Subgroups — C₂×C₉×C₃₇×C₄₇ #44531053

Order 31302.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₃₇×C₄₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₇×C₄₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₃₇×C₄₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₃₇×C₄₇	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₉×C₄₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₉×C₃₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₉×C₄₇	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₃₇	C₂×C₄₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₄₇	C₃×C₃₇	1	1	yes	characteristic
11	C₂×C₃×C₃₇	C₃×C₄₇	1	1	yes	characteristic
12	C₃×C₄₇	C₂×C₃×C₃₇	1	1	yes	characteristic
13	C₃×C₃₇	C₂×C₃×C₄₇	1	1	yes	characteristic
14	C₂×C₄₇	C₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃₇	C₉×C₄₇	1	1	yes	characteristic, direct product factor, Hall
16	C₄₇	C₂×C₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	C₂×C₉×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₉	C₃₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₉	C₂×C₃₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₃₇×C₄₇	1	1	yes	characteristic
21	C₃	C₂×C₃×C₃₇×C₄₇	1	1	yes	characteristic
22	C₂	C₉×C₃₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₃₇×C₄₇
socle, prime radical	C₂×C₃×C₃₇×C₄₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₃₇×C₄₇	C₂	direct (N × H)
4. C₂×C₃₇×C₄₇	C₉	direct (N × H)
5. C₃₇×C₄₇	C₂×C₉	direct (N × H)
6. C₂×C₉×C₄₇	C₃₇	direct (N × H)
7. C₂×C₉×C₃₇	C₄₇	direct (N × H)
8. C₉×C₄₇	C₂×C₃₇	direct (N × H)
9. C₉×C₃₇	C₂×C₄₇	direct (N × H)
14. C₂×C₄₇	C₉×C₃₇	direct (N × H)
15. C₂×C₃₇	C₉×C₄₇	direct (N × H)
16. C₄₇	C₂×C₉×C₃₇	direct (N × H)
17. C₃₇	C₂×C₉×C₄₇	direct (N × H)
18. C₂×C₉	C₃₇×C₄₇	direct (N × H)
19. C₉	C₂×C₃₇×C₄₇	direct (N × H)
22. C₂	C₉×C₃₇×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
C₉×C₃₇×C₄₇	2
C₂×C₃×C₃₇×C₄₇	3
C₂×C₉×C₄₇	37
C₂×C₉×C₃₇	47

Subgroups — C2×C9×C37×C47 #44531053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₃₇×C₄₇ #44531053