Subgroups — C₁₉×C₃⋊(D₆₇⋊C₃) #37523869

Order 22914.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₆₇⋊C₃	—	3	1	no	maximal
3	C₁₉×D₂₀₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₉×C₆₇⋊C₃	—	2	1	no	—
6	C₁₉×C₆₇⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₁₉×D₆₇	—	3	1	no	Hall
8	C₁₉×C₆₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(D₆₇⋊C₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₆₇⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	D₂₀₁	C₃×C₁₉	1	1	yes	characteristic, complemented
12	D₆₇⋊C₃	—	3	1	no	—
13	C₃×D₃×C₁₉	—	67	1	no	maximal, Hall
14	C₃×C₆₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
15	C₆₇⋊C₃	—	2	1	no	—
16	C₆₇⋊C₃	D₃×C₁₉	1	1	yes	characteristic, complemented
17	C₃²×C₁₉	—	67	1	no	Hall
18	D₆₇	—	3	1	no	Hall
19	C₂×C₃×C₁₉	—	201	1	no	—
20	D₃×C₁₉	—	67	1	no	—
21	C₆₇	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₉	—	67	1	no	—
23	C₃×C₁₉	—	134	1	no	—
24	C₃×C₁₉	D₆₇⋊C₃	1	1	yes	characteristic, complemented
25	C₂×C₁₉	—	201	1	no	Hall
26	C₁₉	C₃⋊(D₆₇⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	—	67	1	no	Hall
28	C₃²	—	67	1	no	Sylow
29	C₂×C₃	—	201	1	no	—
30	D₃	—	67	1	no	—
31	C₃	—	67	1	no	—
32	C₃	—	134	1	no	—
33	C₃	C₁₉×D₆₇⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	201	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊(D₆₇⋊C₃)
commutator, cosocle, hypocenter	C₃×C₆₇	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₆₇	C₂×C₃
LCS	G ▷ C₃×C₆₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₆₇⋊C₃	C₂	semidirect
3. C₁₉×D₂₀₁	C₃	semidirect
4. C₃×C₁₉×C₆₇	C₂×C₃	semidirect
6. C₁₉×C₆₇⋊C₃	D₃	semidirect
8. C₁₉×C₆₇	C₃×D₃	semidirect
9. C₃⋊(D₆₇⋊C₃)	C₁₉	direct (N × H)
10. C₃×C₆₇⋊C₃	C₂×C₁₉	semidirect
11. D₂₀₁	C₃×C₁₉	semidirect
14. C₃×C₆₇	C₂×C₃×C₁₉	semidirect
16. C₆₇⋊C₃	D₃×C₁₉	semidirect
21. C₆₇	C₃×D₃×C₁₉	semidirect
24. C₃×C₁₉	D₆₇⋊C₃	semidirect
26. C₁₉	C₃⋊(D₆₇⋊C₃)	direct (N × H)
33. C₃	C₁₉×D₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×C₆₇⋊C₃	2
C₁₉×D₆₇⋊C₃	3
C₁₉×D₂₀₁	3
C₃⋊(D₆₇⋊C₃)	19
C₃×D₃×C₁₉	67

Subgroups — C19×C3⋊(D67⋊C3) #37523869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊(D₆₇⋊C₃) #37523869