Subgroups — 3₋¹⁺²×#10587018 #28354860

Order 13851.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587018	C₃	1	1	yes	maximal, characteristic
2	#17987357	C₃	1	3	yes	maximal, complemented
3	#17987356	C₃	1	3	yes	maximal, complemented
4	C₃²⋊#10587018	C₃	1	2	yes	maximal
5	C₉×#10587018	C₃	1	3	yes	maximal, complemented
6	C₉×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
7	C₃×#10587018	—	3	3	no	—
8	C₃×#10587018	C₃²	1	6	yes	—
9	C₃×#10587018	C₃²	1	1	yes	characteristic
10	C₃×#10587018	C₃²	1	1	yes	characteristic
11	C₃×#10587018	C₃²	1	1	yes	characteristic
12	C₃×C₁₉×3₋¹⁺²	C₉	1	1	yes	characteristic
13	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
14	C₁₉×C₉⋊C₉	C₉	1	6	yes	—
15	C₁₉×C₃²⋊C₉	C₉	1	2	yes	—
16	C₉²×C₁₉	C₃²	1	3	yes	—
17	C₂₇×3₋¹⁺²	—	19	1	no	maximal, Sylow
18	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
19	C₁₉×3₋¹⁺²	C₂₇	1	9	yes	complemented
20	C₃×C₉×C₁₉	—	3	1	no	—
21	C₃×C₉×C₁₉	—	3	2	no	—
22	C₃×C₉×C₁₉	C₃×C₉	1	6	yes	—
23	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
25	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
26	#10587018	—	3	1	no	—
27	#10587018	—	3	1	no	—
28	#10587018	—	3	6	no	—
29	#10587018	3₋¹⁺²	1	3	yes	direct product factor
30	C₃²×C₂₇	—	19	1	no	—
31	C₉×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
32	C₉⋊C₂₇	—	19	3	no	—
33	C₉⋊C₂₇	—	19	3	no	—
34	C₃²⋊C₂₇	—	19	2	no	—
35	C₉×C₂₇	—	19	3	no	—
36	C₃²×C₁₉	—	3	1	no	—
37	C₃²×C₁₉	—	3	2	no	—
38	C₃²×C₁₉	C₃×C₂₇	1	3	yes	—
39	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
40	C₉×C₁₉	—	3	2	no	—
41	C₉×C₁₉	—	3	6	no	—
42	C₉×C₁₉	C₃×C₂₇	1	9	yes	complemented
43	C₉×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
44	C₉×C₁₉	#737	1	2	yes	—
45	C₃×3₋¹⁺²	#4294	1	1	yes	characteristic
46	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
47	C₃×C₂₇	—	19	1	no	—
48	C₃×C₂₇	—	19	6	no	—
49	C₃×C₂₇	—	19	1	no	—
50	C₃×C₂₇	—	19	1	no	—
51	C₃×C₂₇	—	57	3	no	—
52	C₉⋊C₉	#4294	1	6	yes	—
53	C₃²⋊C₉	#4294	1	2	yes	—
54	C₉²	C₃×C₁₉⋊C₃	1	3	yes	—
55	C₃×C₁₉	—	3	3	no	—
56	C₃×C₁₉	C₉×3₋¹⁺²	1	1	yes	characteristic
57	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
58	C₃×C₁₉	#6903	1	2	yes	—
59	C₃³	C₃×#4294	1	1	yes	characteristic
60	3₋¹⁺²	#10587018	1	9	yes	direct product factor
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	2	no	—
63	C₃×C₉	C₃×#4294	1	6	yes	—
64	C₃×C₉	C₃×#4294	1	2	yes	—
65	C₃×C₉	C₃×#4294	1	3	yes	—
66	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
67	C₂₇	—	19	3	no	—
68	C₂₇	—	57	1	no	—
69	C₂₇	—	57	1	no	—
70	C₂₇	—	57	6	no	—
71	C₁₉	C₂₇×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
72	C₃²	—	3	1	no	—
73	C₃²	—	3	2	no	—
74	C₃²	C₃×#10587018	1	3	yes	—
75	C₃²	C₃²×#4294	1	1	yes	characteristic
76	C₉	—	3	2	no	—
77	C₉	—	3	6	no	—
78	C₉	C₃×#10587018	1	9	yes	complemented
79	C₉	3₋¹⁺²×C₁₉⋊C₃	1	1	yes	characteristic
80	C₉	#13095333	1	2	yes	—
81	C₃	—	3	3	no	—
82	C₃	3₋¹⁺²×#4294	1	1	yes	characteristic
83	C₃	C₃²×#10587018	1	1	yes	characteristic
84	C₃	#17987480	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #17987357	C₃	semidirect
3. #17987356	C₃	semidirect
5. C₉×#10587018	C₃	semidirect
19. C₁₉×3₋¹⁺²	C₂₇	semidirect
29. #10587018	3₋¹⁺²	direct (N × H)
42. C₉×C₁₉	C₃×C₂₇	semidirect
60. 3₋¹⁺²	#10587018	direct (N × H)
71. C₁₉	C₂₇×3₋¹⁺²	semidirect
78. C₉	C₃×#10587018	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#10587018	3
#17987357	3
#17987356	3
C₃²⋊#10587018	3
C₉×#10587018	3
C₉×C₁₉×3₋¹⁺²	3
C₂₇×3₋¹⁺²	19

Subgroups — 3−1+2×#10587018 #28354860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 3₋¹⁺²×#10587018 #28354860