Subgroups — #41005260

Order 26973.

254 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582441	C₃	1	9	yes	maximal
2	#22582441	C₃	1	1	yes	maximal, characteristic
3	#22582441	C₃	1	1	yes	maximal, characteristic
4	#22582441	C₃	1	1	yes	maximal, characteristic
5	C₃×C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
6	C₃²×#66524	C₃²	1	3	yes	—
7	C₃²×#66524	C₃²	1	3	yes	—
8	C₃²×#66524	C₃²	1	3	yes	—
9	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
10	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
11	C₃₇×C₉⋊C₉	—	3	3	no	—
12	C₃³×C₃₇	C₃³	1	1	yes	characteristic
13	C₃×C₉×C₃₇	—	3	1	no	—
14	C₃×C₉×C₃₇	—	3	1	no	—
15	C₃×C₉×C₃₇	—	3	1	no	—
16	C₃×C₉×C₃₇	—	3	3	no	—
17	C₃×C₉×C₃₇	—	3	9	no	—
18	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
19	C₃×#66524	—	3	3	no	—
20	C₃×#66524	—	3	3	no	—
21	C₃×#66524	—	3	3	no	—
22	C₃×#66524	—	3	9	no	—
23	C₃×#66524	—	3	9	no	—
24	C₃×#66524	—	3	9	no	—
25	#10624576	—	37	1	no	maximal, Sylow
26	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃²×C₃₇	#737	1	1	yes	characteristic
28	C₃²×C₃₇	#737	1	1	yes	characteristic
29	C₃²×C₃₇	#737	1	1	yes	characteristic
30	C₃²×C₃₇	#737	1	9	yes	—
31	C₉×C₃₇	—	3	3	no	—
32	C₉×C₃₇	—	9	3	no	—
33	#66524	—	9	3	no	—
34	#66524	—	9	3	no	—
35	#66524	—	9	3	no	—
36	C₃×C₉⋊C₉	C₃₇⋊C₃	1	1	yes	characteristic
37	#6855	—	37	9	no	—
38	#6855	—	37	1	no	—
39	#6855	—	37	1	no	—
40	#6855	—	37	1	no	—
41	C₃×C₃₇	#6895	1	1	yes	characteristic
42	C₃×C₃₇	#6897	1	3	yes	—
43	C₃×C₃₇	#6897	1	3	yes	—
44	C₃×C₃₇	#6898	1	3	yes	—
45	C₃×C₃₇	#6899	1	3	yes	—
46	C₃²×C₉	—	37	3	no	—
47	C₃²×C₉	—	37	3	no	—
48	C₃²×C₉	—	37	3	no	—
49	C₃²×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
50	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
51	C₉⋊C₉	—	3	3	no	—
52	C₃₇	#10624576	1	1	yes	characteristic, complemented, Sylow
53	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
54	C₃×C₉	—	3	1	no	—
55	C₃×C₉	—	3	1	no	—
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	—	3	9	no	—
59	C₃×C₉	—	111	3	no	—
60	C₃×C₉	—	111	3	no	—
61	C₃×C₉	—	111	3	no	—
62	C₃×C₉	—	111	9	no	—
63	C₃×C₉	—	111	9	no	—
64	C₃×C₉	—	111	9	no	—
65	C₃×C₉	#11758608	1	3	yes	—
66	C₃²	C₃×#11758608	1	1	yes	characteristic
67	C₃²	#15688531	1	1	yes	characteristic
68	C₃²	#15688531	1	1	yes	characteristic
69	C₃²	#15688531	1	1	yes	characteristic
70	C₃²	#15688532	1	9	yes	—
71	C₉	—	3	3	no	—
72	C₉	—	9	3	no	—
73	C₉	—	333	3	no	—
74	C₉	—	333	3	no	—
75	C₉	—	333	3	no	—
76	C₃	#22582578	1	1	yes	characteristic
77	C₃	#22582588	1	3	yes	—
78	C₃	#22582589	1	3	yes	—
79	C₃	#22582592	1	3	yes	—
80	C₃	#22582594	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₇⋊C₃
commutator, socle, prime radical, cosocle	C₃³×C₃₇	C₃³
Fitting	C₃×C₃₇×C₉⋊C₉	C₃
hypercenter	C₃×C₉⋊C₉	C₃₇⋊C₃
hypocenter	C₃₇	#10624576
LCS	G ▷ C₃³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
52. C₃₇	#10624576	semidirect

Maximal subgroups

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

subgroup	index
#22582441	3
C₃×C₃₇×C₉⋊C₉	3
#10624576	37