Subgroups — C₇×D₃₃×C₆₇ #44526239

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×D₁₁×C₆₇	—	3	1	no	maximal, Hall
3	C₇×C₁₁×C₆₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₃₃×C₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₇×C₆₇	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₆₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₁₁×C₆₇	—	3	1	no	Hall
8	C₃×C₇×C₆₇	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₆₇	—	33	1	no	Hall
10	C₁₁×C₆₇	D₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₇	D₃₃	1	1	yes	characteristic, direct product factor, Hall
12	C₇×D₃₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	D₃×C₆₇	—	11	1	no	Hall
14	C₃×C₇×C₁₁	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₇	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₇×D₁₁	—	3	1	no	Hall
17	C₂×C₆₇	—	33	1	no	Hall
18	C₇×C₁₁	D₃×C₆₇	1	1	yes	characteristic, complemented, Hall
19	C₆₇	C₇×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
20	D₃₃	C₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
21	D₃×C₇	—	11	1	no	Hall
22	C₃×C₁₁	C₂×C₇×C₆₇	1	1	yes	characteristic, complemented, Hall
23	D₁₁	—	3	1	no	Hall
24	C₃×C₇	D₁₁×C₆₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇	—	33	1	no	Hall
26	C₁₁	D₃×C₇×C₆₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	D₃₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	11	1	no	Hall
29	C₃	C₇×D₁₁×C₆₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₆₇	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₇×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₆₇	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₇×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
4. D₃₃×C₆₇	C₇	direct (N × H)
6. C₃×C₁₁×C₆₇	C₂×C₇	semidirect
8. C₃×C₇×C₆₇	D₁₁	semidirect
10. C₁₁×C₆₇	D₃×C₇	semidirect
11. C₇×C₆₇	D₃₃	direct (N × H)
12. C₇×D₃₃	C₆₇	direct (N × H)
14. C₃×C₇×C₁₁	C₂×C₆₇	semidirect
15. C₃×C₆₇	C₇×D₁₁	semidirect
18. C₇×C₁₁	D₃×C₆₇	semidirect
19. C₆₇	C₇×D₃₃	direct (N × H)
20. D₃₃	C₇×C₆₇	direct (N × H)
22. C₃×C₁₁	C₂×C₇×C₆₇	semidirect
24. C₃×C₇	D₁₁×C₆₇	semidirect
26. C₁₁	D₃×C₇×C₆₇	semidirect
27. C₇	D₃₃×C₆₇	direct (N × H)
29. C₃	C₇×D₁₁×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
C₇×D₁₁×C₆₇	3
D₃₃×C₆₇	7
D₃×C₇×C₆₇	11
C₇×D₃₃	67

Subgroups — C7×D33×C67 #44526239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₃₃×C₆₇ #44526239