Subgroups — #28356766

Order 13851.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095335	C₃	1	3	yes	maximal, complemented
2	C₃×C₂₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#13095335	—	3	3	no	—
4	C₃×C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
5	C₃×#10587018	C₉	1	1	yes	characteristic
6	C₃×#10587018	C₃²	1	1	yes	characteristic
7	C₂₇×C₁₉⋊C₃	—	3	1	no	—
8	C₂₇×C₁₉⋊C₃	—	3	2	no	—
9	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic
10	C₃²⋊C₈₁	—	19	1	no	maximal, Sylow
11	C₃²×C₁₉⋊C₃	C₂₇	1	1	yes	characteristic
12	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
13	C₃×#4294	C₂₇	1	2	yes	—
14	C₉×C₁₉⋊C₃	—	3	1	no	—
15	C₉×C₁₉⋊C₃	—	3	1	no	—
16	C₉×C₁₉⋊C₃	—	3	1	no	—
17	C₁₉×C₂₇	—	3	1	no	—
18	#10587018	—	3	1	no	—
19	#10587018	H(3,𝔽₃)	1	1	yes	characteristic
20	#10587018	3₋¹⁺²	1	2	yes	—
21	C₃²×C₂₇	—	19	1	no	—
22	C₃×C₈₁	—	19	3	no	—
23	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
24	C₃×C₁₉⋊C₃	—	3	1	no	—
25	C₃×C₁₉⋊C₃	—	3	1	no	—
26	C₃×C₁₉⋊C₃	—	3	1	no	—
27	C₃×C₁₉⋊C₃	C₈₁	1	3	yes	complemented
28	C₉×C₁₉	C₃²⋊C₉	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	2	no	—
32	C₃²×C₉	—	19	1	no	—
33	C₃×C₂₇	—	19	1	no	—
34	C₃×C₂₇	—	19	1	no	—
35	C₃×C₂₇	—	57	1	no	—
36	C₃×C₂₇	—	57	2	no	—
37	C₃×C₂₇	#4296	1	1	yes	characteristic
38	C₈₁	—	57	3	no	—
39	C₃×C₁₉	C₃²⋊C₂₇	1	1	yes	characteristic
40	C₃×C₁₉	C₃×C₈₁	1	1	yes	characteristic
41	C₃×C₁₉	C₈₁⋊C₃	1	1	yes	characteristic
42	C₃×C₁₉	C₈₁⋊C₃	1	1	yes	characteristic
43	C₁₉⋊C₃	—	3	3	no	—
44	C₃³	—	19	1	no	—
45	C₃×C₉	—	19	2	no	—
46	C₃×C₉	—	57	1	no	—
47	C₃×C₉	—	57	1	no	—
48	C₃×C₉	—	57	1	no	—
49	C₃×C₉	C₃×#4296	1	1	yes	characteristic
50	C₂₇	—	3	1	no	—
51	C₂₇	—	19	1	no	—
52	C₂₇	—	19	2	no	—
53	C₂₇	—	57	1	no	—
54	C₁₉	C₃²⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
55	C₃²	—	19	3	no	—
56	C₃²	—	57	1	no	—
57	C₃²	—	57	1	no	—
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	—	57	3	no	—
65	C₃	#17987557	1	1	yes	characteristic
66	C₃	(C₁₉⋊C₃)⋊C₈₁	1	1	yes	characteristic
67	C₃	#17987583	1	1	yes	characteristic
68	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	C₃²×C₁₉	C₃×C₂₇
prime radical	C₃²×C₁₉⋊C₃	C₂₇
cosocle	C₃×#10587018	C₃²
hypercenter	C₃×C₂₇	#4296
hypocenter	C₁₉	C₃²⋊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
1. C₃×#13095335	C₃	semidirect
27. C₃×C₁₉⋊C₃	C₈₁	semidirect
54. C₁₉	C₃²⋊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
C₃×C₂₇×C₁₉⋊C₃	3
C₃²⋊C₈₁	19