Subgroups — #28356793

Order 13851.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987563	C₃	1	3	yes	maximal
2	#17987403	C₃	1	1	yes	maximal, characteristic
3	#13095342	—	3	3	no	—
4	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
5	#13095305	—	3	1	no	—
6	#13095305	—	3	1	no	—
7	#13095303	—	3	1	no	—
8	C₉×#4294	C₉	1	2	yes	—
9	C₉²×C₁₉	C₉	1	1	yes	characteristic
10	#10624514	—	19	1	no	maximal, Sylow
11	C₃²×C₁₉⋊C₃	3₋¹⁺²	1	1	yes	characteristic
12	C₃×C₉×C₁₉	—	3	1	no	—
13	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₃×#4294	—	3	2	no	—
15	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
17	C₉×C₁₉⋊C₃	—	3	3	no	—
18	#10587020	—	9	3	no	—
19	#6887	—	19	1	no	—
20	#6869	—	19	3	no	—
21	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
22	C₃×C₁₉⋊C₃	—	3	1	no	—
23	C₃×C₁₉⋊C₃	—	9	1	no	—
24	C₉×C₁₉	—	3	1	no	—
25	C₉×C₁₉	—	9	1	no	—
26	#4294	—	3	1	no	—
27	#4294	—	9	2	no	—
28	#4294	#731	1	3	yes	—
29	C₃²×C₉	—	19	1	no	—
30	C₂₇⋊C₃	—	57	3	no	—
31	C₉⋊C₉	—	57	1	no	—
32	C₉⋊C₉	—	57	1	no	—
33	C₃²⋊C₉	—	57	1	no	—
34	C₉²	—	19	2	no	—
35	C₉²	#4296	1	1	yes	characteristic
36	C₃×C₁₉	—	3	1	no	—
37	C₃×C₁₉	#6867	1	1	yes	characteristic
38	C₁₉⋊C₃	—	9	1	no	—
39	C₃³	—	19	1	no	—
40	C₃×C₉	—	3	1	no	—
41	C₃×C₉	—	19	1	no	—
42	C₃×C₉	—	19	1	no	—
43	C₃×C₉	—	57	3	no	—
44	C₃×C₉	—	57	2	no	—
45	C₃×C₉	C₃×#4296	1	1	yes	characteristic
46	C₂₇	—	171	3	no	—
47	C₁₉	#10624514	1	1	yes	characteristic, complemented, Sylow
48	C₃²	—	57	1	no	—
49	C₃²	—	171	1	no	—
50	C₃²	C₃²⋊#4296	1	1	yes	characteristic
51	C₉	—	3	1	no	—
52	C₉	—	9	1	no	—
53	C₉	—	19	3	no	—
54	C₉	—	57	1	no	—
55	C₉	—	171	2	no	—
56	C₃	—	3	1	no	—
57	C₃	—	171	1	no	—
58	C₃	#17987559	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987559
commutator	C₃×C₉×C₁₉	C₃×C₉
Frattini	C₃×C₉	C₃×#4296
Fitting	C₉²×C₁₉	C₉
socle	C₃×C₁₉	#6867
prime radical	C₃²×C₁₉⋊C₃	3₋¹⁺²
cosocle	C₃×C₉×C₁₉⋊C₃	C₃²
hypercenter	C₉²	#4296
hypocenter	C₁₉	#10624514
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
47. C₁₉	#10624514	semidirect

Maximal subgroups

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

subgroup	index
#17987563	3
#17987403	3
#10624514	19