Subgroups — C₄×C₇×C₉×C₁₄₉ #49176282

Order 37548.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇×C₁₄₉	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×C₁₄₉	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₁₄₉	C₂×C₃	1	1	yes	characteristic
5	C₄×C₉×C₁₄₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₇×C₁₄₉	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₁₄₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₉×C₁₄₉	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₁₄₉	C₂×C₉	1	1	yes	characteristic
10	C₃×C₄×C₁₄₉	C₃×C₇	1	1	yes	characteristic
11	C₉×C₁₄₉	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₁₄₉	C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₄₉	C₂×C₃×C₇	1	1	yes	characteristic
14	C₄×C₁₄₉	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₄₉	C₃×C₄×C₇	1	1	yes	characteristic
16	C₂×C₁₄₉	C₂×C₇×C₉	1	1	yes	characteristic
17	C₄×C₇×C₉	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₄₉	C₄×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇×C₉	C₂×C₁₄₉	1	1	yes	characteristic
20	C₃×C₄×C₇	C₃×C₁₄₉	1	1	yes	characteristic
21	C₇×C₉	C₄×C₁₄₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₇	C₂×C₃×C₁₄₉	1	1	yes	characteristic
23	C₄×C₉	C₇×C₁₄₉	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₇	C₉×C₁₄₉	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₇	C₃×C₄×C₁₄₉	1	1	yes	characteristic
26	C₂×C₉	C₂×C₇×C₁₄₉	1	1	yes	characteristic
27	C₂×C₇	C₂×C₉×C₁₄₉	1	1	yes	characteristic
28	C₃×C₄	C₃×C₇×C₁₄₉	1	1	yes	characteristic
29	C₉	C₄×C₇×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₄×C₉×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₇×C₁₄₉	1	1	yes	characteristic
32	C₄	C₇×C₉×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₇×C₁₄₉	1	1	yes	characteristic
34	C₂	C₂×C₇×C₉×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₇×C₁₄₉
socle, prime radical	C₂×C₃×C₇×C₁₄₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×C₉×C₁₄₉	C₄	direct (N × H)
5. C₄×C₉×C₁₄₉	C₇	direct (N × H)
6. C₄×C₇×C₁₄₉	C₉	direct (N × H)
11. C₉×C₁₄₉	C₄×C₇	direct (N × H)
12. C₇×C₁₄₉	C₄×C₉	direct (N × H)
14. C₄×C₁₄₉	C₇×C₉	direct (N × H)
17. C₄×C₇×C₉	C₁₄₉	direct (N × H)
18. C₁₄₉	C₄×C₇×C₉	direct (N × H)
21. C₇×C₉	C₄×C₁₄₉	direct (N × H)
23. C₄×C₉	C₇×C₁₄₉	direct (N × H)
24. C₄×C₇	C₉×C₁₄₉	direct (N × H)
29. C₉	C₄×C₇×C₁₄₉	direct (N × H)
30. C₇	C₄×C₉×C₁₄₉	direct (N × H)
32. C₄	C₇×C₉×C₁₄₉	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×C₇×C₉×C₁₄₉	2
C₃×C₄×C₇×C₁₄₉	3
C₄×C₉×C₁₄₉	7
C₄×C₇×C₉	149

Subgroups — C4×C7×C9×C149 #49176282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₉×C₁₄₉ #49176282