Subgroups — #28354560

Order 13851.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987420	C₃	1	2	yes	maximal
2	#17987419	C₃	1	2	yes	maximal
3	C₁₉⋊#6862	C₃	1	4	yes	maximal, complemented
4	C₁₉⋊#6862	C₃	1	4	yes	maximal, complemented
5	C₁₉×#6862	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×#10587022	—	3	2	no	—
8	C₃×#10587023	—	3	2	no	—
9	C₃²⋊#4294	C₃²	1	4	yes	—
10	C₃²⋊#4294	C₃²	1	4	yes	—
11	#13095303	—	3	4	no	—
12	#13095303	—	3	4	no	—
13	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	—
14	C₁₉×C₃²⋊C₉	C₃²	1	2	yes	—
15	#10624675	—	19	1	no	maximal, Sylow
16	C₃³×C₁₉	C₃³	1	1	yes	characteristic
17	C₃²×C₁₉⋊C₃	—	9	2	no	—
18	C₃²×C₁₉⋊C₃	—	9	2	no	—
19	C₃²×C₁₉⋊C₃	H(3,𝔽₃)	1	2	yes	—
20	C₃²×C₁₉⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₉×C₁₉	—	3	2	no	—
22	C₃×C₉×C₁₉	—	3	2	no	—
23	C₃×#4294	—	3	4	no	—
24	C₃×#4294	—	3	4	no	—
25	#10587023	—	9	6	no	—
26	#10587022	—	9	6	no	—
27	#6891	—	19	2	no	—
28	#6891	—	19	2	no	—
29	#6862	—	19	4	no	—
30	#6862	—	19	4	no	—
31	#6862	C₁₉⋊C₃	1	1	yes	characteristic, complemented
32	C₃²×C₁₉	—	3	2	no	—
33	C₃²×C₁₉	—	3	2	no	—
34	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃×C₁₉⋊C₃	—	3	2	no	—
36	C₃×C₁₉⋊C₃	—	3	2	no	—
37	C₃×C₁₉⋊C₃	—	3	4	no	—
38	C₃×C₁₉⋊C₃	—	3	4	no	—
39	C₃×C₁₉⋊C₃	—	9	9	no	—
40	C₉×C₁₉	—	9	2	no	—
41	C₉×C₁₉	—	9	2	no	—
42	#4294	—	9	4	no	—
43	#4294	—	9	4	no	—
44	C₃⁴	—	19	1	no	—
45	C₃×3₋¹⁺²	—	57	2	no	—
46	C₃×3₋¹⁺²	—	57	2	no	—
47	C₃²⋊C₉	—	19	4	no	—
48	C₃²⋊C₉	—	19	4	no	—
49	C₃²⋊C₉	—	57	4	no	—
50	C₃²⋊C₉	—	57	4	no	—
51	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	—
52	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	—
53	C₃×C₁₉	—	9	1	no	—
54	C₃×C₁₉	#6910	1	2	yes	—
55	C₃×C₁₉	#6910	1	2	yes	—
56	C₁₉⋊C₃	—	9	1	no	—
57	C₁₉⋊C₃	—	9	2	no	—
58	C₃³	—	19	2	no	—
59	C₃³	—	19	1	no	—
60	C₃³	—	171	2	no	—
61	C₃³	—	171	2	no	—
62	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
63	3₋¹⁺²	—	171	6	no	—
64	3₋¹⁺²	—	171	6	no	—
65	C₃×C₉	—	3	2	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	57	4	no	—
68	C₃×C₉	—	57	4	no	—
69	C₁₉	#10624675	1	1	yes	characteristic, complemented, Sylow
70	C₃²	—	3	2	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	57	2	no	—
73	C₃²	—	57	4	no	—
74	C₃²	—	57	2	no	—
75	C₃²	—	57	4	no	—
76	C₃²	—	171	9	no	—
77	C₃²	H(3,𝔽₃)×C₁₉⋊C₃	1	1	yes	characteristic
78	C₉	—	9	2	no	—
79	C₉	—	9	2	no	—
80	C₉	—	171	4	no	—
81	C₉	—	171	4	no	—
82	C₃	—	9	1	no	—
83	C₃	—	171	1	no	—
84	C₃	—	171	2	no	—
85	C₃	#17987507	1	2	yes	—
86	C₃	#17987508	1	2	yes	—

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₁₉⋊C₃
commutator, cosocle	C₃³×C₁₉	C₃³
Frattini	C₃³	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#6862	C₃
socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
prime radical	C₃³×C₁₉⋊C₃	C₃²
hypercenter	#6862	C₁₉⋊C₃
hypocenter	C₁₉	#10624675
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ #6862

Complements

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

N	H ≅ G/N	type
3. C₁₉⋊#6862	C₃	semidirect
4. C₁₉⋊#6862	C₃	semidirect
5. C₁₉×#6862	C₃	semidirect
31. #6862	C₁₉⋊C₃	semidirect
69. C₁₉	#10624675	semidirect

Maximal subgroups

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

subgroup	index
#17987420	3
#17987419	3
C₁₉⋊#6862	3
C₁₉×#6862	3
#10624675	19