Subgroups — #28353191

Order 13851.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987405	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊#10587018	C₃	1	2	yes	maximal
3	C₁₉×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587018	—	3	2	no	—
5	#13095307	—	3	1	no	—
6	#13095306	—	3	1	no	—
7	C₃²⋊#4294	C₉	1	2	yes	—
8	C₃²⋊#4294	C₉	1	1	yes	characteristic
9	C₉×#4294	—	3	1	no	—
10	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
11	C₃×C₁₉×C₂₇	—	3	1	no	—
12	#10624461	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₁₉	—	3	1	no	—
15	C₃×C₉×C₁₉	—	3	2	no	—
16	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
18	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
19	C₃×#4294	—	3	2	no	—
20	C₃×#4294	—	3	1	no	—
21	C₁₉×C₂₇	—	9	1	no	—
22	#10587018	—	9	2	no	—
23	#6887	—	19	1	no	—
24	C₃²⋊C₂₇	—	19	2	no	—
25	C₃²⋊C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
26	C₃²×C₁₉	—	3	1	no	—
27	C₃²×C₁₉	—	3	2	no	—
28	C₃²×C₁₉	—	3	1	no	—
29	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
30	C₉×C₁₉	—	3	1	no	—
31	C₉×C₁₉	—	3	1	no	—
32	C₉×C₁₉	#732	1	1	yes	characteristic
33	C₉×C₁₉	#733	1	2	yes	—
34	#4294	—	9	2	no	—
35	#4294	—	9	1	no	—
36	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
37	C₃×C₂₇	—	3	1	no	—
38	C₃×C₂₇	—	57	2	no	—
39	C₉⋊C₉	—	57	1	no	—
40	C₉⋊C₉	—	57	1	no	—
41	C₃²⋊C₉	—	19	2	no	—
42	C₃²⋊C₉	—	19	1	no	—
43	C₉²	—	57	1	no	—
44	C₃×C₁₉	—	9	1	no	—
45	C₃×C₁₉	#6868	1	1	yes	characteristic
46	C₃×C₁₉	#6873	1	2	yes	—
47	C₃×C₁₉	#6873	1	1	yes	characteristic
48	C₃³	C₉×C₁₉⋊C₃	1	1	yes	characteristic
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	3	2	no	—
51	C₃×C₉	—	57	2	no	—
52	C₃×C₉	—	57	1	no	—
53	C₃×C₉	#10587022	1	1	yes	characteristic
54	C₃×C₉	#10587023	1	1	yes	characteristic
55	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
56	C₂₇	—	9	1	no	—
57	C₂₇	—	171	2	no	—
58	C₁₉	#10624461	1	1	yes	characteristic, complemented, Sylow
59	C₃²	—	3	1	no	—
60	C₃²	—	3	2	no	—
61	C₃²	—	3	1	no	—
62	C₃²	#13095303	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	3	1	no	—
65	C₉	—	171	2	no	—
66	C₉	—	171	1	no	—
67	C₉	#13095319	1	1	yes	characteristic
68	C₉	#13095321	1	2	yes	—
69	C₃	—	9	1	no	—
70	C₃	#17987338	1	1	yes	characteristic
71	C₃	#17987352	1	2	yes	—
72	C₃	#17987354	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₁₉⋊C₃)
commutator, prime radical	C₃³×C₁₉	C₃×C₉
Frattini	C₃²×C₉	C₃×C₁₉⋊C₃
Fitting	C₁₉×C₃²⋊C₂₇	C₃
socle	C₃²×C₁₉	C₃²⋊C₉
cosocle	C₃²×C₉×C₁₉	C₃²
hypercenter	C₃²⋊C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	#10624461
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃²⋊C₂₇

Complements

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

N	H ≅ G/N	type
58. C₁₉	#10624461	semidirect

Maximal subgroups

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

subgroup	index
#17987405	3
C₃²⋊#10587018	3
C₁₉×C₃²⋊C₂₇	3
#10624461	19