C₂×C₃₇	1	1	yes	characteristic
9	C₄×C₃₇	C₄×C₂₉	1	1	yes	characteristic
10	C₄×C₂₉	C₄×C₃₇	1	1	yes	characteristic
11	C₂×C₃₇	C₈×C₂₉	1	1	yes	characteristic
12	C₂×C₂₉	C₈×C₃₇	1	1	yes	characteristic
13	C₃₇	C₁₆×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂₉	C₁₆×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₁₆	C₂₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₈	C₂×C₂₉×C₃₇	1	1	yes	characteristic
17	C₄	C₄×C₂₉×C₃₇	1	1	yes	characteristic
18	C₂	C₈×C₂₉×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₂₉×C₃₇
socle, prime radical	C₂×C₂₉×C₃₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×C₃₇	C₁₆	direct (N × H)
5. C₁₆×C₃₇	C₂₉	direct (N × H)
6. C₁₆×C₂₉	C₃₇	direct (N × H)
13. C₃₇	C₁₆×C₂₉	direct (N × H)
14. C₂₉	C₁₆×C₃₇	direct (N × H)
15. C₁₆	C₂₉×C₃₇	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×C₂₉×C₃₇	2
C₁₆×C₃₇	29
C₁₆×C₂₉	37