Subgroups — #28356767

Order 13851.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987582	C₃	1	3	yes	maximal, complemented
2	C₃²×#10587018	C₃	1	1	yes	maximal, characteristic
3	#13095335	—	3	3	no	—
4	C₃×#10587018	—	3	1	no	—
5	C₃×#10587018	—	3	2	no	—
6	C₃×#10587018	C₉	1	2	yes	—
7	C₃×#10587018	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
9	#10624502	—	19	1	no	maximal, Sylow
10	C₃³×C₁₉	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₁₉	—	3	1	no	—
12	C₃×C₉×C₁₉	—	3	2	no	—
13	C₃×C₉×C₁₉	C₂₇	1	2	yes	—
14	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
15	#10587018	—	3	2	no	—
16	#10587018	H(3,𝔽₃)	1	1	yes	characteristic
17	#10587018	3₋¹⁺²	1	2	yes	—
18	C₃²×C₂₇	—	19	1	no	—
19	C₈₁⋊C₃	—	19	3	no	—
20	C₃²×C₁₉	—	3	3	no	—
21	C₃²×C₁₉	—	3	1	no	—
22	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
23	C₉×C₁₉	—	3	2	no	—
24	C₉×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
25	C₉×C₁₉	C₂₇⋊C₃	1	2	yes	—
26	C₃²×C₉	#4296	1	1	yes	characteristic
27	C₃×C₂₇	—	19	1	no	—
28	C₃×C₂₇	—	19	2	no	—
29	C₃×C₂₇	—	57	1	no	—
30	C₃×C₂₇	—	57	2	no	—
31	C₈₁	—	57	3	no	—
32	C₃×C₁₉	—	3	3	no	—
33	C₃×C₁₉	—	3	1	no	—
34	C₃×C₁₉	C₃²⋊C₂₇	1	1	yes	characteristic
35	C₃³	#10587020	1	1	yes	characteristic
36	C₃×C₉	—	3	1	no	—
37	C₃×C₉	—	3	2	no	—
38	C₃×C₉	#10587020	1	2	yes	—
39	C₃×C₉	C₃×#4296	1	1	yes	characteristic
40	C₂₇	—	19	1	no	—
41	C₂₇	—	19	2	no	—
42	C₂₇	—	57	2	no	—
43	C₁₉	#10624502	1	1	yes	characteristic, complemented, Sylow
44	C₃²	—	3	3	no	—
45	C₃²	—	3	1	no	—
46	C₃²	C₃×#10587020	1	1	yes	characteristic
47	C₉	—	3	2	no	—
48	C₉	C₃²⋊#4296	1	1	yes	characteristic
49	C₉	#13095342	1	2	yes	—
50	C₃	—	3	1	no	—
51	C₃	—	3	3	no	—
52	C₃	C₃²⋊#10587020	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊#4296
commutator	C₃²×C₁₉	C₃×C₂₇
Frattini	C₃×C₉	C₃×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle	C₃×C₁₉	C₃²⋊C₂₇
prime radical	C₃³×C₁₉	C₂₇
cosocle	C₃×#10587018	C₃²
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	#10624502
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #17987582	C₃	semidirect
43. C₁₉	#10624502	semidirect

Maximal subgroups

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

subgroup	index
#17987582	3
C₃²×#10587018	3
#10624502	19