Subgroups — #28356827

Order 13851.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095335	C₃	1	3	yes	maximal
2	C₂₇×#4294	C₃	1	1	yes	maximal, characteristic
3	#13095335	—	3	3	no	—
4	C₃×#10587018	C₉	1	1	yes	characteristic
5	C₃×#10587018	C₃²	1	1	yes	characteristic
6	C₉×#4294	C₉	1	1	yes	characteristic
7	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
8	C₉⋊C₈₁	—	19	1	no	maximal, Sylow
9	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
10	C₃×#4294	C₂₇	1	1	yes	characteristic
11	C₃×#4294	C₂₇	1	1	yes	characteristic
12	C₃×#4294	C₂₇	1	1	yes	characteristic
13	C₁₉×C₂₇	—	3	1	no	—
14	#10587018	—	3	1	no	—
15	#10587018	3₋¹⁺²	1	3	yes	—
16	C₃×C₈₁	—	19	3	no	—
17	C₉×C₂₇	—	19	1	no	—
18	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
19	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
20	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
21	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
22	#4294	—	3	1	no	—
23	#4294	—	3	1	no	—
24	#4294	C₈₁	1	3	yes	complemented
25	C₃×C₂₇	—	19	1	no	—
26	C₃×C₂₇	—	19	1	no	—
27	C₃×C₂₇	#4296	1	1	yes	characteristic
28	C₉²	—	19	1	no	—
29	C₈₁	—	57	3	no	—
30	C₃×C₁₉	C₉⋊C₂₇	1	1	yes	characteristic
31	C₃×C₁₉	C₃×C₈₁	1	1	yes	characteristic
32	C₃×C₁₉	C₈₁⋊C₃	1	1	yes	characteristic
33	C₃×C₁₉	C₈₁⋊C₃	1	1	yes	characteristic
34	C₃×C₉	—	19	1	no	—
35	C₃×C₉	—	19	1	no	—
36	C₃×C₉	—	19	1	no	—
37	C₃×C₉	C₃×#4296	1	1	yes	characteristic
38	C₂₇	—	3	1	no	—
39	C₂₇	—	19	3	no	—
40	C₂₇	—	57	1	no	—
41	C₁₉	C₉⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
42	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
43	C₉	—	19	3	no	—
44	C₉	—	57	1	no	—
45	C₉	—	57	1	no	—
46	C₉	#13095338	1	1	yes	characteristic
47	C₉	#13095342	1	1	yes	characteristic
48	C₉	#13095344	1	1	yes	characteristic
49	C₃	#17987572	1	1	yes	characteristic
50	C₃	(C₁₉⋊C₃)⋊C₈₁	1	1	yes	characteristic
51	C₃	#17987583	1	1	yes	characteristic
52	C₃	#17987584	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×#4296
commutator	C₃×C₁₉	C₃×C₈₁
Fitting	C₃×C₁₉×C₂₇	C₉
socle, prime radical	C₃²×C₁₉	C₃×C₂₇
cosocle	C₃×#10587018	C₃²
hypercenter	C₃×C₂₇	#4296
hypocenter	C₁₉	C₉⋊C₈₁
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
24. #4294	C₈₁	semidirect
41. C₁₉	C₉⋊C₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095335	3
C₂₇×#4294	3
C₉⋊C₈₁	19