Subgroups — C₃×C₁₇×#10621729 #46828331

Order 34476.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#10621729	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₇×#261	—	13	2	no	maximal
7	C₃×#10621729	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₇×D₁₃	—	13	2	no	—
9	C₃×C₁₇×D₁₃	—	26	6	no	—
10	C₃×C₁₃⋊D₁₃	C₂×C₁₇	1	1	yes	characteristic
11	C₁₇×#261	—	13	2	no	—
12	#10621729	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₁₃×C₁₇	—	2	6	no	—
14	C₃×C₁₃×C₁₇	#261	1	2	yes	complemented
15	C₃×C₁₃²	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₁₇×D₁₃	—	13	2	no	—
17	C₁₇×D₁₃	—	26	6	no	—
18	C₁₃⋊D₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
19	C₁₃×C₁₇	—	2	6	no	—
20	C₁₃×C₁₇	C₃×#261	1	2	yes	complemented
21	C₃×C₄×C₁₇	—	169	1	no	Hall
22	C₁₃²	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
23	C₃×#261	—	13	2	no	—
24	C₂×C₃×C₁₇	—	169	1	no	—
25	C₃×D₁₃	—	13	2	no	—
26	C₃×D₁₃	—	26	6	no	—
27	C₄×C₁₇	—	169	1	no	Hall
28	#261	—	13	2	no	—
29	C₃×C₁₇	#10621729	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₃	—	2	6	no	—
31	C₃×C₁₃	C₁₇×#261	1	2	yes	complemented
32	C₂×C₁₇	—	169	1	no	—
33	D₁₃	—	13	2	no	—
34	D₁₃	—	26	6	no	—
35	C₁₇	C₃×#10621729	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₃	—	2	6	no	—
37	C₁₃	C₃×C₁₇×#261	1	2	yes	complemented
38	C₃×C₄	—	169	1	no	Hall
39	C₂×C₃	—	169	1	no	—
40	C₄	—	169	1	no	Sylow
41	C₃	C₁₇×#10621729	1	1	yes	characteristic, direct product factor, Sylow
42	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₇	#10621729
commutator, hypocenter	C₁₃²	C₃×C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₁₇	C₄
prime radical	C₃×C₁₇×C₁₃⋊D₁₃	C₂
cosocle	C₁₃⋊D₁₃	C₂×C₃×C₁₇
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₁₇×#10621729	C₃	direct (N × H)
3. C₃×C₁₃²×C₁₇	C₄	semidirect
5. C₁₃²×C₁₇	C₃×C₄	semidirect
7. C₃×#10621729	C₁₇	direct (N × H)
12. #10621729	C₃×C₁₇	direct (N × H)
14. C₃×C₁₃×C₁₇	#261	semidirect
15. C₃×C₁₃²	C₄×C₁₇	semidirect
20. C₁₃×C₁₇	C₃×#261	semidirect
22. C₁₃²	C₃×C₄×C₁₇	semidirect
29. C₃×C₁₇	#10621729	direct (N × H)
31. C₃×C₁₃	C₁₇×#261	semidirect
35. C₁₇	C₃×#10621729	direct (N × H)
37. C₁₃	C₃×C₁₇×#261	semidirect
41. C₃	C₁₇×#10621729	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×C₁₇×C₁₃⋊D₁₃	2
C₁₇×#10621729	3
C₃×C₁₇×#261	13
C₃×#10621729	17

Subgroups — C3×C17×#10621729 #46828331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×#10621729 #46828331