Subgroups — #41008435

Order 26973.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#66526	C₃	1	3	yes	maximal
2	(C₃×#66526)⋊C₉	C₃	1	9	yes	maximal
3	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×#66526	C₃²	1	9	yes	—
5	C₉×#66526	C₉	1	27	yes	complemented
6	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	—
7	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
8	C₉×#66524	C₉	1	2	yes	complemented
9	C₉×#66524	C₉	1	6	yes	complemented
10	C₉²×C₃₇	C₉	1	1	yes	characteristic, complemented
11	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
12	C₃×#66526	—	3	27	no	—
13	C₃×#66526	C₃×C₉	1	27	yes	—
14	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
15	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
16	C₃×#66524	C₃×C₉	1	6	yes	—
17	C₃×#66524	C₃×C₉	1	2	yes	—
18	C₉×C₃₇⋊C₃	—	3	9	no	—
19	C₉×C₃₇⋊C₃	C₃×C₉	1	9	yes	—
20	#10624544	—	37	1	no	maximal, Sylow
21	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
22	C₃×C₃₇⋊C₃	C₃²×C₉	1	3	yes	—
23	C₃×C₃₇⋊C₃	#737	1	9	yes	—
24	#66526	—	3	27	no	—
25	C₉×C₃₇	—	3	3	no	—
26	C₉×C₃₇	C₉²	1	3	yes	—
27	#66524	—	3	6	no	—
28	#66524	C₉²	1	6	yes	—
29	C₃×C₉²	—	37	3	no	—
30	C₃×C₉²	—	37	1	no	—
31	#6855	—	37	9	no	—
32	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
33	C₃×C₃₇	#6887	1	3	yes	—
34	C₃₇⋊C₃	#6887	1	9	yes	—
35	C₃²×C₉	—	37	1	no	—
36	C₃²×C₉	—	37	9	no	—
37	C₃²×C₉	—	37	3	no	—
38	C₉²	—	37	27	no	—
39	C₉²	—	37	6	no	—
40	C₉²	—	37	2	no	—
41	C₉²	#66526	1	1	yes	characteristic, complemented
42	C₃₇	#10624544	1	1	yes	characteristic, complemented, Sylow
43	C₃³	—	37	1	no	—
44	C₃×C₉	—	37	2	no	—
45	C₃×C₉	—	37	9	no	—
46	C₃×C₉	—	37	27	no	—
47	C₃×C₉	—	37	6	no	—
48	C₃×C₉	—	111	9	no	—
49	C₃×C₉	—	111	27	no	—
50	C₃×C₉	C₃×#66526	1	3	yes	—
51	C₃×C₉	C₃×#66526	1	1	yes	characteristic
52	C₃²	—	37	3	no	—
53	C₃²	—	37	9	no	—
54	C₃²	C₃²×#66526	1	1	yes	characteristic
55	C₉	—	3	3	no	—
56	C₉	—	37	6	no	—
57	C₉	—	111	27	no	—
58	C₉	—	111	6	no	—
59	C₉	C₉×#66526	1	3	yes	—
60	C₃	—	37	9	no	—
61	C₃	C₃×C₉×#66526	1	1	yes	characteristic
62	C₃	#22582722	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×#66526
commutator	C₃×C₃₇	C₃×C₉²
Frattini	C₃²	C₃²×#66526
Fitting	C₉²×C₃₇	C₉
socle	C₃²×C₃₇	C₃²×C₉
prime radical, cosocle	C₃²×C₃₇⋊C₃	C₃³
hypercenter	C₉²	#66526
hypocenter	C₃₇	#10624544
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
5. C₉×#66526	C₉	semidirect
8. C₉×#66524	C₉	semidirect
9. C₉×#66524	C₉	semidirect
10. C₉²×C₃₇	C₉	semidirect
41. C₉²	#66526	semidirect
42. C₃₇	#10624544	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#66526	3
(C₃×#66526)⋊C₉	3
C₉²×C₃₇⋊C₃	3
#10624544	37