Subgroups — #28356796

Order 13851.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987563	C₃	1	3	yes	maximal
2	C₁₉⋊C₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	#13095342	—	3	3	no	—
4	C₃×C₉×C₁₉⋊C₃	—	3	1	no	—
5	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
6	#13095307	C₉	1	1	yes	characteristic
7	#13095306	C₉	1	1	yes	characteristic
8	#13095305	—	3	1	no	—
9	#13095305	—	3	1	no	—
10	C₁₉×C₉⋊C₉	C₉	1	1	yes	characteristic
11	#10624516	—	19	1	no	maximal, Sylow
12	C₃²×C₁₉⋊C₃	3₋¹⁺²	1	1	yes	characteristic
13	C₃×C₉×C₁₉	—	3	1	no	—
14	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃×#4294	—	3	1	no	—
16	C₃×#4294	—	3	1	no	—
17	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
19	C₉×C₁₉⋊C₃	—	3	3	no	—
20	C₉×C₁₉⋊C₃	—	9	3	no	—
21	#10587020	—	9	3	no	—
22	C₃×C₉⋊C₉	—	19	1	no	—
23	#6869	—	19	3	no	—
24	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
25	C₃×C₁₉⋊C₃	—	3	1	no	—
26	C₃×C₁₉⋊C₃	—	3	3	no	—
27	C₉×C₁₉	—	3	1	no	—
28	C₉×C₁₉	—	9	1	no	—
29	#4294	—	3	1	no	—
30	#4294	—	9	1	no	—
31	#4294	—	9	1	no	—
32	#4294	#731	1	3	yes	—
33	C₃²×C₉	—	19	1	no	—
34	C₃²×C₉	—	57	1	no	—
35	C₂₇⋊C₃	—	57	3	no	—
36	C₉⋊C₉	—	19	1	no	—
37	C₉⋊C₉	—	19	1	no	—
38	C₉⋊C₉	—	57	1	no	—
39	C₉⋊C₉	—	57	1	no	—
40	C₉⋊C₉	#4296	1	1	yes	characteristic
41	C₃×C₁₉	—	3	1	no	—
42	C₃×C₁₉	#6867	1	1	yes	characteristic
43	C₁₉⋊C₃	—	3	3	no	—
44	C₃³	—	19	1	no	—
45	C₃×C₉	—	3	1	no	—
46	C₃×C₉	—	19	1	no	—
47	C₃×C₉	—	19	1	no	—
48	C₃×C₉	—	57	3	no	—
49	C₃×C₉	—	57	1	no	—
50	C₃×C₉	—	57	1	no	—
51	C₃×C₉	—	171	3	no	—
52	C₃×C₉	C₃×#4296	1	1	yes	characteristic
53	C₂₇	—	171	3	no	—
54	C₁₉	#10624516	1	1	yes	characteristic, complemented, Sylow
55	C₃²	—	57	3	no	—
56	C₃²	—	57	1	no	—
57	C₃²	C₃²⋊#4296	1	1	yes	characteristic
58	C₉	—	3	1	no	—
59	C₉	—	9	1	no	—
60	C₉	—	19	3	no	—
61	C₉	—	57	1	no	—
62	C₉	—	171	1	no	—
63	C₉	—	171	1	no	—
64	C₃	—	3	1	no	—
65	C₃	—	57	3	no	—
66	C₃	#17987559	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987559
commutator	C₃×C₉×C₁₉	C₃×C₉
Frattini	C₃×C₉	C₃×#4296
Fitting	C₁₉×C₉⋊C₉	C₉
socle	C₃×C₁₉	#6867
prime radical	C₃²×C₁₉⋊C₃	3₋¹⁺²
cosocle	C₃×C₉×C₁₉⋊C₃	C₃²
hypercenter	C₉⋊C₉	#4296
hypocenter	C₁₉	#10624516
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
54. C₁₉	#10624516	semidirect

Maximal subgroups

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

subgroup	index
#17987563	3
C₁₉⋊C₃×C₉⋊C₉	3
#10624516	19