Finite Group Databasebeta

← C₃×Dic₃₈ #90704

Subgroups — C₃×Dic₃₈ #90704

Order 456.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₉	C₂	1	2	yes	maximal
3	Dic₃₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₁₉	C₂²	1	1	yes	characteristic
5	C₄×C₁₉	C₂×C₃	1	1	yes	characteristic
6	Dic₁₉	C₂×C₃	1	2	yes	—
7	C₃×C₁₉	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₉	C₂²×C₃	1	1	yes	characteristic
9	C₃×Q₈	—	19	1	no	maximal, Hall
10	C₁₉	C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₄	—	19	2	no	—
12	C₃×C₄	D₁₉	1	1	yes	characteristic
13	Q₈	—	19	1	no	Sylow
14	C₂×C₃	C₂×D₁₉	1	1	yes	characteristic
15	C₄	—	19	2	no	—
16	C₄	C₃×D₁₉	1	1	yes	characteristic
17	C₃	Dic₃₈	1	1	yes	characteristic, direct product factor, Sylow
18	C₂	C₂×C₃×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₁₉
commutator, cosocle	C₂×C₁₉	C₂²×C₃
Frattini	C₂	C₂×C₃×D₁₉
Fitting	C₃×C₄×C₁₉	C₂
socle, prime radical	C₂×C₃×C₁₉	C₂²
hypercenter	C₃×C₄	D₁₉
hypocenter	C₁₉	C₃×Q₈
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. Dic₃₈	C₃	direct (N × H)
7. C₃×C₁₉	Q₈	semidirect
10. C₁₉	C₃×Q₈	semidirect
17. C₃	Dic₃₈	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×C₄×C₁₉	2
C₃×Dic₁₉	2
Dic₃₈	3
C₃×Q₈	19