Subgroups — #28356724

Order 13851.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	3	yes	maximal
2	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
3	#13095342	—	3	3	no	—
4	#13095342	—	3	3	no	—
5	#13095342	C₉	1	9	yes	complemented
6	C₃×#10587020	—	3	3	no	—
7	C₃²×#4294	C₉	1	1	yes	characteristic
8	C₃²×#4294	C₉	1	1	yes	characteristic
9	C₃²×#4294	C₃²	1	1	yes	characteristic
10	C₉×#4294	—	3	1	no	—
11	C₉×#4294	—	3	2	no	—
12	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
13	#10624467	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	—	3	3	no	—
17	C₃×#4294	—	3	1	no	—
18	C₃×#4294	—	3	1	no	—
19	C₃×#4294	—	3	3	no	—
20	C₃×#4294	—	3	3	no	—
21	C₃×#4294	C₃×C₉	1	3	yes	—
22	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×#4294	3₋¹⁺²	1	3	yes	—
24	C₃×#4294	3₋¹⁺²	1	3	yes	—
25	C₃×#4294	3₋¹⁺²	1	2	yes	—
26	#10587020	—	3	9	no	—
27	C₃×C₂₇⋊C₃	—	19	3	no	—
28	C₃×C₉²	—	19	1	no	—
29	C₃²×C₁₉	—	3	1	no	—
30	C₃²×C₁₉	—	3	1	no	—
31	C₃²×C₁₉	—	3	1	no	—
32	C₃²×C₁₉	C₉²	1	1	yes	characteristic
33	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
34	C₃²×C₁₉	C₉⋊C₉	1	1	yes	characteristic
35	C₃²×C₁₉	C₉⋊C₉	1	1	yes	characteristic
36	C₉×C₁₉	—	3	3	no	—
37	#4294	—	3	3	no	—
38	#4294	—	3	3	no	—
39	#4294	C₃²⋊C₉	1	3	yes	—
40	#4294	C₉⋊C₉	1	6	yes	—
41	C₃²×C₉	—	19	1	no	—
42	C₃²×C₉	—	19	1	no	—
43	C₃²×C₉	—	19	1	no	—
44	C₃²×C₉	#4296	1	1	yes	characteristic
45	C₂₇⋊C₃	—	19	9	no	—
46	C₂₇⋊C₃	—	57	3	no	—
47	C₂₇⋊C₃	—	57	3	no	—
48	C₃×C₂₇	—	57	3	no	—
49	C₉²	—	57	1	no	—
50	C₉²	—	57	2	no	—
51	C₃×C₁₉	—	3	1	no	—
52	C₃×C₁₉	—	3	1	no	—
53	C₃×C₁₉	—	3	1	no	—
54	C₃×C₁₉	#6855	1	1	yes	characteristic
55	C₃×C₁₉	#6869	1	1	yes	characteristic
56	C₃×C₁₉	#6869	1	1	yes	characteristic
57	C₃×C₁₉	#6869	1	1	yes	characteristic
58	C₃³	C₃×#4296	1	1	yes	characteristic
59	C₃×C₉	—	3	1	no	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	19	3	no	—
62	C₃×C₉	—	19	1	no	—
63	C₃×C₉	—	19	2	no	—
64	C₃×C₉	—	19	3	no	—
65	C₃×C₉	—	19	3	no	—
66	C₃×C₉	—	57	1	no	—
67	C₃×C₉	—	57	1	no	—
68	C₃×C₉	—	57	3	no	—
69	C₃×C₉	—	57	3	no	—
70	C₂₇	—	57	9	no	—
71	C₁₉	#10624467	1	1	yes	characteristic, complemented, Sylow
72	C₃²	—	3	1	no	—
73	C₃²	—	3	1	no	—
74	C₃²	—	3	1	no	—
75	C₃²	C₉×#4296	1	1	yes	characteristic
76	C₃²	C₃²⋊#4296	1	1	yes	characteristic
77	C₃²	#13095338	1	1	yes	characteristic
78	C₃²	#13095339	1	1	yes	characteristic
79	C₉	—	3	3	no	—
80	C₉	—	19	3	no	—
81	C₉	—	19	6	no	—
82	C₉	—	57	3	no	—
83	C₉	—	57	3	no	—
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	(C₃×#4296)⋊C₉	1	1	yes	characteristic
88	C₃	#17987561	1	1	yes	characteristic
89	C₃	#17987562	1	1	yes	characteristic
90	C₃	#17987563	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊#4296
commutator	C₃²×C₁₉	C₉²
Frattini	C₃³	C₃×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle	C₃²×C₁₉	C₃²⋊C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃²×#4294	C₃²
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	#10624467
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
5. #13095342	C₉	semidirect
71. C₁₉	#10624467	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095342	3
C₃×C₉×#4294	3
#10624467	19