Subgroups — C₃×C₁₁×D₇×C₆₇ #44526233

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	C₁₁×D₇×C₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₆₇	—	7	1	no	maximal, Hall
5	C₃×D₇×C₆₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₁×C₆₇	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₁×C₆₇	—	7	1	no	Hall
8	C₃×C₇×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	D₇×C₆₇	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₁₁×C₆₇	C₃×D₇	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₆₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×D₇	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₆₇	—	7	1	no	Hall
14	C₃×C₇×C₁₁	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₇	C₁₁×D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁×D₇	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₆₇	—	7	1	no	Hall
18	C₇×C₁₁	C₂×C₃×C₆₇	1	1	yes	characteristic, complemented, Hall
19	C₆₇	C₃×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₁₁	—	7	1	no	Hall
21	C₃×D₇	C₁₁×C₆₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₁	D₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₁	—	7	1	no	Hall
24	C₃×C₇	C₂×C₁₁×C₆₇	1	1	yes	characteristic, complemented, Hall
25	D₇	C₃×C₁₁×C₆₇	1	1	yes	characteristic, direct product factor, Hall
26	C₁₁	C₃×D₇×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₃×C₁₁×C₆₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	7	1	no	Hall
29	C₃	C₁₁×D₇×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₆₇	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₁₁×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₆₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₁×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₆₇	C₂	semidirect
2. C₁₁×D₇×C₆₇	C₃	direct (N × H)
3. C₇×C₁₁×C₆₇	C₂×C₃	semidirect
5. C₃×D₇×C₆₇	C₁₁	direct (N × H)
6. C₃×C₁₁×C₆₇	D₇	direct (N × H)
8. C₃×C₇×C₆₇	C₂×C₁₁	semidirect
9. D₇×C₆₇	C₃×C₁₁	direct (N × H)
10. C₁₁×C₆₇	C₃×D₇	direct (N × H)
11. C₇×C₆₇	C₂×C₃×C₁₁	semidirect
12. C₃×C₁₁×D₇	C₆₇	direct (N × H)
14. C₃×C₇×C₁₁	C₂×C₆₇	semidirect
15. C₃×C₆₇	C₁₁×D₇	direct (N × H)
16. C₁₁×D₇	C₃×C₆₇	direct (N × H)
18. C₇×C₁₁	C₂×C₃×C₆₇	semidirect
19. C₆₇	C₃×C₁₁×D₇	direct (N × H)
21. C₃×D₇	C₁₁×C₆₇	direct (N × H)
22. C₃×C₁₁	D₇×C₆₇	direct (N × H)
24. C₃×C₇	C₂×C₁₁×C₆₇	semidirect
25. D₇	C₃×C₁₁×C₆₇	direct (N × H)
26. C₁₁	C₃×D₇×C₆₇	direct (N × H)
27. C₇	C₂×C₃×C₁₁×C₆₇	semidirect
29. C₃	C₁₁×D₇×C₆₇	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
C₁₁×D₇×C₆₇	3
C₂×C₃×C₁₁×C₆₇	7
C₃×D₇×C₆₇	11
C₃×C₁₁×D₇	67

Subgroups — C3×C11×D7×C67 #44526233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×D₇×C₆₇ #44526233