Subgroups — C₃×#17987453 #28355997

Order 13851.

692 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987453	C₃	1	27	yes	maximal, direct product factor
2	C₃×#13095305	C₃	1	8	yes	maximal, complemented
3	C₃×#13095303	C₃	1	4	yes	maximal
4	C₃×C₉²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
6	C₃²×#4294	C₃²	1	8	yes	—
7	#13095305	C₃²	1	72	yes	complemented
8	#13095303	C₃²	1	36	yes	—
9	C₃²×C₉×C₁₉	C₃²	1	4	yes	—
10	C₉²×C₁₉	C₃²	1	9	yes	complemented
11	C₃×#6897	—	19	1	no	maximal, Sylow
12	C₃³×C₁₉	C₃³	1	1	yes	characteristic
13	C₃²×C₁₉⋊C₃	—	3	12	no	—
14	C₃²×C₁₉⋊C₃	C₃³	1	3	yes	—
15	C₃×C₉×C₁₉	—	3	12	no	—
16	C₃×C₉×C₁₉	C₃³	1	12	yes	—
17	C₃×#4294	—	3	24	no	—
18	C₃×#4294	C₃³	1	24	yes	—
19	#6897	—	19	27	no	—
20	C₃×C₉⋊C₉	—	19	8	no	—
21	C₃×C₃²⋊C₉	—	19	4	no	—
22	C₃×C₉²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
23	C₃²×C₁₉	#737	1	12	yes	—
24	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
25	C₃×C₁₉⋊C₃	—	3	12	no	—
26	C₃×C₁₉⋊C₃	—	9	9	no	—
27	C₉×C₁₉	—	3	12	no	—
28	#4294	—	3	24	no	—
29	C₃⁴	—	19	1	no	—
30	C₃²×C₉	—	19	8	no	—
31	C₃²×C₉	C₃×C₁₉⋊C₃	1	4	yes	—
32	C₉⋊C₉	—	19	72	no	—
33	C₃²⋊C₉	—	19	36	no	—
34	C₉²	C₃×C₁₉⋊C₃	1	9	yes	complemented
35	C₃×C₁₉	#6897	1	9	yes	complemented
36	C₃×C₁₉	C₃×#737	1	4	yes	—
37	C₁₉⋊C₃	—	9	3	no	—
38	C₃³	—	19	3	no	—
39	C₃³	—	57	12	no	—
40	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
41	C₃×C₉	—	3	12	no	—
42	C₃×C₉	—	19	24	no	—
43	C₃×C₉	—	57	24	no	—
44	C₃×C₉	C₃²×C₁₉⋊C₃	1	12	yes	—
45	C₁₉	C₃×#6897	1	1	yes	characteristic, complemented, Sylow
46	C₃²	—	57	12	no	—
47	C₃²	—	171	9	no	—
48	C₃²	#13095332	1	12	yes	—
49	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
50	C₉	—	3	12	no	—
51	C₉	—	57	24	no	—
52	C₃	—	171	3	no	—
53	C₃	#17987453	1	9	yes	direct product factor
54	C₃	C₃×#13095332	1	4	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₁₉⋊C₃
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₃×C₉²×C₁₉	C₃
socle	C₃³×C₁₉	C₃³
prime radical	C₃³×C₁₉⋊C₃	C₃²
hypercenter	C₃×C₉²	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6897
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
1. #17987453	C₃	direct (N × H)
2. C₃×#13095305	C₃	semidirect
4. C₃×C₉²×C₁₉	C₃	semidirect
7. #13095305	C₃²	semidirect
10. C₉²×C₁₉	C₃²	semidirect
22. C₃×C₉²	C₁₉⋊C₃	semidirect
34. C₉²	C₃×C₁₉⋊C₃	semidirect
35. C₃×C₁₉	#6897	semidirect
45. C₁₉	C₃×#6897	semidirect
53. C₃	#17987453	direct (N × H)

Maximal subgroups

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

subgroup	index
#17987453	3
C₃×#13095305	3
C₃×#13095303	3
C₃×C₉²×C₁₉	3
C₃×#6897	19

Subgroups — C3×#17987453 #28355997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987453 #28355997