Subgroups — #28355705

Order 13851.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095307	C₃	1	1	yes	maximal, characteristic
2	#17987361	C₃	1	6	yes	maximal, complemented
3	#17987360	C₃	1	3	yes	maximal, complemented
4	#17987341	C₃	1	2	yes	maximal
5	C₁₉×#6869	C₃	1	1	yes	maximal, characteristic
6	C₃²×#4294	—	3	1	no	—
7	#13095312	C₃²	1	6	yes	—
8	#13095307	—	3	2	no	—
9	#13095307	C₃²	1	1	yes	characteristic
10	#13095307	C₃²	1	2	yes	—
11	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
12	C₁₉×C₂₇⋊C₃	C₃²	1	3	yes	—
13	#10624828	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	—	3	2	no	—
17	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
18	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
19	C₃×#4294	—	3	1	no	—
20	C₃×#4294	—	3	2	no	—
21	C₃×#4294	—	9	3	no	—
22	C₁₉×C₂₇	—	3	3	no	—
23	#10587018	—	3	6	no	—
24	C₃×C₉⋊C₉	—	19	1	no	—
25	#6875	—	19	3	no	—
26	#6875	—	19	6	no	—
27	#6869	—	19	2	no	—
28	#6869	C₁₉⋊C₃	1	1	yes	characteristic
29	C₃²×C₁₉	—	3	3	no	—
30	C₃²×C₁₉	—	3	1	no	—
31	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
32	C₉×C₁₉	—	3	2	no	—
33	C₉×C₁₉	#737	1	1	yes	characteristic
34	C₉×C₁₉	#737	1	2	yes	—
35	#4294	—	9	1	no	—
36	#4294	—	9	2	no	—
37	C₃²×C₉	—	57	1	no	—
38	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
39	C₂₇⋊C₃	—	19	6	no	—
40	C₂₇⋊C₃	C₃×C₁₉⋊C₃	1	3	yes	—
41	C₉⋊C₉	—	19	1	no	—
42	C₉⋊C₉	—	19	2	no	—
43	C₉⋊C₉	—	57	2	no	—
44	C₃×C₁₉	—	3	1	no	—
45	C₃×C₁₉	—	3	3	no	—
46	C₃×C₁₉	#6895	1	1	yes	characteristic
47	C₃³	#10587023	1	1	yes	characteristic
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	—	3	2	no	—
50	C₃×C₉	—	57	1	no	—
51	C₃×C₉	—	57	2	no	—
52	C₃×C₉	—	171	3	no	—
53	C₃×C₉	#10587023	1	2	yes	—
54	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
55	C₂₇	—	3	3	no	—
56	C₂₇	—	57	6	no	—
57	C₁₉	#10624828	1	1	yes	characteristic, complemented, Sylow
58	C₃²	—	3	3	no	—
59	C₃²	—	3	1	no	—
60	C₃²	C₃×#10587023	1	1	yes	characteristic
61	C₉	—	3	2	no	—
62	C₉	—	171	1	no	—
63	C₉	—	171	2	no	—
64	C₉	#13095331	1	1	yes	characteristic
65	C₉	#13095333	1	2	yes	—
66	C₃	—	3	1	no	—
67	C₃	—	3	3	no	—
68	C₃	#17987442	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987442
commutator, cosocle	C₃×C₉×C₁₉	C₃³
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#6869	C₃
socle	C₃×C₁₉	#6895
prime radical	C₃³×C₁₉	3₋¹⁺²
hypercenter	#6869	C₁₉⋊C₃
hypocenter	C₁₉	#10624828
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ #6869

Complements

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

N	H ≅ G/N	type
2. #17987361	C₃	semidirect
3. #17987360	C₃	semidirect
57. C₁₉	#10624828	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095307	3
#17987361	3
#17987360	3
#17987341	3
C₁₉×#6869	3
#10624828	19