Subgroups — #17987428

Order 4617.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587022	C₃	1	3	yes	maximal, complemented
2	C₃×C₃²⋊(C₁₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	C₃²×#4294	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²⋊#4294	C₃	1	1	yes	maximal, characteristic, complemented
5	#13095303	C₃	1	6	yes	maximal, complemented
6	C₁₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃³×C₁₉	C₃²	1	1	yes	characteristic
8	C₃²×C₁₉⋊C₃	C₃²	1	3	yes	—
9	C₃×C₉×C₁₉	C₃²	1	3	yes	—
10	C₃²⋊(C₁₉⋊C₃)	—	3	3	no	—
11	C₃×#4294	—	3	3	no	—
12	C₃×#4294	C₃²	1	2	yes	—
13	C₃×#4294	C₃²	1	3	yes	—
14	C₃×#4294	C₃²	1	1	yes	characteristic
15	#10587022	—	3	9	no	—
16	C₉⋊H(3,𝔽₃)	—	19	1	no	maximal, Sylow
17	C₃²×C₁₉	—	3	1	no	—
18	C₃²×C₁₉	—	3	2	no	—
19	C₃²×C₁₉	3₋¹⁺²	1	3	yes	complemented
20	C₃²×C₁₉	C₃³	1	1	yes	characteristic
21	C₃×C₁₉⋊C₃	—	3	3	no	—
22	C₃×C₁₉⋊C₃	—	3	3	no	—
23	C₃×C₁₉⋊C₃	—	3	6	no	—
24	C₉×C₁₉	—	3	3	no	—
25	#4294	—	3	3	no	—
26	#4294	—	3	2	no	—
27	#4294	H(3,𝔽₃)	1	3	yes	complemented
28	C₃×3₋¹⁺²	—	19	3	no	—
29	C₃×H(3,𝔽₃)	—	19	1	no	—
30	C₃²×C₉	—	19	1	no	—
31	C₃²⋊C₉	—	19	1	no	—
32	C₃²⋊C₉	—	19	6	no	—
33	C₃²⋊C₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
34	C₃×C₁₉	—	3	3	no	—
35	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₃×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
37	C₃×C₁₉	#737	1	2	yes	—
38	C₁₉⋊C₃	—	9	3	no	—
39	C₃³	—	19	3	no	—
40	C₃³	C₃×C₁₉⋊C₃	1	1	yes	characteristic
41	3₋¹⁺²	—	57	9	no	—
42	H(3,𝔽₃)	—	57	3	no	—
43	C₃×C₉	—	19	1	no	—
44	C₃×C₉	—	19	2	no	—
45	C₃×C₉	—	19	3	no	—
46	C₃×C₉	—	57	3	no	—
47	C₃×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
48	C₁₉	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
49	C₃²	—	3	1	no	—
50	C₃²	—	3	2	no	—
51	C₃²	—	57	3	no	—
52	C₃²	—	57	3	no	—
53	C₃²	—	57	6	no	—
54	C₃²	#10587022	1	3	yes	complemented
55	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
56	C₉	—	3	3	no	—
57	C₉	—	19	3	no	—
58	C₉	—	57	2	no	—
59	C₉	—	57	3	no	—
60	C₃	—	3	3	no	—
61	C₃	—	171	3	no	—
62	C₃	H(3,𝔽₃)×C₁₉⋊C₃	1	1	yes	characteristic
63	C₃	C₃×#10587022	1	1	yes	characteristic
64	C₃	#13095333	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃³
Fitting	C₁₉×C₃²⋊C₉	C₃
prime radical	C₃×C₃²⋊(C₁₉⋊C₃)	C₃
hypercenter	C₃²⋊C₉	C₁₉⋊C₃
hypocenter	C₁₉	C₉⋊H(3,𝔽₃)
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
1. C₃×#10587022	C₃	semidirect
3. C₃²×#4294	C₃	semidirect
4. C₃²⋊#4294	C₃	semidirect
5. #13095303	C₃	semidirect
6. C₁₉×C₃²⋊C₉	C₃	semidirect
19. C₃²×C₁₉	3₋¹⁺²	semidirect
27. #4294	H(3,𝔽₃)	semidirect
33. C₃²⋊C₉	C₁₉⋊C₃	semidirect
48. C₁₉	C₉⋊H(3,𝔽₃)	semidirect
54. C₃²	#10587022	semidirect

Maximal subgroups

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

subgroup	index
C₃×#10587022	3
C₃×C₃²⋊(C₁₉⋊C₃)	3
C₃²×#4294	3
C₃²⋊#4294	3
#13095303	3
C₁₉×C₃²⋊C₉	3
C₉⋊H(3,𝔽₃)	19