Subgroups — C₃×#22582500 #41007315

Order 26973.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582500	C₃	1	9	yes	maximal, direct product factor
2	C₃×#15688500	C₃	1	3	yes	maximal, complemented
3	C₃²×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
4	#15688500	C₃²	1	9	yes	complemented
5	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
6	C₃×C₂₇×C₃₇	C₉	1	2	yes	—
7	C₃×C₂₇×C₃₇	C₉	1	6	yes	—
8	C₃×C₂₇×C₃₇	C₃²	1	3	yes	—
9	C₃×C₂₇×C₃₇	C₃²	1	1	yes	characteristic
10	C₃³×C₃₇	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₂₇	1	6	yes	—
12	C₃×C₉×C₃₇	C₂₇	1	2	yes	—
13	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
14	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
15	C₂₇×C₃₇	C₃×C₉	1	6	yes	—
16	C₂₇×C₃₇	C₃×C₉	1	2	yes	—
17	C₂₇×C₃₇	C₃³	1	1	yes	characteristic
18	C₃×C₈₁⋊C₃	—	37	1	no	maximal, Sylow
19	C₃²×C₃₇	—	3	3	no	—
20	C₃²×C₃₇	C₃×C₂₇	1	3	yes	—
21	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
22	C₉×C₃₇	C₃×C₂₇	1	6	yes	—
23	C₉×C₃₇	C₃×C₂₇	1	2	yes	—
24	C₉×C₃₇	C₃²×C₉	1	1	yes	characteristic
25	C₃²×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
26	C₈₁⋊C₃	—	37	9	no	—
27	C₃×C₈₁	—	37	3	no	—
28	C₃×C₃₇	—	3	3	no	—
29	C₃×C₃₇	C₈₁⋊C₃	1	3	yes	complemented
30	C₃×C₃₇	C₃²×C₂₇	1	1	yes	characteristic
31	C₃²×C₉	#66524	1	1	yes	characteristic
32	C₃×C₂₇	#66524	1	2	yes	—
33	C₃×C₂₇	#66524	1	6	yes	—
34	C₃×C₂₇	C₃×C₃₇⋊C₃	1	3	yes	—
35	C₃×C₂₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic
36	C₈₁	—	37	9	no	—
37	C₃₇	C₃×C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₃³	#11758601	1	1	yes	characteristic
39	C₃×C₉	#11758601	1	6	yes	—
40	C₃×C₉	#11758601	1	2	yes	—
41	C₃×C₉	C₃×#66524	1	3	yes	—
42	C₃×C₉	C₃×#66524	1	1	yes	characteristic
43	C₂₇	C₃×#66524	1	6	yes	—
44	C₂₇	C₃×#66524	1	2	yes	—
45	C₂₇	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
46	C₃²	—	3	3	no	—
47	C₃²	C₃×#11758601	1	3	yes	—
48	C₃²	C₃×#11758601	1	1	yes	characteristic
49	C₉	C₃×#11758601	1	6	yes	—
50	C₉	C₃×#11758601	1	2	yes	—
51	C₉	C₃²×#66524	1	1	yes	characteristic
52	C₃	—	3	3	no	—
53	C₃	#22582500	1	3	yes	direct product factor
54	C₃	C₃²×#11758601	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₂₇	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃²×C₂₇
Frattini	C₂₇	C₃²×C₃₇⋊C₃
Fitting	C₃²×C₂₇×C₃₇	C₃
socle	C₃²×C₃₇	C₃×C₂₇
prime radical	C₃³×C₃₇	C₂₇
cosocle	C₂₇×C₃₇	C₃³
hypercenter	C₃²×C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	C₃×C₈₁⋊C₃
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
1. #22582500	C₃	direct (N × H)
2. C₃×#15688500	C₃	semidirect
4. #15688500	C₃²	semidirect
29. C₃×C₃₇	C₈₁⋊C₃	semidirect
37. C₃₇	C₃×C₈₁⋊C₃	semidirect
53. C₃	#22582500	direct (N × H)

Maximal subgroups

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

subgroup	index
#22582500	3
C₃×#15688500	3
C₃²×C₂₇×C₃₇	3
C₃×C₈₁⋊C₃	37

Subgroups — C3×#22582500 #41007315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582500 #41007315