Finite Group Databasebeta

← C₂⁴×C₁₉⋊C₃ #11745003

Subgroups — C₂⁴×C₁₉⋊C₃ #11745003

Order 912.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₉⋊C₃	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²×C₁₉⋊C₃	C₂²	1	35	yes	direct product factor
4	C₂³×C₁₉	C₂×C₃	1	15	yes	complemented
5	C₂×C₁₉⋊C₃	C₂³	1	15	yes	direct product factor
6	C₂²×C₁₉	C₂²×C₃	1	35	yes	complemented
7	C₁₉⋊C₃	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
8	C₂⁴×C₃	—	19	1	no	maximal, Hall
9	C₂×C₁₉	C₂³×C₃	1	15	yes	complemented
10	C₂³×C₃	—	19	15	no	—
11	C₁₉	C₂⁴×C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂⁴	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²×C₃	—	19	35	no	—
14	C₂³	C₂×C₁₉⋊C₃	1	15	yes	direct product factor
15	C₂×C₃	—	19	15	no	—
16	C₂²	C₂²×C₁₉⋊C₃	1	35	yes	direct product factor
17	C₃	—	19	1	no	Sylow
18	C₂	C₂³×C₁₉⋊C₃	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂⁴×C₁₉	C₃	semidirect
3. C₂²×C₁₉⋊C₃	C₂²	direct (N × H)
4. C₂³×C₁₉	C₂×C₃	semidirect
5. C₂×C₁₉⋊C₃	C₂³	direct (N × H)
6. C₂²×C₁₉	C₂²×C₃	semidirect
7. C₁₉⋊C₃	C₂⁴	direct (N × H)
9. C₂×C₁₉	C₂³×C₃	semidirect
11. C₁₉	C₂⁴×C₃	semidirect
12. C₂⁴	C₁₉⋊C₃	direct (N × H)
14. C₂³	C₂×C₁₉⋊C₃	direct (N × H)
16. C₂²	C₂²×C₁₉⋊C₃	direct (N × H)
18. C₂	C₂³×C₁₉⋊C₃	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⋊C₃	2
C₂⁴×C₁₉	3
C₂⁴×C₃	19