Subgroups — #28356944

Order 13851.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095343	C₃	1	3	yes	maximal
2	#17987572	C₃	1	9	yes	maximal, complemented
3	C₉²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	#13095343	—	3	9	no	—
5	C₃×#10587020	C₃²	1	9	yes	—
6	C₃×C₉×C₁₉⋊C₃	C₉	1	3	yes	—
7	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
8	C₉×#4294	C₉	1	1	yes	characteristic
9	C₉×#4294	C₉	1	3	yes	—
10	C₉×#4294	C₉	1	1	yes	characteristic
11	C₉×#4294	C₃²	1	3	yes	—
12	C₉²×C₁₉	C₉	1	1	yes	characteristic
13	#10624706	—	19	1	no	maximal, Sylow
14	C₃²×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
17	C₃×#4294	C₃×C₉	1	3	yes	—
18	C₃×#4294	C₃×C₉	1	1	yes	characteristic
19	C₃×#4294	C₃×C₉	1	3	yes	—
20	C₃×#4294	C₃³	1	1	yes	characteristic
21	C₉×C₁₉⋊C₃	—	3	9	no	—
22	C₉×C₁₉⋊C₃	3₋¹⁺²	1	9	yes	—
23	#10587020	—	3	9	no	—
24	C₃×C₂₇⋊C₃	—	19	3	no	—
25	C₃×C₉²	—	19	1	no	—
26	C₉⋊C₂₇	—	19	9	no	—
27	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
28	C₃×C₁₉⋊C₃	—	3	3	no	—
29	C₃×C₁₉⋊C₃	C₉⋊C₉	1	3	yes	—
30	C₉×C₁₉	—	3	3	no	—
31	C₉×C₁₉	C₉⋊C₉	1	3	yes	—
32	#4294	—	3	3	no	—
33	#4294	C₉⋊C₉	1	3	yes	—
34	#4294	C₂₇⋊C₃	1	9	yes	complemented
35	#4294	C₃×3₋¹⁺²	1	3	yes	—
36	C₃²×C₉	—	19	1	no	—
37	C₃²×C₉	—	19	3	no	—
38	C₂₇⋊C₃	—	57	9	no	—
39	C₃×C₂₇	—	19	9	no	—
40	C₉²	—	19	1	no	—
41	C₉²	—	19	3	no	—
42	C₉²	—	19	1	no	—
43	C₉²	—	19	3	no	—
44	C₉²	#4296	1	1	yes	characteristic
45	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
46	C₃×C₁₉	C₃×C₂₇⋊C₃	1	3	yes	—
47	C₁₉⋊C₃	—	3	3	no	—
48	C₃³	—	19	1	no	—
49	C₃×C₉	—	19	1	no	—
50	C₃×C₉	—	19	3	no	—
51	C₃×C₉	—	19	1	no	—
52	C₃×C₉	—	19	9	no	—
53	C₃×C₉	—	19	3	no	—
54	C₃×C₉	—	57	9	no	—
55	C₃×C₉	C₃×#4296	1	3	yes	—
56	C₃×C₉	C₃×#4296	1	1	yes	characteristic
57	C₂₇	—	57	9	no	—
58	C₁₉	#10624706	1	1	yes	characteristic, complemented, Sylow
59	C₃²	—	19	3	no	—
60	C₃²	—	57	3	no	—
61	C₃²	C₃²×#4296	1	1	yes	characteristic
62	C₉	—	3	3	no	—
63	C₉	—	19	3	no	—
64	C₉	—	19	3	no	—
65	C₉	—	19	9	no	—
66	C₉	—	57	3	no	—
67	C₉	#13095338	1	3	yes	—
68	C₃	—	57	3	no	—
69	C₃	C₃×#13095338	1	1	yes	characteristic
70	C₃	(C₁₉⋊C₃)⋊(C₂₇⋊C₃)	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator, socle	C₃²×C₁₉	C₃²×C₉
Fitting	C₉²×C₁₉	C₉
prime radical	C₃²×C₁₉⋊C₃	C₃×C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₉²	#4296
hypocenter	C₁₉	#10624706
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
2. #17987572	C₃	semidirect
34. #4294	C₂₇⋊C₃	semidirect
58. C₁₉	#10624706	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095343	3
#17987572	3
C₉²×C₁₉⋊C₃	3
#10624706	19