Subgroups — C₃²×(C₁₉⋊C₃)⋊C₂₇ #28357052

Order 13851.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₁₉⋊C₃)⋊C₂₇	C₃	1	36	yes	maximal, direct product factor
2	C₃²×#10587020	C₃	1	3	yes	maximal, complemented
3	C₃²×C₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	(C₁₉⋊C₃)⋊C₂₇	C₃²	1	81	yes	direct product factor
5	C₃×#10587020	C₃²	1	36	yes	complemented
6	C₃³×C₁₉⋊C₃	C₉	1	1	yes	characteristic
7	C₃²×#4294	C₉	1	1	yes	characteristic
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₁₉⋊C₃	C₉	1	24	yes	—
10	C₃×C₉×C₁₉⋊C₃	C₃²	1	12	yes	—
11	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
12	C₃³×C₂₇	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
14	C₃²×C₁₉⋊C₃	C₂₇	1	27	yes	complemented
15	C₃²×C₁₉⋊C₃	C₃×C₉	1	12	yes	—
16	C₃×C₉×C₁₉	C₃×C₉	1	12	yes	—
17	C₃×#4294	C₃×C₉	1	8	yes	—
18	C₃×#4294	C₃×C₉	1	12	yes	—
19	C₃×#4294	C₃³	1	4	yes	—
20	C₉×C₁₉⋊C₃	C₃×C₉	1	72	yes	—
21	C₉×C₁₉⋊C₃	C₃³	1	9	yes	—
22	#10587020	C₃³	1	27	yes	complemented
23	C₃³×C₉	—	19	1	no	—
24	C₃²×C₂₇	—	19	3	no	—
25	C₃²×C₂₇	—	19	36	no	—
26	C₃²×C₁₉	C₃×C₂₇	1	9	yes	complemented
27	C₃²×C₁₉	C₃²×C₉	1	4	yes	—
28	C₃×C₁₉⋊C₃	C₃×C₂₇	1	108	yes	complemented
29	C₃×C₁₉⋊C₃	C₃²×C₉	1	9	yes	—
30	C₉×C₁₉	C₃²×C₉	1	9	yes	—
31	#4294	C₃²×C₉	1	8	yes	—
32	#4294	C₃²×C₉	1	9	yes	—
33	#4294	C₃⁴	1	1	yes	characteristic
34	C₃⁴	—	19	1	no	—
35	C₃²×C₉	—	19	1	no	—
36	C₃²×C₉	—	19	1	no	—
37	C₃²×C₉	—	19	24	no	—
38	C₃²×C₉	—	19	12	no	—
39	C₃²×C₉	#4296	1	1	yes	characteristic
40	C₃×C₂₇	—	19	36	no	—
41	C₃×C₂₇	—	19	81	no	—
42	C₃×C₁₉	C₃²×C₂₇	1	12	yes	complemented
43	C₃×C₁₉	C₃³×C₉	1	1	yes	characteristic
44	C₁₉⋊C₃	C₃²×C₂₇	1	27	yes	complemented
45	C₃³	—	19	27	no	—
46	C₃³	—	19	12	no	—
47	C₃³	C₃×#4296	1	1	yes	characteristic
48	C₃×C₉	—	19	8	no	—
49	C₃×C₉	—	19	12	no	—
50	C₃×C₉	—	19	4	no	—
51	C₃×C₉	—	19	72	no	—
52	C₃×C₉	—	19	9	no	—
53	C₃×C₉	C₃×#4296	1	12	yes	—
54	C₂₇	—	19	27	no	—
55	C₁₉	C₃³×C₂₇	1	1	yes	characteristic, complemented, Sylow
56	C₃²	—	19	108	no	—
57	C₃²	—	19	9	no	—
58	C₃²	(C₁₉⋊C₃)⋊C₂₇	1	9	yes	direct product factor
59	C₃²	C₃²×#4296	1	4	yes	—
60	C₉	—	19	1	no	—
61	C₉	—	19	9	no	—
62	C₉	—	19	8	no	—
63	C₉	C₃²×#4296	1	9	yes	—
64	C₃	—	19	27	no	—
65	C₃	C₃×(C₁₉⋊C₃)⋊C₂₇	1	12	yes	direct product factor
66	C₃	C₃³×#4296	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₉	#4296
commutator, hypocenter	C₁₉	C₃³×C₂₇
Frattini	C₃	C₃³×#4296
Fitting	C₃²×C₉×C₁₉	C₉
socle	C₃³×C₁₉	C₃×C₉
prime radical	C₃³×C₁₉⋊C₃	C₉
cosocle	#4294	C₃⁴
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×(C₁₉⋊C₃)⋊C₂₇	C₃	direct (N × H)
2. C₃²×#10587020	C₃	semidirect
4. (C₁₉⋊C₃)⋊C₂₇	C₃²	direct (N × H)
5. C₃×#10587020	C₃²	semidirect
14. C₃²×C₁₉⋊C₃	C₂₇	semidirect
22. #10587020	C₃³	semidirect
26. C₃²×C₁₉	C₃×C₂₇	semidirect
28. C₃×C₁₉⋊C₃	C₃×C₂₇	semidirect
42. C₃×C₁₉	C₃²×C₂₇	semidirect
44. C₁₉⋊C₃	C₃²×C₂₇	semidirect
55. C₁₉	C₃³×C₂₇	semidirect
58. C₃²	(C₁₉⋊C₃)⋊C₂₇	direct (N × H)
65. C₃	C₃×(C₁₉⋊C₃)⋊C₂₇	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
C₃²×#10587020	3
C₃²×C₉×C₁₉⋊C₃	3
C₃³×C₂₇	19

Subgroups — C32×(C19⋊C3)⋊C27 #28357052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×(C₁₉⋊C₃)⋊C₂₇ #28357052