Subgroups — C₁₁×D₂₁×C₆₇ #44526241

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	—	3	1	no	maximal, Hall
3	C₇×C₁₁×C₆₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃×C₁₁×C₆₇	—	7	1	no	maximal, Hall
5	D₂₁×C₆₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₁×C₆₇	D₇	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₁×C₆₇	—	21	1	no	Hall
8	C₃×C₇×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	D₇×C₆₇	—	3	1	no	Hall
10	C₁₁×C₆₇	D₂₁	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₆₇	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×D₂₁	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	D₃×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, complemented, Hall
16	C₁₁×D₇	—	3	1	no	Hall
17	C₂×C₆₇	—	21	1	no	Hall
18	C₇×C₁₁	D₃×C₆₇	1	1	yes	characteristic, complemented, Hall
19	C₆₇	C₁₁×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
20	D₃×C₁₁	—	7	1	no	Hall
21	D₂₁	C₁₁×C₆₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₁	D₇×C₆₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₁₁	—	21	1	no	Hall
24	C₃×C₇	C₂×C₁₁×C₆₇	1	1	yes	characteristic, complemented, Hall
25	D₇	—	3	1	no	Hall
26	C₁₁	D₂₁×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	D₃×C₁₁×C₆₇	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	7	1	no	Hall
29	C₃	C₁₁×D₇×C₆₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₆₇	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₁₁×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₆₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ 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
3. C₇×C₁₁×C₆₇	D₃	semidirect
5. D₂₁×C₆₇	C₁₁	direct (N × H)
6. C₃×C₁₁×C₆₇	D₇	semidirect
8. C₃×C₇×C₆₇	C₂×C₁₁	semidirect
10. C₁₁×C₆₇	D₂₁	direct (N × H)
11. C₇×C₆₇	D₃×C₁₁	semidirect
12. C₁₁×D₂₁	C₆₇	direct (N × H)
14. C₃×C₇×C₁₁	C₂×C₆₇	semidirect
15. C₃×C₆₇	C₁₁×D₇	semidirect
18. C₇×C₁₁	D₃×C₆₇	semidirect
19. C₆₇	C₁₁×D₂₁	direct (N × H)
21. D₂₁	C₁₁×C₆₇	direct (N × H)
22. C₃×C₁₁	D₇×C₆₇	semidirect
24. C₃×C₇	C₂×C₁₁×C₆₇	semidirect
26. C₁₁	D₂₁×C₆₇	direct (N × H)
27. C₇	D₃×C₁₁×C₆₇	semidirect
29. C₃	C₁₁×D₇×C₆₇	semidirect

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
D₃×C₁₁×C₆₇	7
D₂₁×C₆₇	11
C₁₁×D₂₁	67

Subgroups — C11×D21×C67 #44526241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₂₁×C₆₇ #44526241