Subgroups — C₃×#22582492 #41006329

Order 26973.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688511	C₃	1	2	yes	maximal
2	C₃×#15688505	C₃	1	1	yes	maximal, characteristic
3	#22582492	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₃₇×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃²×#66524	—	3	1	no	—
6	#15688511	—	3	4	no	—
7	#15688511	C₃²	1	6	yes	—
8	C₃×#11758601	—	3	2	no	—
9	#15688505	—	3	2	no	—
10	#15688505	C₃²	1	3	yes	—
11	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
12	C₃₇×C₂₇⋊C₃	C₉	1	6	yes	complemented
13	C₃₇×C₂₇⋊C₃	C₃²	1	3	yes	—
14	C₃×C₂₇×C₃₇	C₉	1	3	yes	complemented
15	C₃³×C₃₇	3₋¹⁺²	1	1	yes	characteristic
16	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
18	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
19	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
20	C₃×C₉×C₃₇	3₋¹⁺²	1	4	yes	—
21	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
22	C₃×#66524	—	3	3	no	—
23	C₃×#66524	—	9	3	no	—
24	C₂₇×C₃₇	C₃×C₉	1	9	yes	complemented
25	#11758601	—	3	6	no	—
26	C₃×#6875	—	37	1	no	maximal, Sylow
27	C₃²×C₃₇	—	3	3	no	—
28	C₃²×C₃₇	C₉⋊C₉	1	2	yes	—
29	C₃²×C₃₇	C₉⋊C₉	1	1	yes	characteristic
30	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
31	C₉×C₃₇	C₉⋊C₉	1	2	yes	—
32	C₉×C₃₇	C₉⋊C₉	1	4	yes	—
33	C₉×C₃₇	C₃²×C₉	1	1	yes	characteristic
34	C₉×C₃₇	C₃×3₋¹⁺²	1	2	yes	—
35	#66524	—	9	3	no	—
36	C₃×C₂₇⋊C₃	—	37	2	no	—
37	C₃×C₂₇⋊C₃	C₃₇⋊C₃	1	1	yes	characteristic
38	C₃×C₉⋊C₉	—	37	1	no	—
39	#6875	—	37	9	no	—
40	C₃×C₃₇	—	3	1	no	—
41	C₃×C₃₇	—	3	2	no	—
42	C₃×C₃₇	#6875	1	3	yes	complemented
43	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
44	C₃²×C₉	—	111	1	no	—
45	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
46	C₂₇⋊C₃	—	37	6	no	—
47	C₂₇⋊C₃	—	111	4	no	—
48	C₂₇⋊C₃	#66524	1	6	yes	complemented
49	C₂₇⋊C₃	C₃×C₃₇⋊C₃	1	3	yes	—
50	C₃×C₂₇	—	111	2	no	—
51	C₃×C₂₇	#66524	1	3	yes	complemented
52	C₉⋊C₉	—	37	3	no	—
53	C₉⋊C₉	—	111	2	no	—
54	C₃₇	C₃×#6875	1	1	yes	characteristic, complemented, Sylow
55	C₃³	#11758605	1	1	yes	characteristic
56	C₃×C₉	—	333	3	no	—
57	C₃×C₉	—	111	3	no	—
58	C₃×C₉	#11758605	1	2	yes	—
59	C₃×C₉	#11758605	1	4	yes	—
60	C₃×C₉	#11758605	1	2	yes	—
61	C₃×C₉	C₃×#66524	1	2	yes	—
62	C₃×C₉	C₃×#66524	1	1	yes	characteristic
63	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
64	C₂₇	—	111	6	no	—
65	C₂₇	C₃×#66524	1	9	yes	complemented
66	C₃²	—	3	3	no	—
67	C₃²	#15688505	1	2	yes	—
68	C₃²	#15688505	1	1	yes	characteristic
69	C₃²	C₃×#11758605	1	1	yes	characteristic
70	C₉	—	333	3	no	—
71	C₉	#15688505	1	2	yes	—
72	C₉	#15688505	1	4	yes	—
73	C₉	C₃²×#66524	1	1	yes	characteristic
74	C₉	C₃×#11758605	1	2	yes	—
75	C₃	—	3	1	no	—
76	C₃	—	3	2	no	—
77	C₃	#22582492	1	3	yes	direct product factor
78	C₃	C₃×#15688505	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#15688505
commutator	C₉×C₃₇	C₃²×C₉
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃×C₃₇×C₂₇⋊C₃	C₃
socle	C₃²×C₃₇	C₉⋊C₉
prime radical	C₃³×C₃₇	3₋¹⁺²
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₃×C₂₇⋊C₃	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6875
LCS	G ▷ C₉×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
3. #22582492	C₃	direct (N × H)
12. C₃₇×C₂₇⋊C₃	C₉	semidirect
14. C₃×C₂₇×C₃₇	C₉	semidirect
24. C₂₇×C₃₇	C₃×C₉	semidirect
42. C₃×C₃₇	#6875	semidirect
48. C₂₇⋊C₃	#66524	semidirect
51. C₃×C₂₇	#66524	semidirect
54. C₃₇	C₃×#6875	semidirect
65. C₂₇	C₃×#66524	semidirect
77. C₃	#22582492	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×#15688511	3
C₃×#15688505	3
#22582492	3
C₃×C₃₇×C₂₇⋊C₃	3
C₃×#6875	37

Subgroups — C3×#22582492 #41006329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22582492 #41006329