Subgroups — #28357060

Order 13851.

828 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987598	C₃	1	27	yes	maximal, complemented
2	C₃×#13095342	C₃	1	12	yes	maximal, complemented
3	C₃×#13095331	C₃	1	1	yes	maximal, characteristic
4	#13095342	C₃²	1	9	yes	—
5	#13095342	C₃²	1	72	yes	complemented
6	C₃×#10587020	C₃²	1	36	yes	complemented
7	#13095331	C₉	1	18	yes	—
8	#13095331	C₃²	1	9	yes	—
9	C₃×#10587025	C₉	1	8	yes	—
10	C₃²×#4294	C₃²	1	4	yes	—
11	C₃×C₁₉×H(3,𝔽₃)	C₉	1	1	yes	characteristic
12	#10624918	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	C₃×C₉	1	4	yes	—
14	C₁₉×H(3,𝔽₃)	C₃×C₉	1	9	yes	—
15	#10587025	C₃×C₉	1	72	yes	—
16	C₃×#4294	C₃×C₉	1	8	yes	—
17	C₃×#4294	C₃×C₉	1	24	yes	—
18	C₃×#4294	C₃³	1	1	yes	characteristic
19	C₃×#4294	C₃³	1	12	yes	—
20	#10587020	C₃³	1	27	yes	—
21	C₃×#737	—	19	1	no	—
22	#6903	—	19	27	no	—
23	C₃×C₂₇⋊C₃	—	19	12	no	—
24	C₃²×C₁₉	—	9	4	no	—
25	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
26	C₃²×C₁₉	C₃²×C₉	1	12	yes	—
27	#4294	C₃²×C₉	1	2	yes	—
28	#4294	C₃²×C₉	1	24	yes	—
29	#4294	C₃⁴	1	1	yes	characteristic
30	#737	—	19	18	no	—
31	#737	—	19	9	no	—
32	C₃×3₋¹⁺²	—	19	8	no	—
33	C₃×H(3,𝔽₃)	#4296	1	1	yes	characteristic
34	C₃²×C₉	—	19	4	no	—
35	C₂₇⋊C₃	—	19	9	no	—
36	C₂₇⋊C₃	—	19	72	no	—
37	C₃×C₂₇	—	19	36	no	—
38	C₃×C₁₉	—	3	1	no	—
39	C₃×C₁₉	—	3	12	no	—
40	C₃×C₁₉	C₃³×C₉	1	1	yes	characteristic
41	C₃³	C₃×#4296	1	4	yes	—
42	3₋¹⁺²	—	19	72	no	—
43	H(3,𝔽₃)	C₃×#4296	1	9	yes	—
44	C₃×C₉	—	19	8	no	—
45	C₃×C₉	—	19	24	no	—
46	C₃×C₉	—	19	12	no	—
47	C₃×C₉	—	19	1	no	—
48	C₂₇	—	19	27	no	—
49	C₁₉	#10624918	1	1	yes	characteristic, complemented, Sylow
50	C₃²	—	9	4	no	—
51	C₃²	C₃²×#4296	1	1	yes	characteristic
52	C₃²	C₃²×#4296	1	12	yes	—
53	C₉	—	19	1	no	—
54	C₉	—	19	2	no	—
55	C₉	—	19	24	no	—
56	C₃	—	3	1	no	—
57	C₃	—	3	12	no	—
58	C₃	C₃³×#4296	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃	C₃³×#4296
commutator, socle	C₃×C₁₉	C₃³×C₉
Fitting, prime radical	C₃×C₁₉×H(3,𝔽₃)	C₉
cosocle	#4294	C₃⁴
hypercenter	C₃×H(3,𝔽₃)	#4296
hypocenter	C₁₉	#10624918
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. #17987598	C₃	semidirect
2. C₃×#13095342	C₃	semidirect
5. #13095342	C₃²	semidirect
6. C₃×#10587020	C₃²	semidirect
49. C₁₉	#10624918	semidirect

Maximal subgroups

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

subgroup	index
#17987598	3
C₃×#13095342	3
C₃×#13095331	3
#10624918	19