Subgroups — C₃×#17987367 #28355722

Order 13851.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987367	C₃	1	9	yes	maximal, direct product factor
2	C₃×#13095301	C₃	1	3	yes	maximal, complemented
3	C₃²×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
4	#13095301	C₃²	1	9	yes	complemented
5	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
6	C₃×C₁₉×C₂₇	C₉	1	2	yes	—
7	C₃×C₁₉×C₂₇	C₉	1	6	yes	—
8	C₃×C₁₉×C₂₇	C₃²	1	3	yes	—
9	C₃×C₁₉×C₂₇	C₃²	1	1	yes	characteristic
10	C₃×C₈₁⋊C₃	—	19	1	no	maximal, Sylow
11	C₃³×C₁₉	C₂₇	1	1	yes	characteristic
12	C₃×C₉×C₁₉	C₂₇	1	6	yes	—
13	C₃×C₉×C₁₉	C₂₇	1	2	yes	—
14	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
15	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
16	C₁₉×C₂₇	C₃×C₉	1	6	yes	—
17	C₁₉×C₂₇	C₃×C₉	1	2	yes	—
18	C₁₉×C₂₇	C₃³	1	1	yes	characteristic
19	C₃²×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
20	C₈₁⋊C₃	—	19	9	no	—
21	C₃×C₈₁	—	19	3	no	—
22	C₃²×C₁₉	—	3	3	no	—
23	C₃²×C₁₉	C₃×C₂₇	1	3	yes	—
24	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
25	C₉×C₁₉	C₃×C₂₇	1	6	yes	—
26	C₉×C₁₉	C₃×C₂₇	1	2	yes	—
27	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
28	C₃²×C₉	#4294	1	1	yes	characteristic
29	C₃×C₂₇	#4294	1	2	yes	—
30	C₃×C₂₇	#4294	1	6	yes	—
31	C₃×C₂₇	C₃×C₁₉⋊C₃	1	3	yes	—
32	C₃×C₂₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic
33	C₈₁	—	19	9	no	—
34	C₃×C₁₉	—	3	3	no	—
35	C₃×C₁₉	C₈₁⋊C₃	1	3	yes	complemented
36	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
37	C₃³	#10587018	1	1	yes	characteristic
38	C₃×C₉	#10587018	1	6	yes	—
39	C₃×C₉	#10587018	1	2	yes	—
40	C₃×C₉	C₃×#4294	1	3	yes	—
41	C₃×C₉	C₃×#4294	1	1	yes	characteristic
42	C₂₇	C₃×#4294	1	6	yes	—
43	C₂₇	C₃×#4294	1	2	yes	—
44	C₂₇	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
45	C₁₉	C₃×C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
46	C₃²	—	3	3	no	—
47	C₃²	C₃×#10587018	1	3	yes	—
48	C₃²	C₃×#10587018	1	1	yes	characteristic
49	C₉	C₃×#10587018	1	6	yes	—
50	C₉	C₃×#10587018	1	2	yes	—
51	C₉	C₃²×#4294	1	1	yes	characteristic
52	C₃	—	3	3	no	—
53	C₃	#17987367	1	3	yes	direct product factor
54	C₃	C₃²×#10587018	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₂₇	C₃×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃²×C₂₇
Frattini	C₂₇	C₃²×C₁₉⋊C₃
Fitting	C₃²×C₁₉×C₂₇	C₃
socle	C₃²×C₁₉	C₃×C₂₇
prime radical	C₃³×C₁₉	C₂₇
cosocle	C₁₉×C₂₇	C₃³
hypercenter	C₃²×C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	C₃×C₈₁⋊C₃
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
1. #17987367	C₃	direct (N × H)
2. C₃×#13095301	C₃	semidirect
4. #13095301	C₃²	semidirect
35. C₃×C₁₉	C₈₁⋊C₃	semidirect
45. C₁₉	C₃×C₈₁⋊C₃	semidirect
53. C₃	#17987367	direct (N × H)

Maximal subgroups

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

subgroup	index
#17987367	3
C₃×#13095301	3
C₃²×C₁₉×C₂₇	3
C₃×C₈₁⋊C₃	19

Subgroups — C3×#17987367 #28355722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987367 #28355722