Subgroups — C₁₇×C₃⋊Dic₁₇₇ #49115653

Order 36108.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₇×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₁₇×Dic₁₇₇	—	3	4	no	maximal
3	C₃²×C₁₇×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₇×C₅₉	D₃	1	4	yes	—
5	C₁₇×Dic₅₉	—	9	1	no	Hall
6	C₃×C₁₇×C₅₉	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₁₇₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₇×C₅₉	C₃⋊D₃	1	1	yes	characteristic
9	C₂×C₃²×C₅₉	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×C₅₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	Dic₁₇₇	—	3	4	no	—
12	C₁₇×C₃⋊Dic₃	—	59	1	no	maximal, Hall
13	C₃²×C₅₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅₉	D₃×C₁₇	1	4	yes	—
15	C₂×C₃²×C₁₇	D₅₉	1	1	yes	characteristic
16	Dic₅₉	—	9	1	no	Hall
17	Dic₃×C₁₇	—	177	4	no	—
18	C₃×C₅₉	Dic₃×C₁₇	1	4	yes	complemented
19	C₃²×C₁₇	Dic₅₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅₉	C₁₇×C₃⋊D₃	1	1	yes	characteristic
21	C₂×C₃×C₁₇	D₁₇₇	1	4	yes	—
22	C₄×C₁₇	—	531	1	no	Hall
23	C₅₉	C₁₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₁₇	Dic₁₇₇	1	4	yes	complemented
25	C₃⋊Dic₃	—	59	1	no	Hall
26	C₂×C₁₇	C₃⋊D₁₇₇	1	1	yes	characteristic
27	C₂×C₃²	C₁₇×D₅₉	1	1	yes	characteristic
28	C₁₇	C₃⋊Dic₁₇₇	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	177	4	no	—
30	C₃²	C₁₇×Dic₅₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₁₇×D₁₇₇	1	4	yes	—
32	C₄	—	531	1	no	Sylow
33	C₃	C₁₇×Dic₁₇₇	1	4	yes	complemented
34	C₂	C₁₇×C₃⋊D₁₇₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊D₁₇₇
commutator, hypocenter	C₃²×C₅₉	C₄×C₁₇
Frattini	C₂	C₁₇×C₃⋊D₁₇₇
Fitting, socle, prime radical	C₂×C₃²×C₁₇×C₅₉	C₂
cosocle	C₂×C₃²×C₅₉	C₂×C₁₇
LCS	G ▷ C₃²×C₅₉
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₁₇×C₅₉	C₄	semidirect
6. C₃×C₁₇×C₅₉	Dic₃	semidirect
7. C₃⋊Dic₁₇₇	C₁₇	direct (N × H)
10. C₁₇×C₅₉	C₃⋊Dic₃	semidirect
13. C₃²×C₅₉	C₄×C₁₇	semidirect
18. C₃×C₅₉	Dic₃×C₁₇	semidirect
19. C₃²×C₁₇	Dic₅₉	semidirect
23. C₅₉	C₁₇×C₃⋊Dic₃	semidirect
24. C₃×C₁₇	Dic₁₇₇	semidirect
28. C₁₇	C₃⋊Dic₁₇₇	direct (N × H)
30. C₃²	C₁₇×Dic₅₉	semidirect
33. C₃	C₁₇×Dic₁₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₇×C₅₉	2
C₁₇×Dic₁₇₇	3
C₃⋊Dic₁₇₇	17
C₁₇×C₃⋊Dic₃	59

Subgroups — C17×C3⋊Dic177 #49115653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₃⋊Dic₁₇₇ #49115653