Subgroups — C₇×C₁₉×D₃₃ #22578613

Order 8778.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₉×D₁₁	—	3	1	no	maximal, Hall
3	C₇×C₁₁×C₁₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₉×D₃₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₇×C₁₉	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×D₃₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×D₁₁	—	3	1	no	Hall
9	C₃×C₇×C₁₉	D₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₁₉	—	33	1	no	Hall
11	C₃×C₇×C₁₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₁₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇×D₁₁	—	3	1	no	Hall
14	C₇×C₁₉	D₃₃	1	1	yes	characteristic, direct product factor, Hall
15	D₃×C₁₉	—	11	1	no	Hall
16	C₇×C₁₁	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
17	D₃₃	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₁₉	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
19	D₃×C₇	—	11	1	no	Hall
20	C₂×C₁₉	—	33	1	no	Hall
21	C₃×C₁₁	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
22	D₁₁	—	3	1	no	Hall
23	C₃×C₇	C₁₉×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₁₉	C₇×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₇	—	33	1	no	Hall
26	C₁₁	D₃×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₁₉×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	11	1	no	Hall
29	C₃	C₇×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₃₃
commutator, hypocenter	C₃×C₁₁	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₁₉	C₂	semidirect
3. C₇×C₁₁×C₁₉	D₃	semidirect
4. C₁₉×D₃₃	C₇	direct (N × H)
6. C₃×C₁₁×C₁₉	C₂×C₇	semidirect
7. C₇×D₃₃	C₁₉	direct (N × H)
9. C₃×C₇×C₁₉	D₁₁	semidirect
11. C₃×C₇×C₁₁	C₂×C₁₉	semidirect
12. C₁₁×C₁₉	D₃×C₇	semidirect
14. C₇×C₁₉	D₃₃	direct (N × H)
16. C₇×C₁₁	D₃×C₁₉	semidirect
17. D₃₃	C₇×C₁₉	direct (N × H)
18. C₃×C₁₉	C₇×D₁₁	semidirect
21. C₃×C₁₁	C₂×C₇×C₁₉	semidirect
23. C₃×C₇	C₁₉×D₁₁	semidirect
24. C₁₉	C₇×D₃₃	direct (N × H)
26. C₁₁	D₃×C₇×C₁₉	semidirect
27. C₇	C₁₉×D₃₃	direct (N × H)
29. C₃	C₇×C₁₉×D₁₁	semidirect

Subgroups — C7×C19×D33 #22578613

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₁₉×D₃₃ #22578613