Subgroups — #28356795

Order 13851.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987559	C₃	1	3	yes	maximal
2	#17987404	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊#4296	—	3	3	no	—
4	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
5	#13095307	C₉	1	1	yes	characteristic, complemented
6	#13095306	C₉	1	1	yes	characteristic, complemented
7	#13095305	—	3	1	no	—
8	#13095303	—	3	1	no	—
9	C₉×#4294	—	3	1	no	—
10	C₁₉×C₉⋊C₉	C₉	1	1	yes	characteristic, complemented
11	#10624515	—	19	1	no	maximal, Sylow
12	C₃²×C₁₉⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×#4296	—	9	3	no	—
14	C₃×C₉×C₁₉	—	3	1	no	—
15	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
16	C₃×#4294	—	3	1	no	—
17	C₃×#4294	—	3	1	no	—
18	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
19	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
20	C₉×C₁₉⋊C₃	—	3	3	no	—
21	#6887	—	19	1	no	—
22	#6867	—	19	3	no	—
23	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
24	C₃×C₁₉⋊C₃	—	9	1	no	—
25	C₃×C₁₉⋊C₃	#731	1	3	yes	—
26	#4296	—	27	3	no	—
27	C₉×C₁₉	—	3	1	no	—
28	C₉×C₁₉	—	9	1	no	—
29	#4294	—	3	1	no	—
30	#4294	—	3	1	no	—
31	#4294	—	9	1	no	—
32	#4294	—	9	1	no	—
33	C₃²×C₉	—	19	1	no	—
34	C₉⋊C₉	—	19	1	no	—
35	C₉⋊C₉	—	19	1	no	—
36	C₉⋊C₉	—	57	1	no	—
37	C₉⋊C₉	#4296	1	1	yes	characteristic, complemented
38	C₃²⋊C₉	—	57	1	no	—
39	C₃²⋊C₉	—	57	3	no	—
40	C₉²	—	57	1	no	—
41	C₃×C₁₉	—	3	1	no	—
42	C₃×C₁₉	#6867	1	1	yes	characteristic
43	C₁₉⋊C₃	—	3	3	no	—
44	C₃³	—	19	1	no	—
45	C₃×C₉	—	3	1	no	—
46	C₃×C₉	—	19	1	no	—
47	C₃×C₉	—	19	1	no	—
48	C₃×C₉	—	57	3	no	—
49	C₃×C₉	—	57	1	no	—
50	C₃×C₉	—	57	1	no	—
51	C₃×C₉	—	171	3	no	—
52	C₃×C₉	C₃×#4296	1	1	yes	characteristic
53	C₁₉	#10624515	1	1	yes	characteristic, complemented, Sylow
54	C₃²	—	19	3	no	—
55	C₃²	—	171	1	no	—
56	C₃²	C₃²⋊#4296	1	1	yes	characteristic
57	C₉	—	513	3	no	—
58	C₉	—	3	1	no	—
59	C₉	—	9	1	no	—
60	C₉	—	57	1	no	—
61	C₉	—	57	1	no	—
62	C₉	—	171	1	no	—
63	C₉	—	171	1	no	—
64	C₃	—	3	1	no	—
65	C₃	—	57	3	no	—
66	C₃	#17987559	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987559
commutator	C₃×C₉×C₁₉	C₃×C₉
Frattini	C₃×C₉	C₃×#4296
Fitting	C₁₉×C₉⋊C₉	C₉
socle	C₃×C₁₉	#6867
prime radical	C₃²×C₁₉⋊C₃	H(3,𝔽₃)
cosocle	C₃×C₉×C₁₉⋊C₃	C₃²
hypercenter	C₉⋊C₉	#4296
hypocenter	C₁₉	#10624515
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
5. #13095307	C₉	semidirect
6. #13095306	C₉	semidirect
10. C₁₉×C₉⋊C₉	C₉	semidirect
37. C₉⋊C₉	#4296	semidirect
53. C₁₉	#10624515	semidirect

Maximal subgroups

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

subgroup	index
#17987559	3
#17987404	3
#10624515	19