Subgroups — C₂×C₃×D₁₇₉₇ #36340730

Order 21564.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₇₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅₉₉	—	3	1	no	maximal
4	C₂×D₁₇₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₅₉₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅₉₉	—	2	1	no	—
7	C₂×C₃×C₅₉₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₅₉₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₁₇₉₇	C₂×C₃	1	2	yes	direct product factor
10	C₃×D₅₉₉	—	3	2	no	—
11	C₂×D₅₉₉	—	3	1	no	Hall
12	C₃×C₅₉₉	—	2	1	no	—
13	C₃×C₅₉₉	C₂×D₃	1	1	yes	characteristic, complemented
14	C₃×C₅₉₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₅₉₉	C₃×D₃	1	1	yes	characteristic, complemented
16	D₅₉₉	—	3	2	no	—
17	C₅₉₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×D₃	—	599	1	no	maximal, Hall
19	C₂×C₃²	D₅₉₉	1	1	yes	characteristic, complemented
20	C₃×D₃	—	599	2	no	—
21	C₂²×C₃	—	1797	1	no	—
22	C₂×D₃	—	599	1	no	—
23	C₃²	C₂×D₅₉₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	2	1	no	—
25	C₂×C₃	—	1797	2	no	—
26	C₂×C₃	C₃×D₅₉₉	1	1	yes	characteristic, complemented
27	C₂×C₃	D₁₇₉₇	1	1	yes	characteristic, direct product factor
28	D₃	—	599	2	no	—
29	C₂²	—	1797	1	no	Sylow
30	C₃	—	2	1	no	—
31	C₃	C₂×D₁₇₉₇	1	1	yes	characteristic, direct product factor
32	C₃	C₂×C₃×D₅₉₉	1	1	yes	characteristic, complemented
33	C₂	—	1797	2	no	—
34	C₂	C₃×D₁₇₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₇₉₇
commutator, cosocle, hypocenter	C₃×C₅₉₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅₉₉	C₂
LCS	G ▷ C₃×C₅₉₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₇₉₇	C₂	direct (N × H)
2. C₂×C₃²×C₅₉₉	C₂	semidirect
4. C₂×D₁₇₉₇	C₃	direct (N × H)
5. C₃²×C₅₉₉	C₂²	semidirect
7. C₂×C₃×C₅₉₉	D₃	semidirect
8. C₂×C₃×C₅₉₉	C₂×C₃	semidirect
9. D₁₇₉₇	C₂×C₃	direct (N × H)
13. C₃×C₅₉₉	C₂×D₃	semidirect
14. C₃×C₅₉₉	C₂²×C₃	semidirect
15. C₂×C₅₉₉	C₃×D₃	semidirect
17. C₅₉₉	C₂×C₃×D₃	semidirect
19. C₂×C₃²	D₅₉₉	semidirect
23. C₃²	C₂×D₅₉₉	semidirect
26. C₂×C₃	C₃×D₅₉₉	semidirect
27. C₂×C₃	D₁₇₉₇	direct (N × H)
31. C₃	C₂×D₁₇₉₇	direct (N × H)
32. C₃	C₂×C₃×D₅₉₉	semidirect
34. C₂	C₃×D₁₇₉₇	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×D₁₇₉₇	2
C₂×C₃²×C₅₉₉	2
C₂×C₃×D₅₉₉	3
C₂×D₁₇₉₇	3
C₂×C₃×D₃	599

Subgroups — C2×C3×D1797 #36340730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₇₉₇ #36340730