Subgroups — #28356773

Order 13851.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987582	C₃	1	2	yes	maximal, complemented
2	C₃×#13095335	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987481	C₃	1	1	yes	maximal, characteristic
4	#13095335	—	3	1	no	—
5	#13095335	—	3	2	no	—
6	#13095332	C₉	1	1	yes	characteristic
7	#13095312	C₉	1	1	yes	characteristic
8	#13095311	—	3	1	no	—
9	#13095310	—	3	1	no	—
10	C₃×#10587018	C₃²	1	1	yes	characteristic
11	C₂₇×C₁₉⋊C₃	—	3	1	no	—
12	C₁₉×C₂₇⋊C₃	C₉	1	1	yes	characteristic
13	#10624504	—	19	1	no	maximal, Sylow
14	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃²⋊(C₁₉⋊C₃)	C₂₇	1	1	yes	characteristic
16	#10587025	C₂₇	1	2	yes	—
17	#10587023	—	3	1	no	—
18	#10587022	—	3	1	no	—
19	C₉×C₁₉⋊C₃	—	3	1	no	—
20	C₁₉×C₂₇	—	3	1	no	—
21	#10587018	—	3	1	no	—
22	#10587018	H(3,𝔽₃)	1	1	yes	characteristic
23	#10587018	3₋¹⁺²	1	1	yes	characteristic
24	#10587018	3₋¹⁺²	1	1	yes	characteristic
25	#6903	—	19	1	no	—
26	C₈₁⋊C₃	—	19	2	no	—
27	C₃×C₈₁	—	19	1	no	—
28	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
29	C₃×C₁₉⋊C₃	—	3	1	no	—
30	C₉×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
31	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
32	C₉×C₁₉	C₂₇⋊C₃	1	1	yes	characteristic
33	#4294	—	3	2	no	—
34	#737	—	19	1	no	—
35	C₂₇⋊C₃	—	19	1	no	—
36	C₂₇⋊C₃	—	57	1	no	—
37	C₂₇⋊C₃	—	57	1	no	—
38	C₂₇⋊C₃	#4296	1	1	yes	characteristic
39	C₃×C₂₇	—	19	1	no	—
40	C₃×C₂₇	—	57	1	no	—
41	C₈₁	—	57	1	no	—
42	C₈₁	—	57	2	no	—
43	C₃×C₁₉	—	3	1	no	—
44	C₃×C₁₉	C₃²⋊C₂₇	1	1	yes	characteristic
45	C₁₉⋊C₃	—	9	1	no	—
46	3₋¹⁺²	—	19	2	no	—
47	3₋¹⁺²	—	57	1	no	—
48	3₋¹⁺²	—	57	1	no	—
49	H(3,𝔽₃)	—	19	1	no	—
50	C₃×C₉	—	57	1	no	—
51	C₃×C₉	C₃×#4296	1	1	yes	characteristic
52	C₂₇	—	3	1	no	—
53	C₂₇	—	19	1	no	—
54	C₂₇	—	19	1	no	—
55	C₂₇	—	19	1	no	—
56	C₂₇	—	57	1	no	—
57	C₁₉	#10624504	1	1	yes	characteristic, complemented, Sylow
58	C₃²	—	57	1	no	—
59	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
60	C₉	—	57	2	no	—
61	C₉	C₃²⋊#4296	1	1	yes	characteristic
62	C₉	#13095343	1	1	yes	characteristic
63	C₉	#13095344	1	1	yes	characteristic
64	C₃	—	3	1	no	—
65	C₃	—	171	1	no	—
66	C₃	#17987557	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊#4296
commutator	C₃²×C₁₉	C₃×C₂₇
Frattini	C₃×C₉	C₃×#4296
Fitting	C₁₉×C₂₇⋊C₃	C₉
socle	C₃×C₁₉	C₃²⋊C₂₇
prime radical	C₃²⋊(C₁₉⋊C₃)	C₂₇
cosocle	C₃×#10587018	C₃²
hypercenter	C₂₇⋊C₃	#4296
hypocenter	C₁₉	#10624504
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
1. #17987582	C₃	semidirect
2. C₃×#13095335	C₃	semidirect
57. C₁₉	#10624504	semidirect

Maximal subgroups

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

subgroup	index
#17987582	3
C₃×#13095335	3
#17987481	3
#10624504	19