Subgroups — C₃×C₉×#11758601 #41006191

Order 26973.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758601	C₃	1	3	yes	maximal
2	C₉×#11758601	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉²×C₃₇	C₃	1	1	yes	maximal, characteristic
4	C₃×#11758601	C₉	1	27	yes	direct product factor
5	C₃×#11758601	C₃²	1	9	yes	—
6	C₃²×C₉×C₃₇	C₉	1	3	yes	—
7	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
8	C₉²×C₃₇	C₉	1	6	yes	—
9	C₉²×C₃₇	C₃²	1	3	yes	—
10	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₂₇	1	27	yes	complemented
12	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
13	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
14	C₃×C₉×C₃₇	C₃×C₉	1	9	yes	—
15	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
16	#11758601	C₃×C₉	1	27	yes	direct product factor
17	C₃×C₉×C₂₇	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	C₉²	1	3	yes	—
19	C₃²×C₃₇	C₃×C₂₇	1	9	yes	—
20	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
21	C₉×C₃₇	C₉²	1	6	yes	—
22	C₉×C₃₇	C₃×C₂₇	1	27	yes	complemented
23	C₉×C₃₇	C₃²×C₉	1	3	yes	—
24	C₃²×C₂₇	—	37	3	no	—
25	C₃×C₉²	C₃₇⋊C₃	1	1	yes	characteristic
26	C₉×C₂₇	—	37	9	no	—
27	C₃×C₃₇	C₉×C₂₇	1	9	yes	complemented
28	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
29	C₃×C₃₇	C₃²×C₂₇	1	3	yes	—
30	C₃²×C₉	#66524	1	3	yes	—
31	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
32	C₃×C₂₇	—	37	27	no	—
33	C₃×C₂₇	—	37	9	no	—
34	C₉²	#66524	1	6	yes	—
35	C₉²	C₃×C₃₇⋊C₃	1	3	yes	—
36	C₃₇	C₃×C₉×C₂₇	1	1	yes	characteristic, complemented, Sylow
37	C₃³	C₃×#66524	1	1	yes	characteristic
38	C₃×C₉	#11758601	1	27	yes	direct product factor
39	C₃×C₉	C₉×C₃₇⋊C₃	1	9	yes	—
40	C₃×C₉	C₃×#66524	1	2	yes	—
41	C₃×C₉	C₃×#66524	1	9	yes	—
42	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
43	C₂₇	—	37	27	no	—
44	C₃²	C₉×#66524	1	3	yes	—
45	C₃²	C₃×#11758601	1	9	yes	—
46	C₃²	C₃²×#66524	1	1	yes	characteristic
47	C₉	C₉×#66524	1	6	yes	—
48	C₉	C₃×#11758601	1	27	yes	direct product factor
49	C₉	C₃×C₉×C₃₇⋊C₃	1	3	yes	—
50	C₃	C₉×#11758601	1	9	yes	direct product factor
51	C₃	C₃×C₉×#66524	1	1	yes	characteristic
52	C₃	C₃²×#11758601	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₃×C₉²	C₃₇⋊C₃
commutator, hypocenter	C₃₇	C₃×C₉×C₂₇
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃×C₉²×C₃₇	C₃
socle, prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. C₉×#11758601	C₃	direct (N × H)
4. C₃×#11758601	C₉	direct (N × H)
11. C₃×C₉×C₃₇	C₂₇	semidirect
16. #11758601	C₃×C₉	direct (N × H)
22. C₉×C₃₇	C₃×C₂₇	semidirect
27. C₃×C₃₇	C₉×C₂₇	semidirect
36. C₃₇	C₃×C₉×C₂₇	semidirect
38. C₃×C₉	#11758601	direct (N × H)
48. C₉	C₃×#11758601	direct (N × H)
50. C₃	C₉×#11758601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#11758601	3
C₉×#11758601	3
C₃×C₉²×C₃₇	3
C₃×C₉×C₂₇	37

Subgroups — C3×C9×#11758601 #41006191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#11758601 #41006191