Subgroups — #28353523

Order 13851.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095307	C₃	1	1	yes	maximal, characteristic
2	C₃×#13095306	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
4	#17987308	C₃	1	9	yes	maximal
5	C₃×C₁₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
6	C₃²×#4294	C₃²	1	3	yes	—
7	C₃²×#4294	C₃²	1	3	yes	—
8	C₃²×#4294	C₃²	1	3	yes	—
9	#13095307	—	3	3	no	—
10	#13095306	—	3	3	no	—
11	C₉×#4294	C₉	1	9	yes	complemented
12	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
13	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
14	C₁₉×C₉⋊C₉	—	3	3	no	—
15	#10624553	—	19	1	no	maximal, Sylow
16	C₃³×C₁₉	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₁₉	—	3	3	no	—
18	C₃×C₉×C₁₉	—	3	9	no	—
19	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
20	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
21	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
22	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
23	C₃×#4294	—	3	9	no	—
24	C₃×#4294	—	3	3	no	—
25	C₃×#4294	—	3	3	no	—
26	C₃×#4294	—	3	9	no	—
27	C₃×#4294	—	3	9	no	—
28	C₃×#4294	C₃×C₉	1	9	yes	—
29	C₃×C₉⋊C₉	—	19	1	no	—
30	C₃×C₉⋊C₉	—	19	1	no	—
31	C₃×C₉⋊C₉	C₁₉⋊C₃	1	1	yes	characteristic
32	C₃×C₉²	—	19	1	no	—
33	#6855	—	19	9	no	—
34	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
35	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
37	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
38	C₃²×C₁₉	#737	1	9	yes	—
39	C₉×C₁₉	—	9	3	no	—
40	C₉×C₁₉	C₉⋊C₉	1	9	yes	—
41	#4294	—	3	9	no	—
42	#4294	—	9	3	no	—
43	#4294	—	9	3	no	—
44	C₃²×C₉	—	19	3	no	—
45	C₃²×C₉	—	19	3	no	—
46	C₃²×C₉	—	19	3	no	—
47	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
48	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
49	C₉⋊C₉	—	3	3	no	—
50	C₉⋊C₉	—	57	3	no	—
51	C₉⋊C₉	—	57	3	no	—
52	C₉²	—	19	9	no	—
53	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
54	C₃×C₁₉	#6887	1	3	yes	—
55	C₃×C₁₉	#6899	1	3	yes	—
56	C₃×C₁₉	#6899	1	3	yes	—
57	C₃×C₁₉	#6899	1	3	yes	—
58	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
59	C₃×C₉	—	3	3	no	—
60	C₃×C₉	—	3	9	no	—
61	C₃×C₉	—	19	9	no	—
62	C₃×C₉	—	57	9	no	—
63	C₃×C₉	—	57	3	no	—
64	C₃×C₉	—	57	3	no	—
65	C₃×C₉	—	57	9	no	—
66	C₃×C₉	—	57	9	no	—
67	C₃×C₉	C₉×C₁₉⋊C₃	1	3	yes	—
68	C₃×C₉	#10587022	1	3	yes	—
69	C₃×C₉	#10587023	1	3	yes	—
70	C₃×C₉	#10587025	1	3	yes	—
71	C₁₉	#10624553	1	1	yes	characteristic, complemented, Sylow
72	C₃²	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
73	C₃²	C₃×#10587023	1	1	yes	characteristic
74	C₃²	C₃×#10587022	1	1	yes	characteristic
75	C₃²	C₃×#10587025	1	1	yes	characteristic
76	C₃²	#13095333	1	9	yes	—
77	C₉	—	9	3	no	—
78	C₉	—	57	9	no	—
79	C₉	—	171	3	no	—
80	C₉	—	171	3	no	—
81	C₉	#13095305	1	9	yes	—
82	C₃	C₃×#13095305	1	1	yes	characteristic
83	C₃	#17987404	1	3	yes	—
84	C₃	#17987461	1	3	yes	—
85	C₃	#17987466	1	3	yes	—
86	C₃	#17987467	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₁₉⋊C₃
commutator	C₃²×C₁₉	C₃²×C₉
Fitting	C₃×C₁₉×C₉⋊C₉	C₃
socle, prime radical, cosocle	C₃³×C₁₉	C₃³
hypercenter	C₃×C₉⋊C₉	C₁₉⋊C₃
hypocenter	C₁₉	#10624553
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
11. C₉×#4294	C₉	semidirect
71. C₁₉	#10624553	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095307	3
C₃×#13095306	3
C₃×C₉×#4294	3
#17987308	3
C₃×C₁₉×C₉⋊C₉	3
#10624553	19