Subgroups — C₃×C₇×D₇×C₇₉ #37551172

Order 23226.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇×C₇₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇×C₇₉	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃×C₇×C₇₉	—	7	1	no	maximal
6	C₃×C₇×C₇₉	—	2	3	no	—
7	C₃×C₇×C₇₉	D₇	1	1	yes	characteristic, direct product factor
8	C₃×C₇×C₇₉	C₂×C₇	1	1	yes	characteristic, complemented
9	C₂×C₇×C₇₉	—	7	1	no	—
10	D₇×C₇₉	C₃×C₇	1	1	yes	characteristic, direct product factor
11	C₇×C₇₉	—	2	3	no	—
12	C₇×C₇₉	C₃×D₇	1	1	yes	characteristic, direct product factor
13	C₇×C₇₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	C₂×C₃×C₇₉	—	7	1	no	Hall
15	C₃×C₇×D₇	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₇₉	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₇₉	—	7	1	no	Hall
18	C₃×C₇²	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
19	C₇×D₇	C₃×C₇₉	1	1	yes	characteristic, direct product factor, Hall
20	C₇₉	C₃×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₇²	C₂×C₃×C₇₉	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₇	—	7	1	no	—
23	C₃×D₇	C₇×C₇₉	1	1	yes	characteristic, direct product factor
24	C₃×C₇	—	2	3	no	—
25	C₃×C₇	D₇×C₇₉	1	1	yes	characteristic, direct product factor
26	C₃×C₇	C₂×C₇×C₇₉	1	1	yes	characteristic, complemented
27	C₂×C₇	—	7	1	no	—
28	D₇	C₃×C₇×C₇₉	1	1	yes	characteristic, direct product factor
29	C₇	—	2	3	no	—
30	C₇	C₂×C₃×C₇×C₇₉	1	1	yes	characteristic, complemented
31	C₇	C₃×D₇×C₇₉	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	7	1	no	Hall
33	C₃	C₇×D₇×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₇₉	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₇×C₇₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₇₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₇×C₇₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₇₉	C₂	semidirect
2. C₇×D₇×C₇₉	C₃	direct (N × H)
3. C₇²×C₇₉	C₂×C₃	semidirect
4. C₃×D₇×C₇₉	C₇	direct (N × H)
7. C₃×C₇×C₇₉	D₇	direct (N × H)
8. C₃×C₇×C₇₉	C₂×C₇	semidirect
10. D₇×C₇₉	C₃×C₇	direct (N × H)
12. C₇×C₇₉	C₃×D₇	direct (N × H)
13. C₇×C₇₉	C₂×C₃×C₇	semidirect
15. C₃×C₇×D₇	C₇₉	direct (N × H)
16. C₃×C₇₉	C₇×D₇	direct (N × H)
18. C₃×C₇²	C₂×C₇₉	semidirect
19. C₇×D₇	C₃×C₇₉	direct (N × H)
20. C₇₉	C₃×C₇×D₇	direct (N × H)
21. C₇²	C₂×C₃×C₇₉	semidirect
23. C₃×D₇	C₇×C₇₉	direct (N × H)
25. C₃×C₇	D₇×C₇₉	direct (N × H)
26. C₃×C₇	C₂×C₇×C₇₉	semidirect
28. D₇	C₃×C₇×C₇₉	direct (N × H)
30. C₇	C₂×C₃×C₇×C₇₉	semidirect
31. C₇	C₃×D₇×C₇₉	direct (N × H)
33. C₃	C₇×D₇×C₇₉	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×C₇²×C₇₉	2
C₇×D₇×C₇₉	3
C₃×D₇×C₇₉	7
C₂×C₃×C₇×C₇₉	7
C₃×C₇×D₇	79

Subgroups — C3×C7×D7×C79 #37551172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₇×C₇₉ #37551172