Subgroups — C₃×D₁₇×D₁₈₁ #49147362

Order 36924.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃₀₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₇×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₁₈₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₁₈₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₀₇₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₇×D₁₈₁	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₇×C₁₈₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₇×C₁₈₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₁₈₁	—	17	1	no	maximal, Hall
11	C₂×C₃×C₁₈₁	—	17	1	no	—
12	C₃×D₁₈₁	—	17	1	no	—
13	C₃×D₁₈₁	D₁₇	1	1	yes	characteristic, direct product factor
14	C₂×D₁₈₁	—	17	1	no	Hall
15	C₃×C₁₈₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₈₁	—	17	1	no	—
17	D₁₈₁	—	17	1	no	—
18	D₁₈₁	C₃×D₁₇	1	1	yes	characteristic, direct product factor
19	C₂×C₃×D₁₇	—	181	1	no	maximal, Hall
20	C₁₈₁	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₇	—	181	1	no	—
22	C₃×D₁₇	—	181	1	no	—
23	C₃×D₁₇	D₁₈₁	1	1	yes	characteristic, direct product factor
24	C₂×D₁₇	—	181	1	no	Hall
25	C₃×C₁₇	C₂×D₁₈₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₇	—	181	1	no	—
27	D₁₇	—	181	1	no	—
28	D₁₇	C₃×D₁₈₁	1	1	yes	characteristic, direct product factor
29	C₁₇	C₂×C₃×D₁₈₁	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	3077	1	no	Hall
31	C₂×C₃	—	3077	1	no	—
32	C₂×C₃	—	17	1	no	—
33	C₂×C₃	—	181	1	no	—
34	C₂²	—	3077	1	no	Sylow
35	C₃	D₁₇×D₁₈₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	3077	1	no	—
37	C₂	—	17	1	no	—
38	C₂	—	181	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₇×D₁₈₁
commutator, cosocle, hypocenter	C₁₇×C₁₈₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₈₁	C₂²
LCS	G ▷ C₁₇×C₁₈₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃₀₇₇	C₂	semidirect
2. C₃×D₁₇×C₁₈₁	C₂	semidirect
3. C₃×C₁₇×D₁₈₁	C₂	semidirect
4. D₁₇×D₁₈₁	C₃	direct (N × H)
5. C₃×C₁₇×C₁₈₁	C₂²	semidirect
6. D₃₀₇₇	C₂×C₃	semidirect
7. C₁₇×D₁₈₁	C₂×C₃	semidirect
8. D₁₇×C₁₈₁	C₂×C₃	semidirect
9. C₁₇×C₁₈₁	C₂²×C₃	semidirect
13. C₃×D₁₈₁	D₁₇	direct (N × H)
15. C₃×C₁₈₁	C₂×D₁₇	semidirect
18. D₁₈₁	C₃×D₁₇	direct (N × H)
20. C₁₈₁	C₂×C₃×D₁₇	semidirect
23. C₃×D₁₇	D₁₈₁	direct (N × H)
25. C₃×C₁₇	C₂×D₁₈₁	semidirect
28. D₁₇	C₃×D₁₈₁	direct (N × H)
29. C₁₇	C₂×C₃×D₁₈₁	semidirect
35. C₃	D₁₇×D₁₈₁	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×D₃₀₇₇	2
C₃×D₁₇×C₁₈₁	2
C₃×C₁₇×D₁₈₁	2
D₁₇×D₁₈₁	3
C₂×C₃×D₁₈₁	17
C₂×C₃×D₁₇	181

Subgroups — C3×D17×D181 #49147362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₇×D₁₈₁ #49147362