Subgroups — #28357003

Order 13851.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987598	C₃	1	3	yes	maximal, complemented
2	C₃×#13095344	C₃	1	1	yes	maximal, characteristic, complemented
3	#17987568	C₃	1	3	yes	maximal, complemented
4	#17987566	C₃	1	3	yes	maximal, complemented
5	#17987562	C₃	1	2	yes	maximal, complemented
6	#17987498	C₃	1	1	yes	maximal, characteristic
7	#13095344	—	3	3	no	—
8	#13095342	—	3	6	no	—
9	#13095342	C₃²	1	6	yes	—
10	C₃×#10587020	—	3	3	no	—
11	C₃×#10587020	C₃²	1	1	yes	characteristic
12	C₃×#10587020	C₃²	1	1	yes	characteristic
13	C₃×#10587020	C₃²	1	1	yes	characteristic
14	#13095331	C₃²	1	3	yes	—
15	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
16	#13095322	C₉	1	2	yes	—
17	#13095316	C₉	1	3	yes	—
18	#13095313	C₉	1	3	yes	—
19	C₁₉×#732	C₉	1	1	yes	characteristic
20	#10624725	—	19	1	no	maximal, Sylow
21	C₃²×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
22	C₁₉×H(3,𝔽₃)	C₃×C₉	1	3	yes	—
23	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
24	#10587025	—	3	6	no	—
25	#10587025	C₃×C₉	1	6	yes	—
26	C₃×#4294	—	3	3	no	—
27	C₃×#4294	C₃×C₉	1	1	yes	characteristic
28	C₃×#4294	C₃³	1	1	yes	characteristic
29	C₉×C₁₉⋊C₃	—	3	1	no	—
30	C₉×C₁₉⋊C₃	—	3	2	no	—
31	#10587020	—	3	6	no	—
32	#10587020	—	3	1	no	—
33	#10587020	—	3	1	no	—
34	#10587020	H(3,𝔽₃)	1	3	yes	—
35	#6908	—	19	1	no	—
36	#6903	—	19	3	no	—
37	C₃×C₂₇⋊C₃	—	19	1	no	—
38	#6873	—	19	3	no	—
39	#6872	—	19	3	no	—
40	#6869	—	19	2	no	—
41	C₃²×C₁₉	—	3	3	no	—
42	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
43	C₃×C₁₉⋊C₃	—	3	1	no	—
44	C₃×C₁₉⋊C₃	—	9	1	no	—
45	C₉×C₁₉	—	3	1	no	—
46	#4294	—	3	1	no	—
47	#4294	—	3	6	no	—
48	#4294	C₃×H(3,𝔽₃)	1	1	yes	characteristic
49	#4294	#737	1	2	yes	—
50	#737	—	19	3	no	—
51	C₃²×C₉	—	19	1	no	—
52	#733	—	19	2	no	—
53	#732	#4296	1	1	yes	characteristic
54	#731	—	19	3	no	—
55	AΣL(1,𝔽₂₇)	—	19	3	no	—
56	C₂₇⋊C₃	—	19	6	no	—
57	C₂₇⋊C₃	—	57	6	no	—
58	C₂₇⋊C₃	—	57	3	no	—
59	C₃×C₂₇	—	19	1	no	—
60	C₃×C₂₇	—	19	1	no	—
61	C₃×C₂₇	—	19	1	no	—
62	C₃×C₂₇	—	57	3	no	—
63	C₃×C₁₉	—	3	1	no	—
64	C₃×C₁₉	—	9	3	no	—
65	C₃×C₁₉	C₉×H(3,𝔽₃)	1	1	yes	characteristic
66	C₁₉⋊C₃	—	9	1	no	—
67	C₃³	—	19	1	no	—
68	3₋¹⁺²	—	19	6	no	—
69	3₋¹⁺²	—	57	6	no	—
70	H(3,𝔽₃)	C₃×#4296	1	3	yes	—
71	C₃×C₉	—	19	1	no	—
72	C₃×C₉	—	19	1	no	—
73	C₃×C₉	—	57	1	no	—
74	C₃×C₉	—	57	2	no	—
75	C₃×C₉	—	57	3	no	—
76	C₃×C₉	C₃×#4296	1	1	yes	characteristic
77	C₂₇	—	19	3	no	—
78	C₂₇	—	57	1	no	—
79	C₂₇	—	57	1	no	—
80	C₂₇	—	57	6	no	—
81	C₁₉	#10624725	1	1	yes	characteristic, complemented, Sylow
82	C₃²	—	3	3	no	—
83	C₃²	—	57	1	no	—
84	C₃²	—	171	1	no	—
85	C₃²	C₃²×#4296	1	1	yes	characteristic
86	C₉	—	3	1	no	—
87	C₉	—	19	1	no	—
88	C₉	—	19	2	no	—
89	C₉	—	57	1	no	—
90	C₉	—	57	6	no	—
91	C₃	—	3	1	no	—
92	C₃	—	9	3	no	—
93	C₃	—	171	1	no	—
94	C₃	H(3,𝔽₃)×#4296	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×#4296
commutator	C₃²×C₁₉	C₃²×C₉
Frattini	C₃²	C₃²×#4296
Fitting	C₁₉×#732	C₉
socle	C₃×C₁₉	C₉×H(3,𝔽₃)
prime radical	#17987498	C₃
cosocle	C₃×#4294	C₃³
hypercenter	#732	#4296
hypocenter	C₁₉	#10624725
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #732

Complements

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

N	H ≅ G/N	type
1. #17987598	C₃	semidirect
2. C₃×#13095344	C₃	semidirect
3. #17987568	C₃	semidirect
4. #17987566	C₃	semidirect
5. #17987562	C₃	semidirect
81. C₁₉	#10624725	semidirect

Maximal subgroups

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

subgroup	index
#17987598	3
C₃×#13095344	3
#17987568	3
#17987566	3
#17987562	3
#17987498	3
#10624725	19