Subgroups — C₃×#17987574 #28356950

Order 13851.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095343	C₃	1	2	yes	maximal
2	C₃×#13095338	C₃	1	1	yes	maximal, characteristic
3	#17987574	C₃	1	9	yes	maximal, direct product factor
4	C₃×#13095311	C₃	1	1	yes	maximal, characteristic
5	C₃²×#4296	—	3	1	no	—
6	#13095343	—	3	4	no	—
7	#13095343	C₃²	1	6	yes	—
8	C₃×#10587020	—	3	2	no	—
9	#13095338	—	3	2	no	—
10	#13095338	C₃²	1	3	yes	—
11	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
12	#13095311	C₉	1	6	yes	complemented
13	#13095311	C₃²	1	3	yes	—
14	C₃×#10587018	C₉	1	2	yes	complemented
15	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic, complemented
16	C₃×#6875	—	19	1	no	maximal, Sylow
17	C₃²×C₁₉⋊C₃	3₋¹⁺²	1	1	yes	characteristic
18	C₃×#4296	—	3	3	no	—
19	C₃×#4296	—	9	3	no	—
20	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
21	C₃×#4294	3₋¹⁺²	1	2	yes	—
22	C₉×C₁₉⋊C₃	C₃×C₉	1	2	yes	—
23	C₉×C₁₉⋊C₃	3₋¹⁺²	1	2	yes	—
24	C₉×C₁₉⋊C₃	3₋¹⁺²	1	4	yes	—
25	C₉×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
26	#10587020	—	3	6	no	—
27	C₁₉×C₂₇	C₃×C₉	1	3	yes	complemented
28	#10587018	C₃×C₉	1	6	yes	complemented
29	C₃×C₂₇⋊C₃	—	19	1	no	—
30	C₃×C₂₇⋊C₃	—	19	2	no	—
31	C₃×C₉⋊C₉	—	19	1	no	—
32	#6875	—	19	9	no	—
33	C₃²×C₁₉	C₉⋊C₉	1	1	yes	characteristic
34	C₃×C₁₉⋊C₃	—	3	3	no	—
35	C₃×C₁₉⋊C₃	C₉⋊C₉	1	2	yes	—
36	C₃×C₁₉⋊C₃	C₃×3₋¹⁺²	1	1	yes	characteristic
37	#4296	—	9	3	no	—
38	C₉×C₁₉	C₉⋊C₉	1	2	yes	—
39	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
40	#4294	C₉⋊C₉	1	4	yes	—
41	#4294	C₃×3₋¹⁺²	1	2	yes	—
42	C₃²×C₉	—	19	1	no	—
43	C₃²×C₉	—	57	1	no	—
44	C₂₇⋊C₃	—	19	6	no	—
45	C₂₇⋊C₃	—	19	3	no	—
46	C₂₇⋊C₃	—	19	6	no	—
47	C₂₇⋊C₃	—	57	4	no	—
48	C₃×C₂₇	—	19	2	no	—
49	C₃×C₂₇	—	57	2	no	—
50	C₃×C₂₇	#4296	1	1	yes	characteristic, complemented
51	C₉⋊C₉	—	19	3	no	—
52	C₉⋊C₉	—	57	2	no	—
53	C₃×C₁₉	#6875	1	3	yes	complemented
54	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
55	C₁₉⋊C₃	—	3	1	no	—
56	C₁₉⋊C₃	—	3	2	no	—
57	C₃³	—	19	1	no	—
58	C₃×C₉	—	19	2	no	—
59	C₃×C₉	—	19	2	no	—
60	C₃×C₉	—	19	4	no	—
61	C₃×C₉	—	19	2	no	—
62	C₃×C₉	—	19	1	no	—
63	C₃×C₉	—	57	3	no	—
64	C₃×C₉	—	171	3	no	—
65	C₃×C₉	C₃×#4296	1	1	yes	characteristic
66	C₂₇	—	19	6	no	—
67	C₂₇	—	57	6	no	—
68	C₂₇	C₃×#4296	1	3	yes	complemented
69	C₁₉	C₃×#6875	1	1	yes	characteristic, complemented, Sylow
70	C₃²	—	19	1	no	—
71	C₃²	—	19	2	no	—
72	C₃²	—	57	3	no	—
73	C₃²	#13095338	1	1	yes	characteristic
74	C₉	—	19	2	no	—
75	C₉	—	19	4	no	—
76	C₉	—	171	3	no	—
77	C₉	#13095338	1	2	yes	—
78	C₉	C₃²×#4296	1	1	yes	characteristic
79	C₃	—	57	1	no	—
80	C₃	—	57	2	no	—
81	C₃	#17987574	1	3	yes	direct product factor
82	C₃	C₃×#13095338	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#13095338
commutator	C₉×C₁₉	C₃²×C₉
Frattini	C₉	C₃²×#4296
Fitting	C₃×C₁₉×C₂₇	C₉
socle	C₃²×C₁₉	C₉⋊C₉
prime radical	C₃²×C₁₉⋊C₃	3₋¹⁺²
cosocle	C₉×C₁₉⋊C₃	C₃³
hypercenter	C₃×C₂₇	#4296
hypocenter	C₁₉	C₃×#6875
LCS	G ▷ C₉×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
3. #17987574	C₃	direct (N × H)
12. #13095311	C₉	semidirect
14. C₃×#10587018	C₉	semidirect
15. C₃×C₁₉×C₂₇	C₉	semidirect
27. C₁₉×C₂₇	C₃×C₉	semidirect
28. #10587018	C₃×C₉	semidirect
50. C₃×C₂₇	#4296	semidirect
53. C₃×C₁₉	#6875	semidirect
68. C₂₇	C₃×#4296	semidirect
69. C₁₉	C₃×#6875	semidirect
81. C₃	#17987574	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#13095343	3
C₃×#13095338	3
#17987574	3
C₃×#13095311	3
C₃×#6875	19

Subgroups — C3×#17987574 #28356950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987574 #28356950