Subgroups — #28353209

Order 13851.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095312	C₃	1	2	yes	maximal
2	C₃²×#10587018	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
4	#13095312	—	3	2	no	—
5	#13095312	—	3	2	no	—
6	#13095312	C₉	1	6	yes	complemented
7	C₃×#10587018	—	3	1	no	—
8	C₃×#10587018	—	3	2	no	—
9	C₃×#10587018	—	3	1	no	—
10	C₃×#10587018	—	3	1	no	—
11	C₃×#10587018	C₉	1	3	yes	complemented
12	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
13	C₁₉×C₉⋊C₉	—	3	2	no	—
14	C₁₉×C₃²⋊C₉	C₉	1	3	yes	—
15	C₉²×C₁₉	—	3	1	no	—
16	#10624469	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₁₉	—	3	3	no	—
19	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
23	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
24	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
25	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
26	C₃×C₉×C₁₉	3₋¹⁺²	1	2	yes	—
27	#10587018	—	3	3	no	—
28	#10587018	—	3	6	no	—
29	C₃×C₂₇⋊C₃	—	19	2	no	—
30	C₃²×C₂₇	—	19	1	no	—
31	#6887	C₁₉⋊C₃	1	1	yes	characteristic
32	C₃²×C₁₉	—	3	3	no	—
33	C₃²×C₁₉	C₉²	1	1	yes	characteristic
34	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
35	C₃²×C₁₉	C₉⋊C₉	1	1	yes	characteristic
36	C₃²×C₁₉	C₉⋊C₉	1	1	yes	characteristic
37	C₉×C₁₉	—	9	3	no	—
38	C₉×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
39	C₉×C₁₉	C₃²⋊C₉	1	2	yes	—
40	C₉×C₁₉	C₉⋊C₉	1	2	yes	—
41	C₉×C₁₉	C₉⋊C₉	1	2	yes	—
42	C₉×C₁₉	C₉⋊C₉	1	2	yes	—
43	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
44	C₂₇⋊C₃	—	19	6	no	—
45	C₂₇⋊C₃	—	57	2	no	—
46	C₂₇⋊C₃	—	57	2	no	—
47	C₃×C₂₇	—	19	3	no	—
48	C₃×C₂₇	—	57	1	no	—
49	C₃×C₂₇	—	57	1	no	—
50	C₃×C₂₇	—	57	1	no	—
51	C₃×C₂₇	—	57	2	no	—
52	C₉⋊C₉	—	3	2	no	—
53	C₃²⋊C₉	#4294	1	3	yes	—
54	C₉²	—	3	1	no	—
55	C₃×C₁₉	—	3	1	no	—
56	C₃×C₁₉	—	3	1	no	—
57	C₃×C₁₉	—	3	1	no	—
58	C₃×C₁₉	#6855	1	1	yes	characteristic
59	C₃×C₁₉	#6872	1	3	yes	—
60	C₃³	C₃×#4294	1	1	yes	characteristic
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
63	C₃×C₉	C₉×C₁₉⋊C₃	1	2	yes	—
64	C₃×C₉	#10587022	1	1	yes	characteristic
65	C₃×C₉	#10587022	1	2	yes	—
66	C₃×C₉	#10587023	1	1	yes	characteristic
67	C₃×C₉	#10587023	1	2	yes	—
68	C₃×C₉	#10587025	1	2	yes	—
69	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
70	C₂₇	—	57	3	no	—
71	C₂₇	—	57	6	no	—
72	C₁₉	#10624469	1	1	yes	characteristic, complemented, Sylow
73	C₃²	—	3	3	no	—
74	C₃²	C₉×#4294	1	1	yes	characteristic
75	C₃²	C₃²⋊#4294	1	1	yes	characteristic
76	C₃²	#13095306	1	1	yes	characteristic
77	C₃²	#13095307	1	1	yes	characteristic
78	C₉	—	9	3	no	—
79	C₉	#13095303	1	1	yes	characteristic
80	C₉	#13095303	1	2	yes	—
81	C₉	#13095305	1	2	yes	—
82	C₉	#13095305	1	2	yes	—
83	C₉	#13095305	1	2	yes	—
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	#17987308	1	1	yes	characteristic
88	C₃	#17987350	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₁₉⋊C₃)
commutator	C₃²×C₁₉	C₉²
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃²×C₁₉	C₃²⋊C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃²×C₉×C₁₉	C₃²
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624469
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
6. #13095312	C₉	semidirect
11. C₃×#10587018	C₉	semidirect
72. C₁₉	#10624469	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095312	3
C₃²×#10587018	3
C₁₉×#6887	3
#10624469	19