Subgroups — C₃×#17987598 #28357057

Order 13851.

848 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₃²	C₃²×#4296
commutator	C₃×C₁₉	C₃³×C₉
Frattini	C₃	C₃³×#4296
Fitting, prime radical	C₃×C₁₉×H(3,𝔽₃)	C₉
socle	C₃²×C₁₉	C₃²×C₉
cosocle	#4294	C₃⁴
hypercenter	C₃×H(3,𝔽₃)	#4296
hypocenter	C₁₉	C₃×#6903
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. #17987598	C₃	direct (N × H)
2. C₃×#13095342	C₃	semidirect
3. C₃²×#10587020	C₃	semidirect
5. #13095342	C₃²	semidirect
8. C₃×#10587020	C₃²	semidirect
44. C₃×C₁₉	#6903	semidirect
55. C₁₉	C₃×#6903	semidirect
63. C₃	#17987598	direct (N × H)

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
C₃²×#10587020	3
C₃×#13095331	3
C₃×#6903	19

Subgroups — C3×#17987598 #28357057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987598 #28357057