Subgroups — #28356703

Order 13851.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#10587020	C₃	1	3	yes	maximal, complemented
2	C₃×#13095331	C₃	1	1	yes	maximal, characteristic
3	C₃×#10587020	—	3	3	no	—
4	#13095331	—	3	9	no	—
5	C₃×#10587025	—	3	2	no	—
6	C₃×#10587025	C₉	1	2	yes	—
7	C₃²×#4294	—	3	1	no	—
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₃×C₁₉×H(3,𝔽₃)	C₉	1	1	yes	characteristic
10	#10624459	—	19	1	no	maximal, Sylow
11	C₃³×C₁₉	—	3	1	no	—
12	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
13	C₁₉×H(3,𝔽₃)	—	3	3	no	—
14	#10587025	—	3	18	no	—
15	#10587025	—	3	6	no	—
16	C₃×#4294	—	3	2	no	—
17	C₃×#4294	—	3	9	no	—
18	C₃×#4294	—	3	3	no	—
19	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×#4294	3₋¹⁺²	1	2	yes	—
21	#10587020	—	9	3	no	—
22	C₃×#737	—	19	1	no	—
23	C₃²⋊C₂₇	—	19	3	no	—
24	C₃²×C₁₉	—	3	1	no	—
25	C₃²×C₁₉	—	3	3	no	—
26	C₃²×C₁₉	—	3	3	no	—
27	C₃²×C₁₉	—	9	3	no	—
28	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
29	#4294	—	3	6	no	—
30	#4294	—	3	2	no	—
31	#4294	AΣL(1,𝔽₂₇)	1	3	yes	—
32	#737	—	57	9	no	—
33	C₃×3₋¹⁺²	—	19	2	no	—
34	C₃×3₋¹⁺²	—	57	2	no	—
35	C₃×H(3,𝔽₃)	#4296	1	1	yes	characteristic
36	C₃²×C₉	—	19	1	no	—
37	C₃²×C₉	—	57	1	no	—
38	C₃×C₂₇	—	57	3	no	—
39	C₃×C₁₉	—	9	1	no	—
40	C₃×C₁₉	—	9	3	no	—
41	C₃×C₁₉	#6866	1	1	yes	characteristic
42	C₃×C₁₉	#6873	1	3	yes	—
43	C₃³	—	3	1	no	—
44	C₃³	C₃×#4296	1	1	yes	characteristic
45	3₋¹⁺²	—	57	18	no	—
46	3₋¹⁺²	—	57	6	no	—
47	H(3,𝔽₃)	—	3	3	no	—
48	C₃×C₉	—	19	1	no	—
49	C₃×C₉	—	19	2	no	—
50	C₃×C₉	—	57	3	no	—
51	C₃×C₉	—	57	9	no	—
52	C₃×C₉	—	57	2	no	—
53	C₂₇	—	171	3	no	—
54	C₁₉	#10624459	1	1	yes	characteristic, complemented, Sylow
55	C₃²	—	3	1	no	—
56	C₃²	—	3	3	no	—
57	C₃²	—	3	3	no	—
58	C₃²	—	9	3	no	—
59	C₃²	C₃²⋊#4296	1	1	yes	characteristic
60	C₉	—	19	3	no	—
61	C₉	—	57	2	no	—
62	C₉	—	57	6	no	—
63	C₃	—	9	1	no	—
64	C₃	—	9	3	no	—
65	C₃	#17987558	1	1	yes	characteristic
66	C₃	#17987568	1	3	yes	—

	subgroup	G/H
center	C₃²	C₃²⋊#4296
commutator	C₃³×C₁₉	C₃×C₉
Frattini	C₃³	C₃×#4296
Fitting, prime radical	C₃×C₁₉×H(3,𝔽₃)	C₉
socle	C₃²×C₁₉	C₃²⋊C₉
cosocle	C₃²×#4294	C₃²
hypercenter	C₃×H(3,𝔽₃)	#4296
hypocenter	C₁₉	#10624459
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃²⋊#10587020	C₃	semidirect
54. C₁₉	#10624459	semidirect

Maximal subgroups

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

subgroup	index
C₃²⋊#10587020	3
C₃×#13095331	3
#10624459	19