Subgroups — C₃×C₄×C₇×C₃₇₃ #44531240

Order 31332.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₃₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₃₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₃₇₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₃₇₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₃₇₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₃₇₃	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₇₃	C₂×C₇	1	1	yes	characteristic
8	C₄×C₃₇₃	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₃₇₃	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₇₃	C₂×C₃×C₇	1	1	yes	characteristic
11	C₃₇₃	C₃×C₄×C₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₄×C₇	C₃₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₇	C₂×C₃₇₃	1	1	yes	characteristic
14	C₄×C₇	C₃×C₃₇₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇	C₄×C₃₇₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₇	C₂×C₃×C₃₇₃	1	1	yes	characteristic
17	C₃×C₄	C₇×C₃₇₃	1	1	yes	characteristic, direct product factor, Hall
18	C₇	C₃×C₄×C₃₇₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₂×C₇×C₃₇₃	1	1	yes	characteristic
20	C₄	C₃×C₇×C₃₇₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₄×C₇×C₃₇₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₇×C₃₇₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₇×C₃₇₃
socle, prime radical	C₂×C₃×C₇×C₃₇₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₃₇₃	C₃	direct (N × H)
3. C₃×C₇×C₃₇₃	C₄	direct (N × H)
5. C₃×C₄×C₃₇₃	C₇	direct (N × H)
6. C₇×C₃₇₃	C₃×C₄	direct (N × H)
8. C₄×C₃₇₃	C₃×C₇	direct (N × H)
9. C₃×C₃₇₃	C₄×C₇	direct (N × H)
11. C₃₇₃	C₃×C₄×C₇	direct (N × H)
12. C₃×C₄×C₇	C₃₇₃	direct (N × H)
14. C₄×C₇	C₃×C₃₇₃	direct (N × H)
15. C₃×C₇	C₄×C₃₇₃	direct (N × H)
17. C₃×C₄	C₇×C₃₇₃	direct (N × H)
18. C₇	C₃×C₄×C₃₇₃	direct (N × H)
20. C₄	C₃×C₇×C₃₇₃	direct (N × H)
21. C₃	C₄×C₇×C₃₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₃₇₃	2
C₄×C₇×C₃₇₃	3
C₃×C₄×C₃₇₃	7
C₃×C₄×C₇	373

Subgroups — C3×C4×C7×C373 #44531240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₇×C₃₇₃ #44531240