Subgroups — #28355708

Order 13851.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987358	C₃	1	9	yes	maximal, complemented
2	#17987341	C₃	1	3	yes	maximal
3	C₃×C₁₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	#13095312	C₃²	1	9	yes	—
5	C₃²×C₉×C₁₉	—	3	1	no	—
6	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
7	C₁₉×C₉⋊C₉	—	3	2	no	—
8	C₁₉×C₉⋊C₉	C₃²	1	3	yes	—
9	#10624828	—	19	1	no	maximal, Sylow
10	C₃³×C₁₉	3₋¹⁺²	1	1	yes	characteristic
11	C₃×C₉×C₁₉	—	3	3	no	—
12	C₃×C₉×C₁₉	—	3	3	no	—
13	C₃×C₉×C₁₉	—	9	3	no	—
14	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
15	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
16	#10587018	—	3	9	no	—
17	C₃×C₉⋊C₉	C₁₉⋊C₃	1	1	yes	characteristic
18	#6875	—	19	9	no	—
19	#6869	—	19	3	no	—
20	C₃²×C₁₉	—	3	3	no	—
21	C₃²×C₁₉	—	3	1	no	—
22	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
23	C₉×C₁₉	—	3	2	no	—
24	C₉×C₁₉	—	9	3	no	—
25	C₉×C₁₉	#737	1	3	yes	—
26	C₃²×C₉	—	3	1	no	—
27	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
28	C₂₇⋊C₃	—	19	9	no	—
29	C₉⋊C₉	—	3	2	no	—
30	C₉⋊C₉	C₃×C₁₉⋊C₃	1	3	yes	—
31	C₃×C₁₉	—	3	1	no	—
32	C₃×C₁₉	—	3	3	no	—
33	C₃×C₁₉	#6895	1	1	yes	characteristic
34	C₃³	#10587025	1	1	yes	characteristic
35	C₃×C₉	—	3	3	no	—
36	C₃×C₉	—	3	3	no	—
37	C₃×C₉	—	9	3	no	—
38	C₃×C₉	#10587025	1	2	yes	—
39	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
40	C₂₇	—	57	9	no	—
41	C₁₉	#10624828	1	1	yes	characteristic, complemented, Sylow
42	C₃²	—	3	3	no	—
43	C₃²	—	3	1	no	—
44	C₃²	C₃×#10587025	1	1	yes	characteristic
45	C₉	—	3	2	no	—
46	C₉	—	9	3	no	—
47	C₉	#13095332	1	3	yes	—
48	C₃	—	3	1	no	—
49	C₃	—	3	3	no	—
50	C₃	#17987445	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987445
commutator, cosocle	C₃×C₉×C₁₉	C₃³
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₃×C₁₉×C₉⋊C₉	C₃
socle	C₃×C₁₉	#6895
prime radical	C₃³×C₁₉	3₋¹⁺²
hypercenter	C₃×C₉⋊C₉	C₁₉⋊C₃
hypocenter	C₁₉	#10624828
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
1. #17987358	C₃	semidirect
41. C₁₉	#10624828	semidirect

Maximal subgroups

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

subgroup	index
#17987358	3
#17987341	3
C₃×C₁₉×C₉⋊C₉	3
#10624828	19