Subgroups — C₃×C₂₇×#4296 #28356869

Order 13851.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₁₉⋊C₃)⋊C₂₇	C₃	1	2	yes	maximal
2	C₃×C₉×#4296	C₃	1	1	yes	maximal, characteristic
3	C₂₇×#4296	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₂₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃²×#4296	C₉	1	3	yes	—
6	(C₁₉⋊C₃)⋊C₂₇	C₉	1	12	yes	complemented
7	(C₁₉⋊C₃)⋊C₂₇	C₃²	1	6	yes	—
8	C₃×#10587020	C₉	1	6	yes	complemented
9	C₉×#4296	C₉	1	6	yes	—
10	C₉×#4296	C₃²	1	3	yes	—
11	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
12	C₃×#10587018	C₉	1	2	yes	complemented
13	C₂₇×C₁₉⋊C₃	C₉	1	6	yes	complemented
14	C₂₇×C₁₉⋊C₃	C₃²	1	3	yes	—
15	C₃×C₁₉×C₂₇	C₉	1	1	yes	characteristic, complemented
16	C₃×C₉×C₂₇	—	19	1	no	maximal, Sylow
17	C₃²×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
18	C₃×#4296	C₂₇	1	27	yes	direct product factor
19	C₃×#4296	C₃×C₉	1	9	yes	—
20	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
21	C₃×#4294	C₃×C₉	1	2	yes	—
22	C₉×C₁₉⋊C₃	C₃×C₉	1	2	yes	—
23	C₉×C₁₉⋊C₃	C₃×C₉	1	2	yes	—
24	C₉×C₁₉⋊C₃	C₃×C₉	1	4	yes	—
25	C₉×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
26	#10587020	C₃×C₉	1	18	yes	complemented
27	C₁₉×C₂₇	C₃×C₉	1	3	yes	complemented
28	#10587018	C₃×C₉	1	6	yes	complemented
29	C₃²×C₂₇	—	19	2	no	—
30	C₃²×C₂₇	—	19	1	no	—
31	C₃×C₉²	—	19	1	no	—
32	C₉×C₂₇	—	19	9	no	—
33	C₃²×C₁₉	C₉²	1	1	yes	characteristic
34	C₃×C₁₉⋊C₃	C₉²	1	2	yes	—
35	C₃×C₁₉⋊C₃	C₃×C₂₇	1	9	yes	—
36	C₃×C₁₉⋊C₃	C₃²×C₉	1	1	yes	characteristic
37	#4296	C₃×C₂₇	1	27	yes	direct product factor
38	C₉×C₁₉	C₉²	1	2	yes	—
39	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
40	#4294	C₉²	1	4	yes	—
41	#4294	C₃²×C₉	1	2	yes	—
42	C₃²×C₉	—	19	3	no	—
43	C₃²×C₉	—	19	1	no	—
44	C₃×C₂₇	—	19	6	no	—
45	C₃×C₂₇	—	19	12	no	—
46	C₃×C₂₇	—	19	6	no	—
47	C₃×C₂₇	—	19	2	no	—
48	C₃×C₂₇	—	19	6	no	—
49	C₃×C₂₇	—	19	3	no	—
50	C₃×C₂₇	#4296	1	1	yes	characteristic, direct product factor
51	C₉²	—	19	6	no	—
52	C₉²	—	19	3	no	—
53	C₃×C₁₉	C₉×C₂₇	1	3	yes	complemented
54	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
55	C₁₉⋊C₃	C₉×C₂₇	1	6	yes	complemented
56	C₁₉⋊C₃	C₃²×C₂₇	1	3	yes	—
57	C₃³	—	19	1	no	—
58	C₃×C₉	—	19	27	no	—
59	C₃×C₉	—	19	9	no	—
60	C₃×C₉	—	19	2	no	—
61	C₃×C₉	—	19	2	no	—
62	C₃×C₉	—	19	4	no	—
63	C₃×C₉	—	19	2	no	—
64	C₃×C₉	—	19	1	no	—
65	C₃×C₉	C₃×#4296	1	1	yes	characteristic
66	C₂₇	—	19	18	no	—
67	C₂₇	—	19	6	no	—
68	C₂₇	C₃×#4296	1	3	yes	direct product factor
69	C₁₉	C₃×C₉×C₂₇	1	1	yes	characteristic, complemented, Sylow
70	C₃²	—	19	1	no	—
71	C₃²	—	19	2	no	—
72	C₃²	—	19	9	no	—
73	C₃²	C₉×#4296	1	1	yes	characteristic
74	C₉	—	19	27	no	—
75	C₉	—	19	2	no	—
76	C₉	—	19	4	no	—
77	C₉	C₉×#4296	1	2	yes	—
78	C₉	C₃²×#4296	1	1	yes	characteristic
79	C₃	—	19	3	no	—
80	C₃	—	19	6	no	—
81	C₃	C₂₇×#4296	1	3	yes	direct product factor
82	C₃	C₃×C₉×#4296	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂₇×#4296	C₃	direct (N × H)
6. (C₁₉⋊C₃)⋊C₂₇	C₉	semidirect
8. C₃×#10587020	C₉	semidirect
12. C₃×#10587018	C₉	semidirect
13. C₂₇×C₁₉⋊C₃	C₉	semidirect
15. C₃×C₁₉×C₂₇	C₉	semidirect
18. C₃×#4296	C₂₇	direct (N × H)
26. #10587020	C₃×C₉	semidirect
27. C₁₉×C₂₇	C₃×C₉	semidirect
28. #10587018	C₃×C₉	semidirect
37. #4296	C₃×C₂₇	direct (N × H)
50. C₃×C₂₇	#4296	direct (N × H)
53. C₃×C₁₉	C₉×C₂₇	semidirect
55. C₁₉⋊C₃	C₉×C₂₇	semidirect
68. C₂₇	C₃×#4296	direct (N × H)
69. C₁₉	C₃×C₉×C₂₇	semidirect
81. C₃	C₂₇×#4296	direct (N × H)

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
C₃×C₉×#4296	3
C₂₇×#4296	3
C₃×C₂₇×C₁₉⋊C₃	3
C₃×C₉×C₂₇	19

Subgroups — C3×C27×#4296 #28356869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₇×#4296 #28356869