Subgroups — C₃×#17987584 #28357036

Order 13851.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987584	C₃	1	9	yes	maximal, direct product factor
2	C₃×#13095335	C₃	1	3	yes	maximal, complemented
3	C₃×C₂₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	#13095335	C₃²	1	9	yes	complemented
5	C₃×C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
6	C₃×#10587018	C₉	1	1	yes	characteristic
7	C₃×#10587018	C₃²	1	1	yes	characteristic
8	C₂₇×C₁₉⋊C₃	C₉	1	6	yes	—
9	C₂₇×C₁₉⋊C₃	C₃²	1	3	yes	—
10	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
11	C₃×C₈₁⋊C₃	—	19	1	no	maximal, Sylow
12	C₃²×C₁₉⋊C₃	C₂₇	1	1	yes	characteristic
13	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₃×#4294	C₂₇	1	2	yes	—
15	C₉×C₁₉⋊C₃	C₂₇	1	6	yes	—
16	C₉×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
17	C₁₉×C₂₇	C₃×C₉	1	3	yes	—
18	#10587018	C₃×C₉	1	2	yes	—
19	#10587018	C₃×C₉	1	3	yes	—
20	#10587018	C₃³	1	1	yes	characteristic
21	C₃²×C₂₇	—	19	1	no	—
22	C₈₁⋊C₃	—	19	9	no	—
23	C₃×C₈₁	—	19	3	no	—
24	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
25	C₃×C₁₉⋊C₃	—	3	3	no	—
26	C₃×C₁₉⋊C₃	C₃×C₂₇	1	3	yes	—
27	C₉×C₁₉	C₃×C₂₇	1	2	yes	—
28	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
29	#4294	C₃×C₂₇	1	6	yes	—
30	C₃²×C₉	—	19	1	no	—
31	C₃×C₂₇	—	19	1	no	—
32	C₃×C₂₇	—	19	1	no	—
33	C₃×C₂₇	—	19	6	no	—
34	C₃×C₂₇	—	19	3	no	—
35	C₃×C₂₇	#4296	1	1	yes	characteristic
36	C₈₁	—	19	9	no	—
37	C₃×C₁₉	C₈₁⋊C₃	1	3	yes	complemented
38	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
39	C₁₉⋊C₃	—	3	3	no	—
40	C₃³	—	19	1	no	—
41	C₃×C₉	—	19	2	no	—
42	C₃×C₉	—	19	6	no	—
43	C₃×C₉	—	19	3	no	—
44	C₃×C₉	C₃×#4296	1	1	yes	characteristic
45	C₂₇	—	19	2	no	—
46	C₂₇	—	19	3	no	—
47	C₂₇	—	19	1	no	—
48	C₂₇	C₃×#4296	1	3	yes	—
49	C₁₉	C₃×C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₃²	—	19	3	no	—
51	C₃²	—	57	3	no	—
52	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
53	C₉	—	19	6	no	—
54	C₉	(C₁₉⋊C₃)⋊C₂₇	1	2	yes	—
55	C₉	C₃²×#4296	1	1	yes	characteristic
56	C₃	—	57	3	no	—
57	C₃	#17987584	1	3	yes	direct product factor
58	C₃	C₃×(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #17987584	C₃	direct (N × H)
2. C₃×#13095335	C₃	semidirect
4. #13095335	C₃²	semidirect
37. C₃×C₁₉	C₈₁⋊C₃	semidirect
49. C₁₉	C₃×C₈₁⋊C₃	semidirect
57. C₃	#17987584	direct (N × H)

Maximal subgroups

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

subgroup	index
#17987584	3
C₃×#13095335	3
C₃×C₂₇×C₁₉⋊C₃	3
C₃×C₈₁⋊C₃	19

Subgroups — C3×#17987584 #28357036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987584 #28357036