Subgroups — C₃×D₆₃₀₇ #49180913

Order 37842.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₃₀₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₇×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₉₀₁	—	7	1	no	maximal, Hall
5	C₃×C₁₇×C₅₃	D₇	1	1	yes	characteristic, complemented, Hall
6	C₃×D₃₇₁	—	17	1	no	maximal, Hall
7	D₉₀₁	—	7	1	no	Hall
8	C₃×C₇×C₅₃	D₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×C₅₃	C₃×D₇	1	1	yes	characteristic, complemented, Hall
10	D₃₇₁	—	17	1	no	Hall
11	C₃×D₁₁₉	—	53	1	no	maximal, Hall
12	C₇×C₅₃	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×C₁₇	D₅₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅₃	—	119	1	no	Hall
15	D₁₁₉	—	53	1	no	Hall
16	C₃×C₅₃	D₁₁₉	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₇	C₃×D₅₃	1	1	yes	characteristic, complemented, Hall
18	D₅₃	—	119	1	no	Hall
19	C₃×D₁₇	—	371	1	no	Hall
20	C₅₃	C₃×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₇	D₃₇₁	1	1	yes	characteristic, complemented, Hall
22	C₃×D₇	—	901	1	no	Hall
23	D₁₇	—	371	1	no	Hall
24	C₃×C₇	D₉₀₁	1	1	yes	characteristic, complemented, Hall
25	C₁₇	C₃×D₃₇₁	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	901	1	no	Hall
27	C₇	C₃×D₉₀₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	6307	1	no	Hall
29	C₃	D₆₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	6307	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₆₃₀₇
commutator, cosocle, hypocenter	C₇×C₁₇×C₅₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₅₃	C₂
LCS	G ▷ C₇×C₁₇×C₅₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×C₅₃	C₂	semidirect
2. D₆₃₀₇	C₃	direct (N × H)
3. C₇×C₁₇×C₅₃	C₂×C₃	semidirect
5. C₃×C₁₇×C₅₃	D₇	semidirect
8. C₃×C₇×C₅₃	D₁₇	semidirect
9. C₁₇×C₅₃	C₃×D₇	semidirect
12. C₇×C₅₃	C₃×D₁₇	semidirect
13. C₃×C₇×C₁₇	D₅₃	semidirect
16. C₃×C₅₃	D₁₁₉	semidirect
17. C₇×C₁₇	C₃×D₅₃	semidirect
20. C₅₃	C₃×D₁₁₉	semidirect
21. C₃×C₁₇	D₃₇₁	semidirect
24. C₃×C₇	D₉₀₁	semidirect
25. C₁₇	C₃×D₃₇₁	semidirect
27. C₇	C₃×D₉₀₁	semidirect
29. C₃	D₆₃₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇×C₅₃	2
D₆₃₀₇	3
C₃×D₉₀₁	7
C₃×D₃₇₁	17
C₃×D₁₁₉	53

Subgroups — C3×D6307 #49180913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₆₃₀₇ #49180913