Subgroups — #28356819

Order 13851.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095343	C₃	1	1	yes	maximal, characteristic, complemented
2	#17987562	C₃	1	2	yes	maximal, complemented
3	#17987498	C₃	1	1	yes	maximal, characteristic
4	#13095343	—	3	3	no	—
5	#13095342	—	3	2	no	—
6	C₃×#10587020	—	3	1	no	—
7	#13095331	—	3	1	no	—
8	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
9	#13095322	C₉	1	2	yes	—
10	#13095316	—	3	1	no	—
11	#13095313	—	3	1	no	—
12	C₁₉×#732	C₉	1	1	yes	characteristic
13	#10624530	—	19	1	no	maximal, Sylow
14	C₃²×C₁₉⋊C₃	3₋¹⁺²	1	1	yes	characteristic
15	C₁₉×H(3,𝔽₃)	—	3	1	no	—
16	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
17	#10587025	—	3	2	no	—
18	#10587025	—	9	1	no	—
19	#10587025	—	9	1	no	—
20	C₃×#4294	—	9	1	no	—
21	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
23	C₉×C₁₉⋊C₃	—	3	1	no	—
24	C₉×C₁₉⋊C₃	—	3	1	no	—
25	C₉×C₁₉⋊C₃	—	3	1	no	—
26	#10587020	—	3	3	no	—
27	#10587020	—	9	2	no	—
28	#6908	—	19	1	no	—
29	C₃×C₂₇⋊C₃	—	19	1	no	—
30	#6869	—	19	2	no	—
31	C₃²×C₁₉	—	9	1	no	—
32	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
33	C₃×C₁₉⋊C₃	—	3	1	no	—
34	C₃×C₁₉⋊C₃	—	9	1	no	—
35	C₉×C₁₉	—	3	1	no	—
36	#4294	—	3	1	no	—
37	#4294	—	9	2	no	—
38	#4294	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	#4294	#731	1	1	yes	characteristic
40	#4294	#732	1	1	yes	characteristic
41	#737	—	57	1	no	—
42	C₃²×C₉	—	19	1	no	—
43	#733	—	19	2	no	—
44	#732	#4296	1	1	yes	characteristic
45	#731	—	57	1	no	—
46	AΣL(1,𝔽₂₇)	—	57	1	no	—
47	C₂₇⋊C₃	—	57	3	no	—
48	C₂₇⋊C₃	—	57	2	no	—
49	C₃×C₂₇	—	57	1	no	—
50	C₃×C₁₉	—	3	1	no	—
51	C₃×C₁₉	—	27	1	no	—
52	C₃×C₁₉	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
53	C₁₉⋊C₃	—	9	1	no	—
54	C₃³	—	19	1	no	—
55	3₋¹⁺²	—	57	2	no	—
56	3₋¹⁺²	—	171	1	no	—
57	3₋¹⁺²	—	171	1	no	—
58	H(3,𝔽₃)	—	3	1	no	—
59	C₃×C₉	—	19	1	no	—
60	C₃×C₉	—	19	1	no	—
61	C₃×C₉	—	57	1	no	—
62	C₃×C₉	—	57	1	no	—
63	C₃×C₉	—	57	1	no	—
64	C₃×C₉	—	171	1	no	—
65	C₃×C₉	C₃×#4296	1	1	yes	characteristic
66	C₂₇	—	57	3	no	—
67	C₂₇	—	171	2	no	—
68	C₁₉	#10624530	1	1	yes	characteristic, complemented, Sylow
69	C₃²	—	9	1	no	—
70	C₃²	—	57	1	no	—
71	C₃²	—	171	1	no	—
72	C₃²	C₃²⋊#4296	1	1	yes	characteristic
73	C₉	—	3	1	no	—
74	C₉	—	19	1	no	—
75	C₉	—	19	1	no	—
76	C₉	—	19	1	no	—
77	C₉	—	57	1	no	—
78	C₉	—	171	2	no	—
79	C₃	—	3	1	no	—
80	C₃	—	27	1	no	—
81	C₃	—	171	1	no	—
82	C₃	H(3,𝔽₃)⋊#4296	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)⋊#4296
commutator	C₃×C₉×C₁₉	C₃×C₉
Frattini	C₃×C₉	C₃×#4296
Fitting	C₁₉×#732	C₉
socle	C₃×C₁₉	H(3,𝔽₃)⋊C₉
prime radical	#17987498	C₃
cosocle	C₃×C₉×C₁₉⋊C₃	C₃²
hypercenter	#732	#4296
hypocenter	C₁₉	#10624530
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ #732

Complements

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

N	H ≅ G/N	type
1. C₃×#13095343	C₃	semidirect
2. #17987562	C₃	semidirect
68. C₁₉	#10624530	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095343	3
#17987562	3
#17987498	3
#10624530	19