Subgroups — C₃×C₇×D₇₃₇ #44526232

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₃₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×D₆₇	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₆₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₇₃₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₆₇	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₇×D₆₇	—	11	1	no	Hall
10	C₁₁×C₆₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₇	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×D₁₁	—	67	1	no	maximal, Hall
13	C₃×D₆₇	—	11	1	no	Hall
14	C₃×C₇×C₁₁	D₆₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₇	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₇×D₁₁	—	67	1	no	Hall
17	D₆₇	—	11	1	no	Hall
18	C₇×C₁₁	C₃×D₆₇	1	1	yes	characteristic, complemented, Hall
19	C₆₇	C₃×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
20	C₃×D₁₁	—	67	1	no	Hall
21	C₂×C₃×C₇	—	737	1	no	Hall
22	C₃×C₁₁	C₇×D₆₇	1	1	yes	characteristic, complemented, Hall
23	D₁₁	—	67	1	no	Hall
24	C₃×C₇	D₇₃₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	737	1	no	Hall
26	C₁₁	C₃×C₇×D₆₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₇₃₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	737	1	no	Hall
29	C₃	C₇×D₇₃₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	737	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇₃₇
commutator, cosocle, hypocenter	C₁₁×C₆₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₆₇	C₂
LCS	G ▷ C₁₁×C₆₇
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₆₇	C₂	semidirect
2. C₇×D₇₃₇	C₃	direct (N × H)
3. C₇×C₁₁×C₆₇	C₂×C₃	semidirect
4. C₃×D₇₃₇	C₇	direct (N × H)
6. C₃×C₁₁×C₆₇	C₂×C₇	semidirect
7. D₇₃₇	C₃×C₇	direct (N × H)
8. C₃×C₇×C₆₇	D₁₁	semidirect
10. C₁₁×C₆₇	C₂×C₃×C₇	semidirect
11. C₇×C₆₇	C₃×D₁₁	semidirect
14. C₃×C₇×C₁₁	D₆₇	semidirect
15. C₃×C₆₇	C₇×D₁₁	semidirect
18. C₇×C₁₁	C₃×D₆₇	semidirect
19. C₆₇	C₃×C₇×D₁₁	semidirect
22. C₃×C₁₁	C₇×D₆₇	semidirect
24. C₃×C₇	D₇₃₇	direct (N × H)
26. C₁₁	C₃×C₇×D₆₇	semidirect
27. C₇	C₃×D₇₃₇	direct (N × H)
29. C₃	C₇×D₇₃₇	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×C₁₁×C₆₇	2
C₇×D₇₃₇	3
C₃×D₇₃₇	7
C₃×C₇×D₆₇	11
C₃×C₇×D₁₁	67

Subgroups — C3×C7×D737 #44526232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₇₃₇ #44526232