Subgroups — C₂×C₃×C₇²×C₆₇ #34089136

Order 19698.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₆₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇²×C₆₇	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₆₇	C₇	1	8	yes	maximal, direct product factor
5	C₃×C₇×C₆₇	C₂×C₇	1	8	yes	direct product factor
6	C₂×C₇×C₆₇	C₃×C₇	1	8	yes	direct product factor
7	C₇×C₆₇	C₂×C₃×C₇	1	8	yes	direct product factor
8	C₂×C₃×C₆₇	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₇²	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₆₇	C₂×C₇²	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇²	C₂×C₆₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₆₇	C₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₇²	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
14	C₆₇	C₂×C₃×C₇²	1	1	yes	characteristic, direct product factor, Sylow
15	C₇²	C₂×C₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₇	C₇×C₆₇	1	8	yes	direct product factor
17	C₃×C₇	C₂×C₇×C₆₇	1	8	yes	direct product factor
18	C₂×C₇	C₃×C₇×C₆₇	1	8	yes	direct product factor
19	C₇	C₂×C₃×C₇×C₆₇	1	8	yes	direct product factor
20	C₂×C₃	C₇²×C₆₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₇²×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₇²×C₆₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×C₆₇	C₂	direct (N × H)
2. C₂×C₇²×C₆₇	C₃	direct (N × H)
3. C₇²×C₆₇	C₂×C₃	direct (N × H)
4. C₂×C₃×C₇×C₆₇	C₇	direct (N × H)
5. C₃×C₇×C₆₇	C₂×C₇	direct (N × H)
6. C₂×C₇×C₆₇	C₃×C₇	direct (N × H)
7. C₇×C₆₇	C₂×C₃×C₇	direct (N × H)
8. C₂×C₃×C₆₇	C₇²	direct (N × H)
9. C₂×C₃×C₇²	C₆₇	direct (N × H)
10. C₃×C₆₇	C₂×C₇²	direct (N × H)
11. C₃×C₇²	C₂×C₆₇	direct (N × H)
12. C₂×C₆₇	C₃×C₇²	direct (N × H)
13. C₂×C₇²	C₃×C₆₇	direct (N × H)
14. C₆₇	C₂×C₃×C₇²	direct (N × H)
15. C₇²	C₂×C₃×C₆₇	direct (N × H)
16. C₂×C₃×C₇	C₇×C₆₇	direct (N × H)
17. C₃×C₇	C₂×C₇×C₆₇	direct (N × H)
18. C₂×C₇	C₃×C₇×C₆₇	direct (N × H)
19. C₇	C₂×C₃×C₇×C₆₇	direct (N × H)
20. C₂×C₃	C₇²×C₆₇	direct (N × H)
21. C₃	C₂×C₇²×C₆₇	direct (N × H)
22. C₂	C₃×C₇²×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×C₇²×C₆₇	2
C₂×C₇²×C₆₇	3
C₂×C₃×C₇×C₆₇	7
C₂×C₃×C₇²	67

Subgroups — C2×C3×C72×C67 #34089136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇²×C₆₇ #34089136