Subgroups — #28353239

Order 13851.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987421	C₃	1	2	yes	maximal
2	#17987335	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#6866	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587025	—	3	2	no	—
5	C₃²⋊#4294	—	3	6	no	—
6	C₃²⋊#4294	—	3	1	no	—
7	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×C₃²⋊C₉	—	3	1	no	—
9	#10624476	—	19	1	no	maximal, Sylow
10	C₃³×C₁₉	—	3	2	no	—
11	C₃³×C₁₉	—	3	1	no	—
12	C₃³×C₁₉	—	3	1	no	—
13	C₃³×C₁₉	—	9	3	no	—
14	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃×C₉×C₁₉	—	9	1	no	—
16	#10587025	—	9	2	no	—
17	#10587025	—	9	2	no	—
18	#10587025	—	9	2	no	—
19	C₃×#4294	—	3	6	no	—
20	C₃×#4294	—	9	1	no	—
21	#6891	—	19	2	no	—
22	#6866	—	19	1	no	—
23	#6866	C₁₉⋊C₃	1	1	yes	characteristic
24	C₃²×C₁₉	—	3	6	no	—
25	C₃²×C₁₉	—	9	1	no	—
26	C₃²×C₁₉	—	9	3	no	—
27	C₃²×C₁₉	—	9	3	no	—
28	C₃²×C₁₉	—	9	4	no	—
29	C₃²×C₁₉	—	9	1	no	—
30	C₃²×C₁₉	AΣL(1,𝔽₂₇)	1	2	yes	—
31	C₃²×C₁₉	#732	1	1	yes	characteristic
32	C₃²×C₁₉	#732	1	1	yes	characteristic
33	C₉×C₁₉	—	27	1	no	—
34	#4294	—	9	6	no	—
35	#4294	—	27	1	no	—
36	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	57	2	no	—
38	C₃²⋊C₉	—	3	1	no	—
39	C₃²⋊C₉	—	57	6	no	—
40	C₃²⋊C₉	—	57	1	no	—
41	C₃×C₁₉	—	3	1	no	—
42	C₃×C₁₉	—	3	1	no	—
43	C₃×C₁₉	—	3	2	no	—
44	C₃×C₁₉	—	9	3	no	—
45	C₃×C₁₉	#6856	1	1	yes	characteristic
46	C₃³	—	3	2	no	—
47	C₃³	—	3	1	no	—
48	C₃³	—	3	1	no	—
49	C₃³	—	9	3	no	—
50	C₃³	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
51	3₋¹⁺²	—	171	2	no	—
52	3₋¹⁺²	—	171	2	no	—
53	3₋¹⁺²	—	171	2	no	—
54	C₃×C₉	—	9	1	no	—
55	C₃×C₉	—	57	6	no	—
56	C₃×C₉	—	171	1	no	—
57	C₁₉	#10624476	1	1	yes	characteristic, complemented, Sylow
58	C₃²	—	3	6	no	—
59	C₃²	—	9	1	no	—
60	C₃²	—	9	3	no	—
61	C₃²	—	9	3	no	—
62	C₃²	—	9	4	no	—
63	C₃²	—	9	1	no	—
64	C₃²	#13095315	1	2	yes	—
65	C₃²	#13095319	1	1	yes	characteristic
66	C₃²	#13095320	1	1	yes	characteristic
67	C₉	—	513	1	no	—
68	C₉	—	27	1	no	—
69	C₉	—	171	6	no	—
70	C₃	—	3	1	no	—
71	C₃	—	3	1	no	—
72	C₃	—	3	2	no	—
73	C₃	—	9	3	no	—
74	C₃	#17987310	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987310
commutator, prime radical, cosocle	C₃⁴×C₁₉	C₃²
Frattini	C₃⁴	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6866	C₃
socle	C₃×C₁₉	#6856
hypercenter	#6866	C₁₉⋊C₃
hypocenter	C₁₉	#10624476
LCS	G ▷ C₃⁴×C₁₉ ▷ C₃³×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃⁴ ◁ #6866

Complements

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

N	H ≅ G/N	type
57. C₁₉	#10624476	semidirect

Maximal subgroups

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

subgroup	index
#17987421	3
#17987335	3
C₁₉×#6866	3
#10624476	19