Subgroups — #17987355

Order 4617.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587018	C₃	1	1	yes	maximal, characteristic
2	C₃×#10587018	C₃	1	1	yes	maximal, characteristic
3	C₉×#4294	C₃	1	1	yes	maximal, characteristic
4	C₃×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
5	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
6	C₃×#4294	C₉	1	1	yes	characteristic
7	C₃×#4294	C₉	1	1	yes	characteristic
8	C₃×#4294	C₉	1	1	yes	characteristic
9	C₁₉×C₂₇	—	3	1	no	—
10	#10587018	—	3	1	no	—
11	#10587018	—	3	1	no	—
12	C₉⋊C₂₇	—	19	1	no	maximal, Sylow
13	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
15	C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
16	C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
17	#4294	—	3	1	no	—
18	#4294	—	3	1	no	—
19	#4294	C₂₇	1	3	yes	complemented
20	C₃×C₂₇	—	19	1	no	—
21	C₃×C₂₇	—	19	1	no	—
22	C₃×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
23	C₉²	—	19	1	no	—
24	C₃×C₁₉	C₉⋊C₉	1	1	yes	characteristic
25	C₃×C₁₉	C₃×C₂₇	1	1	yes	characteristic
26	C₃×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
27	C₃×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
28	C₃×C₉	—	19	1	no	—
29	C₃×C₉	—	19	1	no	—
30	C₃×C₉	—	19	1	no	—
31	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
32	C₂₇	—	3	1	no	—
33	C₂₇	—	57	1	no	—
34	C₂₇	—	57	1	no	—
35	C₁₉	C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
36	C₃²	C₉×C₁₉⋊C₃	1	1	yes	characteristic
37	C₉	—	19	3	no	—
38	C₉	—	57	1	no	—
39	C₉	—	57	1	no	—
40	C₉	#10587022	1	1	yes	characteristic
41	C₉	#10587023	1	1	yes	characteristic
42	C₉	#10587025	1	1	yes	characteristic
43	C₃	#13095305	1	1	yes	characteristic
44	C₃	C₂₇×C₁₉⋊C₃	1	1	yes	characteristic
45	C₃	#13095310	1	1	yes	characteristic
46	C₃	#13095311	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃×C₂₇
Fitting	C₃×C₁₉×C₂₇	C₃
socle, prime radical	C₃²×C₁₉	C₃×C₉
cosocle	C₃×C₉×C₁₉	C₃²
hypercenter	C₃×C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	C₉⋊C₂₇
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
19. #4294	C₂₇	semidirect
35. C₁₉	C₉⋊C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×#10587018	3
C₉×#4294	3
C₃×C₁₉×C₂₇	3
C₉⋊C₂₇	19