Subgroups — C₉×C₁₇×#1181 #31801608

Order 17748.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₇×#1181	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₂₉	C₂×C₃	1	1	yes	characteristic
5	C₁₇×#1181	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₇×C₂₉	C₃×C₄	1	1	yes	characteristic
7	C₉×#1181	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×D₂₉	C₂×C₉	1	1	yes	characteristic
9	C₄×C₉×C₁₇	—	29	1	no	maximal, Hall
10	C₉×D₂₉	C₂×C₁₇	1	1	yes	characteristic
11	C₁₇×C₂₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×#1181	C₃×C₁₇	1	1	yes	characteristic
13	C₂×C₉×C₁₇	—	29	1	no	—
14	C₉×C₂₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄×C₁₇	—	29	1	no	—
16	C₃×D₂₉	C₂×C₃×C₁₇	1	1	yes	characteristic
17	C₉×C₁₇	#1181	1	1	yes	characteristic, direct product factor, Hall
18	#1181	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₁₇	—	29	1	no	—
20	C₃×C₂₉	C₃×C₄×C₁₇	1	1	yes	characteristic
21	C₄×C₁₇	—	29	1	no	Hall
22	D₂₉	C₂×C₉×C₁₇	1	1	yes	characteristic
23	C₃×C₁₇	C₃×#1181	1	1	yes	characteristic
24	C₄×C₉	—	29	1	no	Hall
25	C₂×C₁₇	—	29	1	no	—
26	C₂₉	C₄×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	29	1	no	—
28	C₁₇	C₉×#1181	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₄	—	29	1	no	—
30	C₉	C₁₇×#1181	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	29	1	no	—
32	C₄	—	29	1	no	Sylow
33	C₃	C₃×C₁₇×#1181	1	1	yes	characteristic
34	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₇	#1181
commutator, hypocenter	C₂₉	C₄×C₉×C₁₇
Frattini	C₃	C₃×C₁₇×#1181
Fitting	C₉×C₁₇×C₂₉	C₄
socle	C₃×C₁₇×C₂₉	C₃×C₄
prime radical	C₃×C₁₇×D₂₉	C₂×C₃
cosocle	C₃×D₂₉	C₂×C₃×C₁₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₉×C₁₇

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₇×C₂₉	C₄	semidirect
5. C₁₇×#1181	C₉	direct (N × H)
7. C₉×#1181	C₁₇	direct (N × H)
11. C₁₇×C₂₉	C₄×C₉	semidirect
14. C₉×C₂₉	C₄×C₁₇	semidirect
17. C₉×C₁₇	#1181	direct (N × H)
18. #1181	C₉×C₁₇	direct (N × H)
26. C₂₉	C₄×C₉×C₁₇	semidirect
28. C₁₇	C₉×#1181	direct (N × H)
30. C₉	C₁₇×#1181	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₇×D₂₉	2
C₃×C₁₇×#1181	3
C₉×#1181	17
C₄×C₉×C₁₇	29

Subgroups — C9×C17×#1181 #31801608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₇×#1181 #31801608