Subgroups — C₃²×#13095342 #28357053

Order 13851.

944 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	36	yes	maximal, direct product factor
2	C₃²×#10587020	C₃	1	3	yes	maximal, complemented
3	C₃³×#4294	C₃	1	1	yes	maximal, characteristic
4	#13095342	C₃²	1	81	yes	direct product factor
5	C₃×#10587020	C₃²	1	36	yes	complemented
6	C₃²×#4294	C₉	1	24	yes	—
7	C₃²×#4294	C₉	1	2	yes	—
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₃²×#4294	C₃²	1	12	yes	—
10	C₃⁴×C₁₉	C₉	1	1	yes	characteristic
11	C₃²×C₂₇⋊C₃	—	19	1	no	maximal, Sylow
12	C₃³×C₁₉	—	3	9	no	—
13	C₃³×C₁₉	C₃×C₉	1	12	yes	—
14	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃×#4294	C₃×C₉	1	72	yes	—
16	C₃×#4294	C₃×C₉	1	8	yes	—
17	C₃×#4294	C₃×C₉	1	24	yes	—
18	C₃×#4294	C₃³	1	4	yes	—
19	C₃×#4294	C₃³	1	9	yes	—
20	#10587020	C₃³	1	27	yes	complemented
21	C₃³×C₉	—	19	1	no	—
22	C₃×C₂₇⋊C₃	—	19	36	no	—
23	C₃²×C₂₇	—	19	3	no	—
24	C₃²×C₁₉	—	3	36	no	—
25	C₃²×C₁₉	C₂₇⋊C₃	1	9	yes	complemented
26	C₃²×C₁₉	C₃²×C₉	1	9	yes	—
27	C₃²×C₁₉	C₃²×C₉	1	4	yes	—
28	#4294	C₃²×C₉	1	8	yes	—
29	#4294	C₃²×C₉	1	18	yes	—
30	#4294	C₃⁴	1	1	yes	characteristic
31	C₃⁴	#4296	1	1	yes	characteristic
32	C₃²×C₉	—	19	24	no	—
33	C₃²×C₉	—	19	12	no	—
34	C₃²×C₉	—	19	2	no	—
35	C₃²×C₉	—	19	1	no	—
36	C₂₇⋊C₃	—	19	81	no	—
37	C₃×C₂₇	—	19	36	no	—
38	C₃×C₁₉	—	3	9	no	—
39	C₃×C₁₉	C₃×C₂₇⋊C₃	1	12	yes	complemented
40	C₃×C₁₉	C₃³×C₉	1	1	yes	characteristic
41	C₃³	—	3	9	no	—
42	C₃³	C₃×#4296	1	12	yes	—
43	C₃³	C₃×#4296	1	1	yes	characteristic
44	C₃×C₉	—	19	72	no	—
45	C₃×C₉	—	19	8	no	—
46	C₃×C₉	—	19	24	no	—
47	C₃×C₉	—	19	4	no	—
48	C₃×C₉	—	19	9	no	—
49	C₂₇	—	19	27	no	—
50	C₁₉	C₃²×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₃²	—	3	36	no	—
52	C₃²	#13095342	1	9	yes	direct product factor
53	C₃²	C₃²×#4296	1	9	yes	—
54	C₃²	C₃²×#4296	1	4	yes	—
55	C₉	—	19	1	no	—
56	C₉	—	19	8	no	—
57	C₉	—	19	18	no	—
58	C₃	—	3	9	no	—
59	C₃	C₃×#13095342	1	12	yes	direct product factor
60	C₃	C₃³×#4296	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×#13095342	C₃	direct (N × H)
2. C₃²×#10587020	C₃	semidirect
4. #13095342	C₃²	direct (N × H)
5. C₃×#10587020	C₃²	semidirect
20. #10587020	C₃³	semidirect
25. C₃²×C₁₉	C₂₇⋊C₃	semidirect
39. C₃×C₁₉	C₃×C₂₇⋊C₃	semidirect
50. C₁₉	C₃²×C₂₇⋊C₃	semidirect
52. C₃²	#13095342	direct (N × H)
59. C₃	C₃×#13095342	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×#13095342	3
C₃²×#10587020	3
C₃³×#4294	3
C₃²×C₂₇⋊C₃	19

Subgroups — C32×#13095342 #28357053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#13095342 #28357053