Subgroups — #28356934

Order 13851.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₁₉⋊C₃)⋊C₂₇	C₃	1	3	yes	maximal
2	#17987572	C₃	1	6	yes	maximal, complemented
3	#17987570	C₃	1	3	yes	maximal, complemented
4	C₉²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
5	(C₁₉⋊C₃)⋊C₂₇	—	3	9	no	—
6	C₃×#10587020	C₃²	1	9	yes	—
7	C₃×C₉×C₁₉⋊C₃	C₉	1	2	yes	—
8	C₃×C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
9	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
10	C₉×#4294	C₉	1	1	yes	characteristic
11	C₉×#4294	C₉	1	2	yes	—
12	C₉×#4294	C₉	1	2	yes	—
13	C₉×#4294	C₃²	1	1	yes	characteristic
14	C₉×#4294	C₃²	1	2	yes	—
15	C₉²×C₁₉	C₉	1	1	yes	characteristic
16	C₃×C₉⋊C₂₇	—	19	1	no	maximal, Sylow
17	C₃²×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
19	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
21	C₃×#4294	C₃×C₉	1	2	yes	—
22	C₃×#4294	C₃×C₉	1	2	yes	—
23	C₃×#4294	C₃×C₉	1	1	yes	characteristic
24	C₃×#4294	C₃×C₉	1	2	yes	—
25	C₃×#4294	C₃³	1	1	yes	characteristic
26	C₉×C₁₉⋊C₃	—	3	6	no	—
27	C₉×C₁₉⋊C₃	C₂₇	1	9	yes	complemented
28	C₉×C₁₉⋊C₃	3₋¹⁺²	1	9	yes	—
29	#10587020	—	3	9	no	—
30	C₃²×C₂₇	—	19	3	no	—
31	C₃×C₉²	—	19	1	no	—
32	C₉⋊C₂₇	—	19	3	no	—
33	C₉⋊C₂₇	—	19	6	no	—
34	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
35	C₃×C₁₉⋊C₃	C₉⋊C₉	1	3	yes	—
36	C₃×C₁₉⋊C₃	C₃×C₂₇	1	3	yes	—
37	C₃×C₁₉⋊C₃	C₂₇⋊C₃	1	6	yes	—
38	C₉×C₁₉	—	3	2	no	—
39	C₉×C₁₉	C₉⋊C₉	1	3	yes	—
40	C₉×C₁₉	C₃×C₂₇	1	3	yes	complemented
41	#4294	—	3	2	no	—
42	#4294	—	3	2	no	—
43	#4294	C₉⋊C₉	1	3	yes	—
44	#4294	C₃×C₂₇	1	6	yes	complemented
45	#4294	C₃×3₋¹⁺²	1	3	yes	—
46	C₃²×C₉	—	19	1	no	—
47	C₃²×C₉	—	19	1	no	—
48	C₃²×C₉	—	19	2	no	—
49	C₃×C₂₇	—	19	9	no	—
50	C₃×C₂₇	—	57	9	no	—
51	C₉²	—	19	2	no	—
52	C₉²	—	19	1	no	—
53	C₉²	—	19	2	no	—
54	C₉²	—	19	1	no	—
55	C₉²	—	19	2	no	—
56	C₉²	#4296	1	1	yes	characteristic
57	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
58	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
59	C₃×C₁₉	C₃×C₂₇⋊C₃	1	2	yes	—
60	C₁₉⋊C₃	C₉⋊C₂₇	1	9	yes	complemented
61	C₃³	—	19	1	no	—
62	C₃×C₉	—	19	1	no	—
63	C₃×C₉	—	19	2	no	—
64	C₃×C₉	—	19	1	no	—
65	C₃×C₉	—	19	9	no	—
66	C₃×C₉	—	19	9	no	—
67	C₃×C₉	—	19	2	no	—
68	C₃×C₉	—	19	2	no	—
69	C₃×C₉	—	57	6	no	—
70	C₃×C₉	C₃×#4296	1	2	yes	—
71	C₃×C₉	C₃×#4296	1	1	yes	characteristic
72	C₃×C₉	C₃×#4296	1	1	yes	characteristic
73	C₂₇	—	57	9	no	—
74	C₁₉	C₃×C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
75	C₃²	—	19	3	no	—
76	C₃²	—	19	3	no	—
77	C₃²	—	19	6	no	—
78	C₃²	C₃²×#4296	1	1	yes	characteristic
79	C₉	—	3	2	no	—
80	C₉	—	19	3	no	—
81	C₉	—	19	3	no	—
82	C₉	—	19	6	no	—
83	C₉	—	57	2	no	—
84	C₉	—	57	2	no	—
85	C₉	#13095338	1	3	yes	—
86	C₉	(C₁₉⋊C₃)⋊C₂₇	1	3	yes	complemented
87	C₃	—	19	9	no	—
88	C₃	C₃×#13095338	1	1	yes	characteristic
89	C₃	C₃×(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic
90	C₃	(C₁₉⋊C₃)⋊(C₂₇⋊C₃)	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×#4296
commutator	C₃×C₁₉	C₃²×C₂₇
Frattini	C₃²	C₃²×#4296
Fitting	C₉²×C₁₉	C₉
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃²×C₁₉⋊C₃	C₃×C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₉²	#4296
hypocenter	C₁₉	C₃×C₉⋊C₂₇
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
2. #17987572	C₃	semidirect
3. #17987570	C₃	semidirect
27. C₉×C₁₉⋊C₃	C₂₇	semidirect
40. C₉×C₁₉	C₃×C₂₇	semidirect
44. #4294	C₃×C₂₇	semidirect
60. C₁₉⋊C₃	C₉⋊C₂₇	semidirect
74. C₁₉	C₃×C₉⋊C₂₇	semidirect
86. C₉	(C₁₉⋊C₃)⋊C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×(C₁₉⋊C₃)⋊C₂₇	3
#17987572	3
#17987570	3
C₉²×C₁₉⋊C₃	3
C₃×C₉⋊C₂₇	19