Subgroups — #28356962

Order 13851.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987571	C₃	1	3	yes	maximal, complemented
2	#17987570	C₃	1	3	yes	maximal, complemented
3	C₃²⋊#10587020	C₃	1	3	yes	maximal
4	C₉×#10587020	C₃	1	3	yes	maximal, complemented
5	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
6	C₃×#10587020	C₃²	1	9	yes	—
7	C₃²×#4294	C₉	1	2	yes	—
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₉×#4294	C₉	1	2	yes	—
10	C₉×#4294	C₉	1	2	yes	—
11	C₉×#4294	C₉	1	2	yes	—
12	C₉×#4294	C₃²	1	1	yes	characteristic
13	C₉×#4294	C₃²	1	1	yes	characteristic
14	C₉×#4294	C₃²	1	1	yes	characteristic
15	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
16	#10624710	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₁₉	C₂₇	1	9	yes	complemented
19	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
22	C₃×#4294	—	3	6	no	—
23	C₃×#4294	—	3	3	no	—
24	C₃×#4294	C₃×C₉	1	2	yes	—
25	C₃×#4294	C₃×C₉	1	2	yes	—
26	C₃×#4294	C₃×C₉	1	2	yes	—
27	C₃×#4294	C₃×C₉	1	2	yes	—
28	C₃×#4294	C₃³	1	1	yes	characteristic
29	#10587020	—	3	9	no	—
30	C₃×C₉²	—	19	1	no	—
31	C₉⋊C₂₇	—	19	3	no	—
32	C₉⋊C₂₇	—	19	3	no	—
33	C₃²⋊C₂₇	—	19	3	no	—
34	C₉×C₂₇	—	19	3	no	—
35	C₃²×C₁₉	—	3	1	no	—
36	C₃²×C₁₉	—	3	2	no	—
37	C₃²×C₁₉	C₃×C₂₇	1	3	yes	—
38	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
39	C₉×C₁₉	C₃×C₂₇	1	3	yes	—
40	C₉×C₁₉	C₃×C₂₇	1	3	yes	—
41	C₉×C₁₉	C₃×C₂₇	1	3	yes	—
42	#4294	—	3	2	no	—
43	#4294	—	3	2	no	—
44	#4294	—	3	2	no	—
45	#4294	C₂₇⋊C₃	1	6	yes	—
46	#4294	#737	1	3	yes	—
47	C₃²×C₉	—	19	2	no	—
48	C₃²×C₉	—	19	1	no	—
49	C₃²×C₉	#4296	1	1	yes	characteristic
50	C₃×C₂₇	—	19	9	no	—
51	C₉²	—	19	2	no	—
52	C₉²	—	19	2	no	—
53	C₉²	—	19	1	no	—
54	C₉²	—	19	1	no	—
55	C₉²	—	19	2	no	—
56	C₉²	—	19	1	no	—
57	C₃×C₁₉	—	3	3	no	—
58	C₃×C₁₉	#6887	1	1	yes	characteristic
59	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
60	C₃×C₁₉	C₃×C₂₇⋊C₃	1	2	yes	—
61	C₃³	C₃×#4296	1	1	yes	characteristic
62	C₃×C₉	—	19	2	no	—
63	C₃×C₉	—	19	1	no	—
64	C₃×C₉	—	19	2	no	—
65	C₃×C₉	—	19	2	no	—
66	C₃×C₉	—	19	2	no	—
67	C₃×C₉	—	57	3	no	—
68	C₃×C₉	—	57	6	no	—
69	C₃×C₉	#10587020	1	9	yes	complemented
70	C₃×C₉	C₃×#4296	1	1	yes	characteristic
71	C₃×C₉	C₃×#4296	1	1	yes	characteristic
72	C₃×C₉	C₃×#4296	1	1	yes	characteristic
73	C₂₇	—	57	9	no	—
74	C₁₉	#10624710	1	1	yes	characteristic, complemented, Sylow
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	C₃×#10587020	1	3	yes	—
78	C₃²	C₃²×#4296	1	1	yes	characteristic
79	C₉	—	19	3	no	—
80	C₉	—	19	6	no	—
81	C₉	—	57	2	no	—
82	C₉	—	57	2	no	—
83	C₉	—	57	2	no	—
84	C₉	C₃×#10587020	1	3	yes	—
85	C₉	C₃×#10587020	1	3	yes	—
86	C₉	C₃×#10587020	1	3	yes	—
87	C₃	—	3	3	no	—
88	C₃	#17987589	1	1	yes	characteristic
89	C₃	C₃²×#10587020	1	1	yes	characteristic
90	C₃	(C₁₉⋊C₃)⋊(C₂₇⋊C₃)	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×#4296
commutator	C₃×C₁₉	C₃²×C₂₇
Frattini	C₃²	C₃²×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	#10624710
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #17987571	C₃	semidirect
2. #17987570	C₃	semidirect
4. C₉×#10587020	C₃	semidirect
18. C₃×C₉×C₁₉	C₂₇	semidirect
69. C₃×C₉	#10587020	semidirect
74. C₁₉	#10624710	semidirect

Maximal subgroups

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

subgroup	index
#17987571	3
#17987570	3
C₃²⋊#10587020	3
C₉×#10587020	3
C₃×C₉×#4294	3
#10624710	19