Subgroups — C₃×C₂₇×#4294 #28354597

Order 13851.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587018	C₃	1	2	yes	maximal
2	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
3	C₂₇×#4294	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
5	C₃²×#4294	C₉	1	3	yes	—
6	C₃×#10587018	C₉	1	18	yes	complemented
7	C₃×#10587018	C₃²	1	6	yes	—
8	C₉×#4294	C₉	1	6	yes	—
9	C₉×#4294	C₃²	1	3	yes	—
10	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
11	C₃×C₁₉×C₂₇	C₉	1	9	yes	complemented
12	C₃×C₁₉×C₂₇	C₃²	1	3	yes	—
13	C₃×C₉×C₂₇	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
16	C₃×C₉×C₁₉	C₃×C₉	1	6	yes	—
17	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
18	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
19	C₃×#4294	C₂₇	1	27	yes	direct product factor
20	C₃×#4294	C₃×C₉	1	9	yes	—
21	C₁₉×C₂₇	C₃×C₉	1	9	yes	complemented
22	#10587018	C₃×C₉	1	18	yes	complemented
23	C₃²×C₂₇	—	19	2	no	—
24	C₃²×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
25	C₃×C₉²	—	19	1	no	—
26	C₉×C₂₇	—	19	9	no	—
27	C₃²×C₁₉	C₉²	1	3	yes	—
28	C₃²×C₁₉	C₃×C₂₇	1	9	yes	—
29	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
30	C₉×C₁₉	C₉²	1	6	yes	—
31	C₉×C₁₉	C₃²×C₉	1	2	yes	—
32	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
33	#4294	C₃×C₂₇	1	27	yes	direct product factor
34	C₃²×C₉	—	19	3	no	—
35	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
36	C₃×C₂₇	—	19	18	no	—
37	C₃×C₂₇	—	19	6	no	—
38	C₃×C₂₇	#4294	1	9	yes	direct product factor
39	C₃×C₂₇	C₃×C₁₉⋊C₃	1	3	yes	—
40	C₉²	—	19	6	no	—
41	C₉²	—	19	3	no	—
42	C₃×C₁₉	C₉×C₂₇	1	9	yes	complemented
43	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
44	C₃×C₁₉	C₃²×C₂₇	1	3	yes	—
45	C₃³	C₉×C₁₉⋊C₃	1	1	yes	characteristic
46	C₃×C₉	—	19	27	no	—
47	C₃×C₉	—	19	9	no	—
48	C₃×C₉	C₉×C₁₉⋊C₃	1	2	yes	—
49	C₃×C₉	C₉×C₁₉⋊C₃	1	6	yes	—
50	C₃×C₉	C₃×#4294	1	3	yes	—
51	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
52	C₂₇	—	19	18	no	—
53	C₂₇	C₃×#4294	1	9	yes	direct product factor
54	C₁₉	C₃×C₉×C₂₇	1	1	yes	characteristic, complemented, Sylow
55	C₃²	C₉×#4294	1	3	yes	—
56	C₃²	C₂₇×C₁₉⋊C₃	1	9	yes	—
57	C₃²	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
58	C₉	—	19	27	no	—
59	C₉	C₉×#4294	1	6	yes	—
60	C₉	C₃×C₉×C₁₉⋊C₃	1	2	yes	—
61	C₉	C₃²×#4294	1	1	yes	characteristic
62	C₃	C₂₇×#4294	1	9	yes	direct product factor
63	C₃	C₃×C₉×#4294	1	1	yes	characteristic
64	C₃	C₃×C₂₇×C₁₉⋊C₃	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂₇×#4294	C₃	direct (N × H)
6. C₃×#10587018	C₉	semidirect
11. C₃×C₁₉×C₂₇	C₉	semidirect
19. C₃×#4294	C₂₇	direct (N × H)
21. C₁₉×C₂₇	C₃×C₉	semidirect
22. #10587018	C₃×C₉	semidirect
33. #4294	C₃×C₂₇	direct (N × H)
38. C₃×C₂₇	#4294	direct (N × H)
42. C₃×C₁₉	C₉×C₂₇	semidirect
53. C₂₇	C₃×#4294	direct (N × H)
54. C₁₉	C₃×C₉×C₂₇	semidirect
62. C₃	C₂₇×#4294	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#10587018	3
C₃×C₉×#4294	3
C₂₇×#4294	3
C₃²×C₁₉×C₂₇	3
C₃×C₉×C₂₇	19

Subgroups — C3×C27×#4294 #28354597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₇×#4294 #28354597