Subgroups — C₃×#22582688 #41008467

Order 26973.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758603	C₃	1	3	yes	maximal
2	#22582688	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉×#66524	C₃	1	1	yes	maximal, characteristic
4	C₃×#11758603	C₉	1	27	yes	complemented
5	C₃×#11758603	C₃²	1	9	yes	—
6	C₃²×#66524	C₉	1	1	yes	characteristic
7	C₃²×#66524	C₉	1	1	yes	characteristic
8	C₃²×#66524	C₃²	1	1	yes	characteristic
9	C₉×#66524	C₉	1	6	yes	—
10	C₉×#66524	C₃²	1	3	yes	—
11	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
12	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₃₇	—	3	3	no	—
14	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
15	C₃×#66524	—	3	3	no	—
16	C₃×#66524	—	3	3	no	—
17	C₃×#66524	C₃×C₉	1	3	yes	—
18	C₃×#66524	C₃×C₉	1	3	yes	—
19	C₃×#66524	C₃×C₉	1	2	yes	—
20	C₃×#66524	C₃×C₉	1	9	yes	—
21	C₃×#66524	C₃³	1	1	yes	characteristic
22	#11758603	C₃×C₉	1	27	yes	complemented
23	C₃×#6864	—	37	1	no	maximal, Sylow
24	C₃²×C₃₇	C₉²	1	3	yes	—
25	C₃²×C₃₇	C₂₇⋊C₃	1	3	yes	—
26	C₃²×C₃₇	C₂₇⋊C₃	1	3	yes	—
27	C₃²×C₃₇	C₂₇⋊C₃	1	3	yes	—
28	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
29	C₉×C₃₇	—	3	3	no	—
30	#66524	—	3	3	no	—
31	#66524	—	3	3	no	—
32	#66524	C₉²	1	6	yes	—
33	#66524	C₃²×C₉	1	3	yes	—
34	C₃²×C₂₇	—	37	3	no	—
35	C₃×C₉²	—	37	1	no	—
36	#6864	—	37	9	no	—
37	C₃×C₃₇	#6864	1	9	yes	complemented
38	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
39	C₃×C₃₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
40	C₃×C₃₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
41	C₃×C₃₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
42	C₃²×C₉	—	37	1	no	—
43	C₃²×C₉	—	37	1	no	—
44	C₃²×C₉	—	37	1	no	—
45	C₃²×C₉	#66526	1	1	yes	characteristic
46	C₃×C₂₇	—	37	27	no	—
47	C₃×C₂₇	—	37	9	no	—
48	C₉²	—	37	6	no	—
49	C₉²	—	37	3	no	—
50	C₃₇	C₃×#6864	1	1	yes	characteristic, complemented, Sylow
51	C₃³	C₃×#66526	1	1	yes	characteristic
52	C₃×C₉	—	3	3	no	—
53	C₃×C₉	—	37	9	no	—
54	C₃×C₉	—	37	2	no	—
55	C₃×C₉	—	37	1	no	—
56	C₃×C₉	—	37	3	no	—
57	C₃×C₉	—	37	3	no	—
58	C₃×C₉	—	111	3	no	—
59	C₃×C₉	—	111	3	no	—
60	C₃×C₉	C₃×#66526	1	3	yes	—
61	C₂₇	—	37	27	no	—
62	C₃²	C₉×#66526	1	3	yes	—
63	C₃²	#15688541	1	3	yes	—
64	C₃²	#15688542	1	3	yes	—
65	C₃²	#15688543	1	3	yes	—
66	C₃²	C₃²×#66526	1	1	yes	characteristic
67	C₉	—	3	3	no	—
68	C₉	—	37	3	no	—
69	C₉	—	37	6	no	—
70	C₉	—	111	3	no	—
71	C₉	—	111	3	no	—
72	C₃	#22582688	1	9	yes	direct product factor
73	C₃	C₃×C₉×#66526	1	1	yes	characteristic
74	C₃	C₃×#15688541	1	1	yes	characteristic
75	C₃	C₃×#15688542	1	1	yes	characteristic
76	C₃	C₃×#15688543	1	1	yes	characteristic

	subgroup	G/H
center	C₃³	C₃×#66526
commutator	C₃×C₃₇	C₃×C₉²
Frattini	C₃²	C₃²×#66526
Fitting	C₃²×C₉×C₃₇	C₉
socle, prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×#66524	C₃³
hypercenter	C₃²×C₉	#66526
hypocenter	C₃₇	C₃×#6864
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. #22582688	C₃	direct (N × H)
4. C₃×#11758603	C₉	semidirect
22. #11758603	C₃×C₉	semidirect
37. C₃×C₃₇	#6864	semidirect
50. C₃₇	C₃×#6864	semidirect
72. C₃	#22582688	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×#11758603	3
#22582688	3
C₃×C₉×#66524	3
C₃×#6864	37

Subgroups — C3×#22582688 #41008467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582688 #41008467