Subgroups — #17987352

Order 4617.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095332	C₃	1	1	yes	maximal, characteristic
2	#13095312	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#10587018	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
6	C₃²⋊(C₁₉⋊C₃)	C₉	1	1	yes	characteristic
7	#10587025	C₉	1	2	yes	—
8	#10587023	—	3	1	no	—
9	#10587022	—	3	1	no	—
10	C₉×C₁₉⋊C₃	—	3	1	no	—
11	C₁₉×C₂₇	—	3	1	no	—
12	#10587018	—	3	1	no	—
13	#10587018	—	3	1	no	—
14	#6873	—	19	1	no	maximal, Sylow
15	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
16	C₃×C₁₉⋊C₃	—	3	1	no	—
17	C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
18	C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
19	C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
20	#4294	—	3	2	no	—
21	#737	—	19	1	no	—
22	C₂₇⋊C₃	—	19	1	no	—
23	C₂₇⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
24	C₃×C₂₇	—	19	1	no	—
25	C₃×C₁₉	—	3	1	no	—
26	C₃×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
27	C₁₉⋊C₃	—	9	1	no	—
28	3₋¹⁺²	—	19	2	no	—
29	3₋¹⁺²	—	57	1	no	—
30	3₋¹⁺²	—	57	1	no	—
31	H(3,𝔽₃)	—	19	1	no	—
32	C₃×C₉	—	57	1	no	—
33	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
34	C₂₇	—	3	1	no	—
35	C₂₇	—	57	1	no	—
36	C₂₇	—	57	1	no	—
37	C₁₉	#6873	1	1	yes	characteristic, complemented, Sylow
38	C₃²	—	57	1	no	—
39	C₃²	C₉×C₁₉⋊C₃	1	1	yes	characteristic
40	C₉	—	57	2	no	—
41	C₉	#10587022	1	1	yes	characteristic
42	C₉	#10587023	1	1	yes	characteristic
43	C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
44	C₃	—	3	1	no	—
45	C₃	—	171	1	no	—
46	C₃	#13095303	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊(C₁₉⋊C₃)
commutator	C₃²×C₁₉	C₃×C₉
Frattini	C₃×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×C₂₇⋊C₃	C₃
socle	C₃×C₁₉	C₃²⋊C₉
prime radical	C₃²⋊(C₁₉⋊C₃)	C₉
cosocle	C₃×C₉×C₁₉	C₃²
hypercenter	C₂₇⋊C₃	C₁₉⋊C₃
hypocenter	C₁₉	#6873
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #13095312	C₃	semidirect
3. C₃×#10587018	C₃	semidirect
4. C₁₉×C₂₇⋊C₃	C₃	semidirect
23. C₂₇⋊C₃	C₁₉⋊C₃	semidirect
37. C₁₉	#6873	semidirect

Maximal subgroups

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

subgroup	index
#13095332	3
#13095312	3
C₃×#10587018	3
C₁₉×C₂₇⋊C₃	3
#6873	19