Subgroups — C₁₇×#157×C₄₉ #44472469

Order 29988.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₃×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₇×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₇×C₄₉	—	6	2	no	—
4	C₇×C₁₇×#157	C₇	1	1	yes	maximal, characteristic
5	C₄×C₁₇×C₄₉	—	9	1	no	maximal, Hall
6	C₃×C₁₇×C₄₉	—	2	2	no	—
7	C₇×C₁₇×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
8	#157×C₄₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₇×C₄₉	—	9	1	no	—
10	C₃²×C₇×C₁₇	C₄×C₇	1	1	yes	characteristic
11	C₃⋊D₃×C₄₉	C₂×C₁₇	1	1	yes	characteristic
12	C₁₇×C₄₉	#157	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₇×C₁₇	—	6	2	no	—
14	C₁₇×#157	C₄₉	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₇×C₁₇	—	9	1	no	—
16	C₃²×C₄₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇×C₁₇	—	2	2	no	—
18	C₁₇×C₃⋊D₃	C₂×C₄₉	1	1	yes	characteristic
19	D₃×C₄₉	—	6	2	no	—
20	C₇×#157	C₇×C₁₇	1	1	yes	characteristic
21	C₂×C₇×C₁₇	—	9	1	no	—
22	C₄×C₄₉	—	9	1	no	Hall
23	C₃²×C₁₇	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₄₉	—	2	2	no	—
25	C₇×C₃⋊D₃	C₂×C₇×C₁₇	1	1	yes	characteristic
26	C₇×C₁₇	C₇×#157	1	1	yes	characteristic
27	D₃×C₁₇	—	6	2	no	—
28	C₂×C₄₉	—	9	1	no	—
29	C₄×C₁₇	—	9	1	no	Hall
30	C₃²×C₇	C₄×C₇×C₁₇	1	1	yes	characteristic
31	C₃×C₁₇	—	2	2	no	—
32	C₄₉	C₁₇×#157	1	1	yes	characteristic, direct product factor, Sylow
33	D₃×C₇	—	6	2	no	—
34	#157	C₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₁₇	—	9	1	no	—
36	C₄×C₇	—	9	1	no	—
37	C₃×C₇	—	2	2	no	—
38	C₃⋊D₃	C₂×C₁₇×C₄₉	1	1	yes	characteristic
39	C₁₇	#157×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	—	9	1	no	—
41	C₃²	C₄×C₁₇×C₄₉	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₇×C₁₇×#157	1	1	yes	characteristic
43	D₃	—	6	2	no	—
44	C₄	—	9	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇×C₄₉	#157
commutator, hypocenter	C₃²	C₄×C₁₇×C₄₉
Frattini	C₇	C₇×C₁₇×#157
Fitting	C₃²×C₁₇×C₄₉	C₄
socle	C₃²×C₇×C₁₇	C₄×C₇
prime radical	C₇×C₁₇×C₃⋊D₃	C₂×C₇
cosocle	C₇×C₃⋊D₃	C₂×C₇×C₁₇
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₇×C₄₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₇×C₄₉	C₄	semidirect
8. #157×C₄₉	C₁₇	direct (N × H)
12. C₁₇×C₄₉	#157	direct (N × H)
14. C₁₇×#157	C₄₉	direct (N × H)
16. C₃²×C₄₉	C₄×C₁₇	semidirect
23. C₃²×C₁₇	C₄×C₄₉	semidirect
32. C₄₉	C₁₇×#157	direct (N × H)
34. #157	C₁₇×C₄₉	direct (N × H)
39. C₁₇	#157×C₄₉	direct (N × H)
41. C₃²	C₄×C₁₇×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₃⋊D₃×C₄₉	2
C₇×C₁₇×#157	7
C₄×C₁₇×C₄₉	9
#157×C₄₉	17

Subgroups — C17×#157×C49 #44472469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#157×C₄₉ #44472469