Subgroups — #28356770

Order 13851.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987582	C₃	1	2	yes	maximal, complemented
2	C₃×#13095335	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987480	C₃	1	1	yes	maximal, characteristic
4	#13095335	—	3	1	no	—
5	#13095335	—	3	2	no	—
6	#13095312	—	3	2	no	—
7	#13095312	C₉	1	2	yes	—
8	C₃×#10587018	—	3	1	no	—
9	C₃×#10587018	C₃²	1	1	yes	characteristic
10	C₁₉×#737	C₉	1	1	yes	characteristic
11	#10624503	—	19	1	no	maximal, Sylow
12	C₁₉×3₋¹⁺²	—	3	2	no	—
13	C₁₉×3₋¹⁺²	C₂₇	1	2	yes	—
14	C₁₉×H(3,𝔽₃)	C₂₇	1	1	yes	characteristic
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
17	#10587018	—	3	2	no	—
18	#10587018	H(3,𝔽₃)	1	1	yes	characteristic
19	#10587018	3₋¹⁺²	1	2	yes	—
20	#6903	—	19	1	no	—
21	C₈₁⋊C₃	—	19	2	no	—
22	C₃×C₈₁	—	19	1	no	—
23	C₃²×C₁₉	—	3	1	no	—
24	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
25	C₉×C₁₉	—	3	2	no	—
26	C₉×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
27	C₉×C₁₉	C₂₇⋊C₃	1	2	yes	—
28	#737	#4296	1	1	yes	characteristic
29	C₂₇⋊C₃	—	19	2	no	—
30	C₂₇⋊C₃	—	57	2	no	—
31	C₃×C₂₇	—	19	1	no	—
32	C₃×C₂₇	—	57	1	no	—
33	C₈₁	—	57	1	no	—
34	C₈₁	—	57	2	no	—
35	C₃×C₁₉	—	3	1	no	—
36	C₃×C₁₉	—	9	1	no	—
37	C₃×C₁₉	C₃²⋊C₂₇	1	1	yes	characteristic
38	3₋¹⁺²	—	3	2	no	—
39	3₋¹⁺²	#10587020	1	2	yes	—
40	H(3,𝔽₃)	#10587020	1	1	yes	characteristic
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	C₃×#4296	1	1	yes	characteristic
43	C₂₇	—	19	1	no	—
44	C₂₇	—	19	2	no	—
45	C₂₇	—	57	2	no	—
46	C₁₉	#10624503	1	1	yes	characteristic, complemented, Sylow
47	C₃²	—	3	1	no	—
48	C₃²	C₃×#10587020	1	1	yes	characteristic
49	C₉	—	3	2	no	—
50	C₉	C₃²⋊#4296	1	1	yes	characteristic
51	C₉	#13095342	1	2	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	9	1	no	—
54	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	C₁₉×#737	C₉
socle	C₃×C₁₉	C₃²⋊C₂₇
prime radical	C₁₉×H(3,𝔽₃)	C₂₇
cosocle	C₃×#10587018	C₃²
hypercenter	#737	#4296
hypocenter	C₁₉	#10624503
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ #737

Complements

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

N	H ≅ G/N	type
1. #17987582	C₃	semidirect
2. C₃×#13095335	C₃	semidirect
46. C₁₉	#10624503	semidirect

Maximal subgroups

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

subgroup	index
#17987582	3
C₃×#13095335	3
#17987480	3
#10624503	19