Finite Group Databasebeta

← C₂⁴×C₁₉×C₇₃ #72199648

Subgroups — C₂⁴×C₁₉×C₇₃ #72199648

Order 22192.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₉×C₇₃	C₂	1	15	yes	maximal, direct product factor
2	C₂²×C₁₉×C₇₃	C₂²	1	35	yes	direct product factor
3	C₂×C₁₉×C₇₃	C₂³	1	15	yes	direct product factor
4	C₁₉×C₇₃	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
5	C₂⁴×C₇₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₇₃	C₂×C₁₉	1	15	yes	direct product factor
7	C₂⁴×C₁₉	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₇₃	C₂²×C₁₉	1	35	yes	direct product factor
9	C₂³×C₁₉	C₂×C₇₃	1	15	yes	direct product factor
10	C₂×C₇₃	C₂³×C₁₉	1	15	yes	direct product factor
11	C₂²×C₁₉	C₂²×C₇₃	1	35	yes	direct product factor
12	C₇₃	C₂⁴×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₁₉	C₂³×C₇₃	1	15	yes	direct product factor
14	C₁₉	C₂⁴×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₂⁴	C₁₉×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂³	C₂×C₁₉×C₇₃	1	15	yes	direct product factor
17	C₂²	C₂²×C₁₉×C₇₃	1	35	yes	direct product factor
18	C₂	C₂³×C₁₉×C₇₃	1	15	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. C₂³×C₁₉×C₇₃	C₂	direct (N × H)
2. C₂²×C₁₉×C₇₃	C₂²	direct (N × H)
3. C₂×C₁₉×C₇₃	C₂³	direct (N × H)
4. C₁₉×C₇₃	C₂⁴	direct (N × H)
5. C₂⁴×C₇₃	C₁₉	direct (N × H)
6. C₂³×C₇₃	C₂×C₁₉	direct (N × H)
7. C₂⁴×C₁₉	C₇₃	direct (N × H)
8. C₂²×C₇₃	C₂²×C₁₉	direct (N × H)
9. C₂³×C₁₉	C₂×C₇₃	direct (N × H)
10. C₂×C₇₃	C₂³×C₁₉	direct (N × H)
11. C₂²×C₁₉	C₂²×C₇₃	direct (N × H)
12. C₇₃	C₂⁴×C₁₉	direct (N × H)
13. C₂×C₁₉	C₂³×C₇₃	direct (N × H)
14. C₁₉	C₂⁴×C₇₃	direct (N × H)
15. C₂⁴	C₁₉×C₇₃	direct (N × H)
16. C₂³	C₂×C₁₉×C₇₃	direct (N × H)
17. C₂²	C₂²×C₁₉×C₇₃	direct (N × H)
18. C₂	C₂³×C₁₉×C₇₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₉×C₇₃	2
C₂⁴×C₇₃	19
C₂⁴×C₁₉	73