Subgroups — #28356713

Order 13851.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987570	C₃	1	1	yes	maximal, characteristic
2	#17987570	C₃	1	1	yes	maximal, characteristic
3	#17987570	C₃	1	1	yes	maximal, characteristic
4	#17987330	C₃	1	1	yes	maximal, characteristic
5	C₃×#10587020	—	3	1	no	—
6	C₃×#10587020	—	3	1	no	—
7	C₃×#10587020	—	3	1	no	—
8	C₃×#10587018	C₉	1	1	yes	characteristic
9	C₃×#10587018	C₉	1	1	yes	characteristic
10	C₉×#4294	C₃²	1	1	yes	characteristic
11	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
12	#10624462	—	19	1	no	maximal, Sylow
13	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
15	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
16	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
17	#10587020	—	9	1	no	—
18	#10587020	—	9	1	no	—
19	#10587020	—	9	1	no	—
20	C₁₉×C₂₇	—	3	1	no	—
21	#10587018	—	3	1	no	—
22	#10587018	C₂₇	1	3	yes	complemented
23	C₉⋊C₂₇	—	19	1	no	—
24	C₉⋊C₂₇	—	19	1	no	—
25	C₉⋊C₂₇	—	19	1	no	—
26	#6864	—	19	1	no	—
27	C₃²×C₁₉	C₉⋊C₉	1	1	yes	characteristic
28	C₉×C₁₉	C₃×C₂₇	1	1	yes	characteristic
29	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
30	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
31	#4294	—	3	1	no	—
32	#4294	—	3	1	no	—
33	#4294	—	3	1	no	—
34	C₃×C₂₇	—	19	1	no	—
35	C₃×C₂₇	—	19	1	no	—
36	C₃×C₂₇	—	57	1	no	—
37	C₃×C₂₇	—	57	1	no	—
38	C₃×C₂₇	—	57	1	no	—
39	C₃×C₂₇	#4296	1	1	yes	characteristic
40	C₉²	—	19	1	no	—
41	C₃×C₁₉	C₉⋊C₂₇	1	1	yes	characteristic
42	C₃×C₁₉	#6875	1	1	yes	characteristic
43	C₃×C₁₉	#6875	1	1	yes	characteristic
44	C₃×C₁₉	#6875	1	1	yes	characteristic
45	C₃×C₉	—	19	1	no	—
46	C₃×C₉	—	19	1	no	—
47	C₃×C₉	—	19	1	no	—
48	C₃×C₉	C₃×#4296	1	1	yes	characteristic
49	C₂₇	—	3	1	no	—
50	C₂₇	—	19	3	no	—
51	C₂₇	—	57	1	no	—
52	C₂₇	—	171	1	no	—
53	C₂₇	—	171	1	no	—
54	C₂₇	—	171	1	no	—
55	C₁₉	#10624462	1	1	yes	characteristic, complemented, Sylow
56	C₃²	#13095338	1	1	yes	characteristic
57	C₉	—	57	1	no	—
58	C₉	—	57	1	no	—
59	C₉	—	57	1	no	—
60	C₉	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
61	C₉	#13095342	1	1	yes	characteristic
62	C₉	#13095344	1	1	yes	characteristic
63	C₃	#17987572	1	1	yes	characteristic
64	C₃	#17987574	1	1	yes	characteristic
65	C₃	#17987576	1	1	yes	characteristic
66	C₃	#17987578	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#13095338
commutator	C₉×C₁₉	C₃×C₂₇
Frattini	C₃×C₉	C₃×#4296
Fitting	C₃×C₁₉×C₂₇	C₉
socle, prime radical	C₃²×C₁₉	C₉⋊C₉
cosocle	C₉×#4294	C₃²
hypercenter	C₃×C₂₇	#4296
hypocenter	C₁₉	#10624462
LCS	G ▷ C₉×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
22. #10587018	C₂₇	semidirect
55. C₁₉	#10624462	semidirect

Maximal subgroups

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

subgroup	index
#17987570	3
#17987330	3
#10624462	19