Subgroups — #28356856

Order 13851.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095339	C₃	1	3	yes	maximal
2	(C₃×#4296)⋊C₉	C₃	1	9	yes	maximal
3	C₉²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×#4296	C₃²	1	9	yes	—
5	#13095339	—	3	9	no	—
6	C₃×C₉×C₁₉⋊C₃	C₃²	1	3	yes	—
7	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
8	C₉×#4294	C₉	1	2	yes	complemented
9	C₉×#4294	C₉	1	6	yes	complemented
10	C₉²×C₁₉	C₉	1	1	yes	characteristic, complemented
11	#10624553	—	19	1	no	maximal, Sylow
12	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
13	C₃×#4296	—	3	9	no	—
14	C₃×#4296	—	3	27	no	—
15	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
17	C₃×#4294	C₃×C₉	1	6	yes	—
18	C₃×#4294	C₃×C₉	1	2	yes	—
19	C₉×C₁₉⋊C₃	—	3	9	no	—
20	C₉×C₁₉⋊C₃	3₋¹⁺²	1	9	yes	—
21	C₃×C₉⋊C₉	—	19	3	no	—
22	C₃×C₉²	—	19	1	no	—
23	#6855	—	19	9	no	—
24	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
25	C₃×C₁₉⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
26	C₃×C₁₉⋊C₃	#737	1	9	yes	—
27	#4296	—	9	9	no	—
28	C₉×C₁₉	—	3	3	no	—
29	C₉×C₁₉	C₉⋊C₉	1	3	yes	—
30	#4294	—	3	6	no	—
31	#4294	C₉⋊C₉	1	6	yes	—
32	C₃²×C₉	—	19	1	no	—
33	C₃²×C₉	—	19	3	no	—
34	C₃²×C₉	—	19	9	no	—
35	C₉⋊C₉	—	57	9	no	—
36	C₉²	—	19	6	no	—
37	C₉²	—	19	2	no	—
38	C₉²	#4296	1	1	yes	characteristic, complemented
39	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
40	C₃×C₁₉	#6887	1	3	yes	—
41	C₁₉⋊C₃	#6899	1	9	yes	—
42	C₃³	—	19	1	no	—
43	C₃×C₉	—	19	2	no	—
44	C₃×C₉	—	19	9	no	—
45	C₃×C₉	—	19	6	no	—
46	C₃×C₉	—	57	9	no	—
47	C₃×C₉	—	57	9	no	—
48	C₃×C₉	—	57	27	no	—
49	C₃×C₉	C₃×#4296	1	3	yes	—
50	C₃×C₉	C₃×#4296	1	1	yes	characteristic
51	C₁₉	#10624553	1	1	yes	characteristic, complemented, Sylow
52	C₃²	—	19	3	no	—
53	C₃²	—	19	9	no	—
54	C₃²	C₃²×#4296	1	1	yes	characteristic
55	C₉	—	3	3	no	—
56	C₉	—	19	6	no	—
57	C₉	—	57	6	no	—
58	C₉	—	171	9	no	—
59	C₉	#13095339	1	3	yes	—
60	C₃	—	19	9	no	—
61	C₃	C₃×#13095339	1	1	yes	characteristic
62	C₃	#17987589	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator, socle	C₃²×C₁₉	C₃²×C₉
Fitting	C₉²×C₁₉	C₉
prime radical, cosocle	C₃²×C₁₉⋊C₃	C₃³
hypercenter	C₉²	#4296
hypocenter	C₁₉	#10624553
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
8. C₉×#4294	C₉	semidirect
9. C₉×#4294	C₉	semidirect
10. C₉²×C₁₉	C₉	semidirect
38. C₉²	#4296	semidirect
51. 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×#13095339	3
(C₃×#4296)⋊C₉	3
C₉²×C₁₉⋊C₃	3
#10624553	19