Subgroups — D₃×C₁₉×C₉₇⋊C₃ #45684331

Order 33174.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₉₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₉×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×C₉₇⋊C₃	—	3	1	no	maximal
4	C₃×C₁₉×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₉×C₉₇⋊C₃	—	2	1	no	—
6	C₁₉×C₉₇⋊C₃	D₃	1	1	yes	characteristic, direct product factor
7	C₂×C₁₉×C₉₇	—	3	1	no	Hall
8	C₁₉×C₉₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	D₃×C₉₇⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₉₇⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	D₃×C₉₇	C₃×C₁₉	1	1	yes	characteristic, complemented
12	C₂×C₉₇⋊C₃	—	3	1	no	—
13	C₃×D₃×C₁₉	—	97	1	no	maximal, Hall
14	C₃×C₉₇	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
15	C₉₇⋊C₃	—	2	1	no	—
16	C₉₇⋊C₃	D₃×C₁₉	1	1	yes	characteristic, direct product factor
17	C₂×C₉₇	—	3	1	no	Hall
18	C₃²×C₁₉	—	97	1	no	Hall
19	C₂×C₃×C₁₉	—	291	1	no	—
20	D₃×C₁₉	C₉₇⋊C₃	1	1	yes	characteristic, direct product factor
21	C₉₇	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₉	—	97	1	no	—
23	C₃×C₁₉	—	194	1	no	—
24	C₃×C₁₉	C₂×C₉₇⋊C₃	1	1	yes	characteristic, complemented
25	C₂×C₁₉	—	3	1	no	Hall
26	C₁₉	D₃×C₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×D₃	—	97	1	no	Hall
28	C₃²	—	97	1	no	Sylow
29	C₂×C₃	—	291	1	no	—
30	D₃	C₁₉×C₉₇⋊C₃	1	1	yes	characteristic, direct product factor
31	C₃	—	97	1	no	—
32	C₃	—	194	1	no	—
33	C₃	C₂×C₁₉×C₉₇⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₃×C₉₇⋊C₃
commutator, cosocle, hypocenter	C₃×C₉₇	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₉₇	C₂×C₃
LCS	G ▷ C₃×C₉₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₉₇⋊C₃	C₂	semidirect
2. D₃×C₁₉×C₉₇	C₃	semidirect
4. C₃×C₁₉×C₉₇	C₂×C₃	semidirect
6. C₁₉×C₉₇⋊C₃	D₃	direct (N × H)
8. C₁₉×C₉₇	C₃×D₃	semidirect
9. D₃×C₉₇⋊C₃	C₁₉	direct (N × H)
10. C₃×C₉₇⋊C₃	C₂×C₁₉	semidirect
11. D₃×C₉₇	C₃×C₁₉	semidirect
14. C₃×C₉₇	C₂×C₃×C₁₉	semidirect
16. C₉₇⋊C₃	D₃×C₁₉	direct (N × H)
20. D₃×C₁₉	C₉₇⋊C₃	direct (N × H)
21. C₉₇	C₃×D₃×C₁₉	semidirect
24. C₃×C₁₉	C₂×C₉₇⋊C₃	semidirect
26. C₁₉	D₃×C₉₇⋊C₃	direct (N × H)
30. D₃	C₁₉×C₉₇⋊C₃	direct (N × H)
33. C₃	C₂×C₁₉×C₉₇⋊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×C₉₇⋊C₃	2
D₃×C₁₉×C₉₇	3
C₂×C₁₉×C₉₇⋊C₃	3
D₃×C₉₇⋊C₃	19
C₃×D₃×C₁₉	97

Subgroups — D3×C19×C97⋊C3 #45684331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉×C₉₇⋊C₃ #45684331