Subgroups — #41008411

Order 26973.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688538	C₃	1	1	yes	maximal, characteristic
2	#22582693	C₃	1	2	yes	maximal
3	#733×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×#66526	—	3	1	no	—
5	#15688538	—	3	3	no	—
6	C₃²⋊#66526	—	3	2	no	—
7	3₋¹⁺²×C₃₇⋊C₃	—	3	1	no	—
8	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
9	#15688521	C₉	1	2	yes	complemented
10	#15688520	—	3	2	no	—
11	C₃₇×#733	C₉	1	1	yes	characteristic, complemented
12	C₃²×C₃₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×#66526	—	3	3	no	—
14	C₃×#66526	—	9	1	no	—
15	C₃×#66526	—	9	2	no	—
16	C₃×#66526	—	9	2	no	—
17	3₋¹⁺²×C₃₇	—	3	1	no	—
18	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
19	#11758608	—	3	2	no	—
20	C₃×#66524	3₋¹⁺²	1	2	yes	—
21	#11758606	—	9	1	no	—
22	#11758605	—	9	1	no	—
23	C₉×C₃₇⋊C₃	—	3	1	no	—
24	C₉×C₃₇⋊C₃	—	3	1	no	—
25	C₉×C₃₇⋊C₃	—	3	1	no	—
26	C₉×C₃₇⋊C₃	—	9	1	no	—
27	#10624529	—	37	1	no	maximal, Sylow
28	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
29	C₃×C₃₇⋊C₃	—	3	1	no	—
30	C₃×C₃₇⋊C₃	—	3	2	no	—
31	C₃×C₃₇⋊C₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
32	C₃×C₃₇⋊C₃	#731	1	1	yes	characteristic
33	C₃×C₃₇⋊C₃	#732	1	1	yes	characteristic
34	#66526	—	9	3	no	—
35	#66526	—	27	2	no	—
36	C₉×C₃₇	—	3	1	no	—
37	C₉×C₃₇	—	9	1	no	—
38	#66524	—	3	2	no	—
39	#66524	—	9	2	no	—
40	C₃×#733	—	37	1	no	—
41	C₃×C₉⋊C₉	—	37	1	no	—
42	#6868	—	37	2	no	—
43	C₃×C₃₇	—	3	1	no	—
44	C₃×C₃₇	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
45	C₃₇⋊C₃	—	3	1	no	—
46	C₃₇⋊C₃	—	3	1	no	—
47	C₃₇⋊C₃	#6882	1	1	yes	characteristic
48	C₃₇⋊C₃	#6883	1	2	yes	—
49	C₃×3₋¹⁺²	—	111	1	no	—
50	C₃²×C₉	—	37	1	no	—
51	C₃²×C₉	—	111	1	no	—
52	#733	—	37	2	no	—
53	#733	—	111	2	no	—
54	#733	#66526	1	1	yes	characteristic, complemented
55	C₉⋊C₉	—	111	3	no	—
56	C₃²⋊C₉	—	111	2	no	—
57	C₃₇	#10624529	1	1	yes	characteristic, complemented, Sylow
58	C₃³	—	37	1	no	—
59	3₋¹⁺²	—	3	1	no	—
60	3₋¹⁺²	—	333	1	no	—
61	3₋¹⁺²	—	333	1	no	—
62	3₋¹⁺²	—	111	2	no	—
63	C₃×C₉	—	37	2	no	—
64	C₃×C₉	—	333	1	no	—
65	C₃×C₉	—	333	2	no	—
66	C₃×C₉	—	333	1	no	—
67	C₃×C₉	—	333	2	no	—
68	C₃×C₉	—	111	1	no	—
69	C₃×C₉	—	111	1	no	—
70	C₃×C₉	—	111	1	no	—
71	C₃×C₉	—	111	3	no	—
72	C₃×C₉	C₃×#66526	1	1	yes	characteristic
73	C₃²	—	37	1	no	—
74	C₃²	—	37	1	no	—
75	C₃²	—	37	1	no	—
76	C₃²	—	111	2	no	—
77	C₃²	—	111	1	no	—
78	C₃²	C₃²⋊#66526	1	1	yes	characteristic
79	C₉	—	3	1	no	—
80	C₉	—	9	1	no	—
81	C₉	—	333	3	no	—
82	C₉	—	333	2	no	—
83	C₉	—	111	2	no	—
84	C₉	—	999	2	no	—
85	C₃	—	3	1	no	—
86	C₃	—	37	2	no	—
87	C₃	—	37	1	no	—
88	C₃	—	111	1	no	—
89	C₃	—	111	1	no	—
90	C₃	H(3,𝔽₃)⋊#66526	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)⋊#66526
commutator	C₃×C₉×C₃₇	C₃×C₉
Frattini	C₃×C₉	C₃×#66526
Fitting	C₃₇×#733	C₉
socle	C₃×C₃₇	H(3,𝔽₃)⋊C₉
prime radical	C₃²×C₃₇⋊C₃	H(3,𝔽₃)
cosocle	C₃×C₉×C₃₇⋊C₃	C₃²
hypercenter	#733	#66526
hypocenter	C₃₇	#10624529
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ #733

Complements

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

N	H ≅ G/N	type
9. #15688521	C₉	semidirect
11. C₃₇×#733	C₉	semidirect
54. #733	#66526	semidirect
57. C₃₇	#10624529	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688538	3
#22582693	3
#733×C₃₇⋊C₃	3
#10624529	37