Subgroups — C₂²×C₃×C₂₃×C₆₇ #32914965

Order 18492.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₃×C₆₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₂₃×C₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₃×C₆₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₂₃×C₆₇	C₂×C₃	1	3	yes	direct product factor
5	C₂₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₃×C₆₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₆₇	C₂×C₂₃	1	3	yes	direct product factor
8	C₂²×C₃×C₂₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₆₇	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₆₇	C₂²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₂₃	C₂×C₆₇	1	3	yes	direct product factor
12	C₂×C₆₇	C₂×C₃×C₂₃	1	3	yes	direct product factor
13	C₂²×C₂₃	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₃	C₂²×C₆₇	1	1	yes	characteristic, direct product factor, Hall
15	C₆₇	C₂²×C₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₃	C₂×C₃×C₆₇	1	3	yes	direct product factor
17	C₂₃	C₂²×C₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃	C₂₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₂₃×C₆₇	1	3	yes	direct product factor
20	C₂²	C₃×C₂₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂²×C₂₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₂₃×C₆₇	1	3	yes	direct product factor

	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. C₂×C₃×C₂₃×C₆₇	C₂	direct (N × H)
2. C₂²×C₂₃×C₆₇	C₃	direct (N × H)
3. C₃×C₂₃×C₆₇	C₂²	direct (N × H)
4. C₂×C₂₃×C₆₇	C₂×C₃	direct (N × H)
5. C₂₃×C₆₇	C₂²×C₃	direct (N × H)
6. C₂²×C₃×C₆₇	C₂₃	direct (N × H)
7. C₂×C₃×C₆₇	C₂×C₂₃	direct (N × H)
8. C₂²×C₃×C₂₃	C₆₇	direct (N × H)
9. C₂²×C₆₇	C₃×C₂₃	direct (N × H)
10. C₃×C₆₇	C₂²×C₂₃	direct (N × H)
11. C₂×C₃×C₂₃	C₂×C₆₇	direct (N × H)
12. C₂×C₆₇	C₂×C₃×C₂₃	direct (N × H)
13. C₂²×C₂₃	C₃×C₆₇	direct (N × H)
14. C₃×C₂₃	C₂²×C₆₇	direct (N × H)
15. C₆₇	C₂²×C₃×C₂₃	direct (N × H)
16. C₂×C₂₃	C₂×C₃×C₆₇	direct (N × H)
17. C₂₃	C₂²×C₃×C₆₇	direct (N × H)
18. C₂²×C₃	C₂₃×C₆₇	direct (N × H)
19. C₂×C₃	C₂×C₂₃×C₆₇	direct (N × H)
20. C₂²	C₃×C₂₃×C₆₇	direct (N × H)
21. C₃	C₂²×C₂₃×C₆₇	direct (N × H)
22. C₂	C₂×C₃×C₂₃×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
C₂×C₃×C₂₃×C₆₇	2
C₂²×C₂₃×C₆₇	3
C₂²×C₃×C₆₇	23
C₂²×C₃×C₂₃	67

Subgroups — C22×C3×C23×C67 #32914965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₂₃×C₆₇ #32914965