Subgroups — C₄₉×#10597480 #44472471

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×#10597480	C₇	1	1	yes	maximal, characteristic
5	C₄₉×Dic₁₇	—	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	—	17	1	no	maximal, Hall
9	C₂×C₁₇×C₄₉	—	9	1	no	—
10	C₃²×C₇×C₁₇	C₄×C₇	1	1	yes	characteristic
11	C₃⋊D₃×C₄₉	D₁₇	1	1	yes	characteristic
12	C₁₇×C₄₉	#157	1	1	yes	characteristic, complemented, Hall
13	D₃×C₇×C₁₇	—	6	2	no	—
14	#10597480	C₄₉	1	1	yes	characteristic, direct product factor, Hall
15	C₇×Dic₁₇	—	9	1	no	—
16	C₃²×C₄₉	Dic₁₇	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	—	17	1	no	—
21	C₂×C₇×C₁₇	—	9	1	no	—
22	C₄×C₄₉	—	153	1	no	Hall
23	C₃²×C₁₇	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₄₉	—	2	2	no	—
25	C₇×C₃⋊D₃	C₇×D₁₇	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	Dic₁₇	—	9	1	no	Hall
30	C₃²×C₇	C₇×Dic₁₇	1	1	yes	characteristic
31	C₃×C₁₇	—	2	2	no	—
32	C₄₉	#10597480	1	1	yes	characteristic, direct product factor, Sylow
33	D₃×C₇	—	6	2	no	—
34	#157	—	17	1	no	Hall
35	C₂×C₁₇	—	9	1	no	—
36	C₄×C₇	—	153	1	no	—
37	C₃×C₇	—	2	2	no	—
38	C₃⋊D₃	D₁₇×C₄₉	1	1	yes	characteristic
39	C₁₇	#157×C₄₉	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	9	1	no	—
41	C₃²	C₄₉×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₇×#10597480	1	1	yes	characteristic
43	D₃	—	6	2	no	—
44	C₄	—	153	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₄₉	#10597480
commutator, hypocenter	C₃²×C₁₇	C₄×C₄₉
Frattini	C₇	C₇×#10597480
Fitting	C₃²×C₁₇×C₄₉	C₄
socle	C₃²×C₇×C₁₇	C₄×C₇
prime radical, cosocle	C₇×C₁₇×C₃⋊D₃	C₂×C₇
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₄₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₇×C₄₉	C₄	semidirect
12. C₁₇×C₄₉	#157	semidirect
14. #10597480	C₄₉	direct (N × H)
16. C₃²×C₄₉	Dic₁₇	semidirect
23. C₃²×C₁₇	C₄×C₄₉	semidirect
32. C₄₉	#10597480	direct (N × H)
39. C₁₇	#157×C₄₉	semidirect
41. C₃²	C₄₉×Dic₁₇	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×#10597480	7
C₄₉×Dic₁₇	9
#157×C₄₉	17

Subgroups — C49×#10597480 #44472471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₉×#10597480 #44472471