Subgroups — C₃×#17987572 #28356936

Order 13851.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587020	C₃	1	3	yes	maximal
2	#17987572	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587020	—	3	9	no	—
5	C₃×#10587020	C₃²	1	9	yes	—
6	C₃²×#4294	C₉	1	1	yes	characteristic
7	C₃²×#4294	C₉	1	1	yes	characteristic
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₉×#4294	C₉	1	6	yes	—
10	C₉×#4294	C₃²	1	3	yes	—
11	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
12	C₃×C₉⋊C₂₇	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₁₉	—	3	3	no	—
15	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
16	C₃×#4294	—	3	3	no	—
17	C₃×#4294	C₂₇	1	9	yes	complemented
18	C₃×#4294	C₃×C₉	1	3	yes	—
19	C₃×#4294	C₃×C₉	1	2	yes	—
20	C₃×#4294	C₃×C₉	1	3	yes	—
21	C₃×#4294	3₋¹⁺²	1	9	yes	—
22	C₃×#4294	C₃³	1	1	yes	characteristic
23	#10587020	—	3	9	no	—
24	C₃²×C₂₇	—	19	3	no	—
25	C₃×C₉²	—	19	1	no	—
26	C₉⋊C₂₇	—	19	9	no	—
27	C₃²×C₁₉	C₉⋊C₉	1	3	yes	—
28	C₃²×C₁₉	C₃×C₂₇	1	3	yes	—
29	C₃²×C₁₉	C₂₇⋊C₃	1	3	yes	—
30	C₃²×C₁₉	C₂₇⋊C₃	1	3	yes	—
31	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
32	C₉×C₁₉	—	3	3	no	—
33	#4294	—	3	3	no	—
34	#4294	C₉⋊C₉	1	6	yes	—
35	#4294	C₃×C₂₇	1	9	yes	complemented
36	#4294	C₃×3₋¹⁺²	1	3	yes	—
37	C₃²×C₉	—	19	1	no	—
38	C₃²×C₉	—	19	1	no	—
39	C₃²×C₉	—	19	1	no	—
40	C₃²×C₉	#4296	1	1	yes	characteristic
41	C₃×C₂₇	—	19	9	no	—
42	C₃×C₂₇	—	57	9	no	—
43	C₉²	—	19	6	no	—
44	C₉²	—	19	3	no	—
45	C₃×C₁₉	C₉⋊C₂₇	1	9	yes	complemented
46	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
47	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
48	C₃×C₁₉	C₃×C₂₇⋊C₃	1	1	yes	characteristic
49	C₃×C₁₉	C₃×C₂₇⋊C₃	1	1	yes	characteristic
50	C₃³	C₃×#4296	1	1	yes	characteristic
51	C₃×C₉	—	3	3	no	—
52	C₃×C₉	—	19	9	no	—
53	C₃×C₉	—	19	9	no	—
54	C₃×C₉	—	19	2	no	—
55	C₃×C₉	—	19	3	no	—
56	C₃×C₉	—	19	1	no	—
57	C₃×C₉	—	19	3	no	—
58	C₃×C₉	—	57	3	no	—
59	C₃×C₉	C₃×#4296	1	3	yes	—
60	C₂₇	—	57	9	no	—
61	C₁₉	C₃×C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
62	C₃²	#13095338	1	3	yes	—
63	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	3	yes	—
64	C₃²	#13095342	1	3	yes	—
65	C₃²	#13095344	1	3	yes	—
66	C₃²	C₃²×#4296	1	1	yes	characteristic
67	C₉	—	3	3	no	—
68	C₉	—	19	3	no	—
69	C₉	—	19	6	no	—
70	C₉	—	19	9	no	—
71	C₉	—	57	3	no	—
72	C₃	#17987572	1	9	yes	direct product factor
73	C₃	C₃×#13095338	1	1	yes	characteristic
74	C₃	C₃×(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
75	C₃	C₃×#13095342	1	1	yes	characteristic
76	C₃	C₃×#13095344	1	1	yes	characteristic

	subgroup	G/H
center	C₃³	C₃×#4296
commutator	C₃×C₁₉	C₃²×C₂₇
Frattini	C₃²	C₃²×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle, prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	C₃×C₉⋊C₂₇
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. #17987572	C₃	direct (N × H)
17. C₃×#4294	C₂₇	semidirect
35. #4294	C₃×C₂₇	semidirect
45. C₃×C₁₉	C₉⋊C₂₇	semidirect
61. C₁₉	C₃×C₉⋊C₂₇	semidirect
72. C₃	#17987572	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×#10587020	3
#17987572	3
C₃×C₉×#4294	3
C₃×C₉⋊C₂₇	19

Subgroups — C3×#17987572 #28356936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987572 #28356936