Subgroups — #28356852

Order 13851.

374 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095339	C₃	1	3	yes	maximal
2	C₃×#13095338	C₃	1	3	yes	maximal
3	(C₃×#4296)⋊C₉	C₃	1	6	yes	maximal
4	C₉²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃²×#4296	C₃²	1	9	yes	—
6	#13095339	—	3	9	no	—
7	#13095338	—	3	9	no	—
8	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	—
9	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
11	C₉×#4294	C₉	1	2	yes	complemented
12	C₉×#4294	C₉	1	2	yes	complemented
13	C₉×#4294	C₉	1	4	yes	complemented
14	C₉²×C₁₉	C₉	1	1	yes	characteristic, complemented
15	#10624550	—	19	1	no	maximal, Sylow
16	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
17	C₃×#4296	—	3	9	no	—
18	C₃×#4296	—	3	9	no	—
19	C₃×#4296	—	3	18	no	—
20	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
23	C₃×#4294	C₃×C₉	1	4	yes	—
24	C₃×#4294	C₃×C₉	1	2	yes	—
25	C₃×#4294	C₃×C₉	1	2	yes	—
26	C₉×C₁₉⋊C₃	—	3	6	no	—
27	C₉×C₁₉⋊C₃	3₋¹⁺²	1	9	yes	—
28	C₉×C₁₉⋊C₃	3₋¹⁺²	1	9	yes	—
29	C₃×C₉⋊C₉	—	19	3	no	—
30	C₃×C₉⋊C₉	—	19	3	no	—
31	C₃×C₉²	—	19	1	no	—
32	#6855	—	19	6	no	—
33	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
34	C₃×C₁₉⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
35	C₃×C₁₉⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
36	C₃×C₁₉⋊C₃	#737	1	6	yes	—
37	#4296	—	9	9	no	—
38	C₉×C₁₉	—	3	2	no	—
39	C₉×C₁₉	C₉⋊C₉	1	3	yes	complemented
40	C₉×C₁₉	C₉⋊C₉	1	3	yes	complemented
41	#4294	—	3	4	no	—
42	#4294	C₉⋊C₉	1	6	yes	complemented
43	#4294	C₉⋊C₉	1	6	yes	complemented
44	C₃²×C₉	—	19	1	no	—
45	C₃²×C₉	—	19	1	no	—
46	C₃²×C₉	—	19	2	no	—
47	C₃²×C₉	—	19	9	no	—
48	C₉⋊C₉	—	57	9	no	—
49	C₉⋊C₉	—	57	9	no	—
50	C₉²	—	19	4	no	—
51	C₉²	—	19	2	no	—
52	C₉²	—	19	2	no	—
53	C₉²	#4296	1	1	yes	characteristic, complemented
54	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
55	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
56	C₃×C₁₉	#6887	1	2	yes	—
57	C₁₉⋊C₃	#6896	1	9	yes	—
58	C₃³	—	19	1	no	—
59	C₃×C₉	—	19	2	no	—
60	C₃×C₉	—	19	2	no	—
61	C₃×C₉	—	19	9	no	—
62	C₃×C₉	—	19	9	no	—
63	C₃×C₉	—	19	4	no	—
64	C₃×C₉	—	57	6	no	—
65	C₃×C₉	—	57	9	no	—
66	C₃×C₉	—	57	9	no	—
67	C₃×C₉	—	57	18	no	—
68	C₃×C₉	C₃×#4296	1	2	yes	—
69	C₃×C₉	C₃×#4296	1	1	yes	characteristic
70	C₃×C₉	C₃×#4296	1	1	yes	characteristic
71	C₁₉	#10624550	1	1	yes	characteristic, complemented, Sylow
72	C₃²	—	19	3	no	—
73	C₃²	—	19	3	no	—
74	C₃²	—	19	6	no	—
75	C₃²	C₃²×#4296	1	1	yes	characteristic
76	C₉	—	3	2	no	—
77	C₉	—	19	6	no	—
78	C₉	—	19	6	no	—
79	C₉	—	57	4	no	—
80	C₉	—	171	9	no	—
81	C₉	#13095338	1	3	yes	complemented
82	C₉	#13095339	1	3	yes	complemented
83	C₃	—	19	9	no	—
84	C₃	C₃×#13095338	1	1	yes	characteristic
85	C₃	C₃×#13095339	1	1	yes	characteristic
86	C₃	#17987589	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator, socle	C₃²×C₁₉	C₃²×C₉
Fitting	C₉²×C₁₉	C₉
prime radical, cosocle	C₃²×C₁₉⋊C₃	C₃³
hypercenter	C₉²	#4296
hypocenter	C₁₉	#10624550
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
11. C₉×#4294	C₉	semidirect
12. C₉×#4294	C₉	semidirect
13. C₉×#4294	C₉	semidirect
14. C₉²×C₁₉	C₉	semidirect
39. C₉×C₁₉	C₉⋊C₉	semidirect
40. C₉×C₁₉	C₉⋊C₉	semidirect
42. #4294	C₉⋊C₉	semidirect
43. #4294	C₉⋊C₉	semidirect
53. C₉²	#4296	semidirect
71. C₁₉	#10624550	semidirect
81. C₉	#13095338	semidirect
82. C₉	#13095339	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095339	3
C₃×#13095338	3
(C₃×#4296)⋊C₉	3
C₉²×C₁₉⋊C₃	3
#10624550	19