Subgroups — C₃×C₁₇×Dic₁₆₉ #46828126

Order 34476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic
2	C₁₇×Dic₁₆₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×C₁₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₁₆₉	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₁₆₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₇×Dic₁₃	—	13	1	no	maximal
7	C₃×Dic₁₆₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₃×C₁₇	D₁₃	1	1	yes	characteristic
9	C₂×C₃×C₁₆₉	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×Dic₁₃	—	13	1	no	—
11	Dic₁₆₉	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₃×C₁₇	Dic₁₃	1	1	yes	characteristic
13	C₃×C₁₆₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₁₇	C₃×D₁₃	1	1	yes	characteristic
15	C₂×C₁₆₉	C₂×C₃×C₁₇	1	1	yes	characteristic
16	C₁₃×C₁₇	C₃×Dic₁₃	1	1	yes	characteristic
17	C₃×C₄×C₁₇	—	169	1	no	Hall
18	C₁₆₉	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
19	C₃×Dic₁₃	—	13	1	no	—
20	C₂×C₃×C₁₇	D₁₆₉	1	1	yes	characteristic
21	C₂×C₃×C₁₃	C₁₇×D₁₃	1	1	yes	characteristic
22	C₄×C₁₇	—	169	1	no	Hall
23	Dic₁₃	—	13	1	no	—
24	C₃×C₁₇	Dic₁₆₉	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₁₃	C₁₇×Dic₁₃	1	1	yes	characteristic
26	C₂×C₁₇	C₃×D₁₆₉	1	1	yes	characteristic
27	C₂×C₁₃	C₃×C₁₇×D₁₃	1	1	yes	characteristic
28	C₁₇	C₃×Dic₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₁₃	C₃×C₁₇×Dic₁₃	1	1	yes	characteristic
30	C₃×C₄	—	169	1	no	Hall
31	C₂×C₃	C₁₇×D₁₆₉	1	1	yes	characteristic
32	C₄	—	169	1	no	Sylow
33	C₃	C₁₇×Dic₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₁₇×D₁₆₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₁₆₉
commutator, hypocenter	C₁₆₉	C₃×C₄×C₁₇
Frattini	C₂×C₁₃	C₃×C₁₇×D₁₃
Fitting	C₂×C₃×C₁₇×C₁₆₉	C₂
socle, prime radical	C₂×C₃×C₁₃×C₁₇	D₁₃
cosocle	C₂×C₁₆₉	C₂×C₃×C₁₇
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₁₇×Dic₁₆₉	C₃	direct (N × H)
3. C₃×C₁₇×C₁₆₉	C₄	semidirect
5. C₁₇×C₁₆₉	C₃×C₄	semidirect
7. C₃×Dic₁₆₉	C₁₇	direct (N × H)
11. Dic₁₆₉	C₃×C₁₇	direct (N × H)
13. C₃×C₁₆₉	C₄×C₁₇	semidirect
18. C₁₆₉	C₃×C₄×C₁₇	semidirect
24. C₃×C₁₇	Dic₁₆₉	direct (N × H)
28. C₁₇	C₃×Dic₁₆₉	direct (N × H)
33. C₃	C₁₇×Dic₁₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₇×C₁₆₉	2
C₁₇×Dic₁₆₉	3
C₃×C₁₇×Dic₁₃	13
C₃×Dic₁₆₉	17

Subgroups — C3×C17×Dic169 #46828126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×Dic₁₆₉ #46828126