Subgroups — C₃×#17987582 #28357033

Order 13851.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987582	C₃	1	9	yes	maximal, direct product factor
2	C₃×#13095335	C₃	1	3	yes	maximal, complemented
3	C₃²×#10587018	C₃	1	1	yes	maximal, characteristic
4	#13095335	C₃²	1	9	yes	complemented
5	C₃×#10587018	C₉	1	6	yes	—
6	C₃×#10587018	C₉	1	2	yes	—
7	C₃×#10587018	C₃²	1	1	yes	characteristic
8	C₃×#10587018	C₃²	1	3	yes	—
9	C₃²×C₉×C₁₉	C₉	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	#10587018	C₃×C₉	1	2	yes	—
17	#10587018	C₃×C₉	1	6	yes	—
18	#10587018	C₃³	1	1	yes	characteristic
19	C₃²×C₂₇	—	19	1	no	—
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	#4296	1	1	yes	characteristic
29	C₃×C₂₇	—	19	6	no	—
30	C₃×C₂₇	—	19	3	no	—
31	C₃×C₂₇	—	19	2	no	—
32	C₃×C₂₇	—	19	1	no	—
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	#10587020	1	1	yes	characteristic
38	C₃×C₉	#10587020	1	2	yes	—
39	C₃×C₉	#10587020	1	6	yes	—
40	C₃×C₉	C₃×#4296	1	3	yes	—
41	C₃×C₉	C₃×#4296	1	1	yes	characteristic
42	C₂₇	—	19	2	no	—
43	C₂₇	—	19	6	no	—
44	C₂₇	—	19	1	no	—
45	C₁₉	C₃×C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
46	C₃²	—	3	3	no	—
47	C₃²	C₃×#10587020	1	3	yes	—
48	C₃²	C₃×#10587020	1	1	yes	characteristic
49	C₉	C₃×#10587020	1	6	yes	—
50	C₉	C₃×#10587020	1	2	yes	—
51	C₉	C₃²×#4296	1	1	yes	characteristic
52	C₃	—	3	3	no	—
53	C₃	#17987582	1	3	yes	direct product factor
54	C₃	C₃²×#10587020	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×#4296
commutator	C₃×C₁₉	C₃²×C₂₇
Frattini	C₉	C₃²×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle	C₃²×C₁₉	C₃×C₂₇
prime radical	C₃³×C₁₉	C₂₇
cosocle	#10587018	C₃³
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	C₃×C₈₁⋊C₃
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #17987582	C₃	direct (N × H)
2. C₃×#13095335	C₃	semidirect
4. #13095335	C₃²	semidirect
35. C₃×C₁₉	C₈₁⋊C₃	semidirect
45. C₁₉	C₃×C₈₁⋊C₃	semidirect
53. C₃	#17987582	direct (N × H)

Maximal subgroups

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

subgroup	index
#17987582	3
C₃×#13095335	3
C₃²×#10587018	3
C₃×C₈₁⋊C₃	19

Subgroups — C3×#17987582 #28357033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987582 #28357033