Subgroups — #41004909

Order 26973.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582472	C₃	1	1	yes	maximal, characteristic
2	#22582472	C₃	1	2	yes	maximal
3	C₃₇×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃²⋊#66524	—	3	1	no	—
5	C₃²⋊#66524	—	3	2	no	—
6	C₃²×C₉×C₃₇	—	3	1	no	—
7	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
8	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₉×C₃₇	—	3	3	no	—
10	C₃×C₉×C₃₇	—	3	1	no	—
11	C₃×C₉×C₃₇	—	3	1	no	—
12	C₃×C₉×C₃₇	—	3	2	no	—
13	C₃×C₉×C₃₇	—	9	2	no	—
14	C₃×C₉×C₃₇	—	9	1	no	—
15	C₃×#66524	—	9	1	no	—
16	C₃×#66524	—	9	2	no	—
17	#10624492	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	—	3	1	no	—
19	C₃²×C₃₇	—	3	2	no	—
20	C₃²×C₃₇	#731	1	1	yes	characteristic
21	C₃²×C₃₇	#732	1	1	yes	characteristic
22	C₃²×C₃₇	#733	1	2	yes	—
23	C₉×C₃₇	—	9	3	no	—
24	C₉×C₃₇	—	9	1	no	—
25	#66524	—	27	1	no	—
26	#66524	—	27	2	no	—
27	#6868	—	37	1	no	—
28	#6868	—	37	2	no	—
29	#6855	C₃₇⋊C₃	1	1	yes	characteristic
30	C₃×C₃₇	—	3	1	no	—
31	C₃×C₃₇	—	3	2	no	—
32	C₃×C₃₇	#6861	1	1	yes	characteristic
33	C₃×C₃₇	#6878	1	1	yes	characteristic
34	C₃×C₃₇	#6883	1	2	yes	—
35	C₃²×C₉	—	3	1	no	—
36	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
37	C₃²⋊C₉	—	111	1	no	—
38	C₃²⋊C₉	—	111	2	no	—
39	C₃₇	#10624492	1	1	yes	characteristic, complemented, Sylow
40	C₃³	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	2	no	—
45	C₃×C₉	—	9	2	no	—
46	C₃×C₉	—	9	1	no	—
47	C₃×C₉	—	333	1	no	—
48	C₃×C₉	—	333	2	no	—
49	C₃²	—	3	1	no	—
50	C₃²	—	3	2	no	—
51	C₃²	#15688515	1	1	yes	characteristic
52	C₃²	#15688519	1	1	yes	characteristic
53	C₃²	#15688520	1	2	yes	—
54	C₉	—	9	3	no	—
55	C₉	—	9	1	no	—
56	C₉	—	999	1	no	—
57	C₉	—	999	2	no	—
58	C₃	—	3	1	no	—
59	C₃	—	3	2	no	—
60	C₃	#22582456	1	1	yes	characteristic
61	C₃	#22582502	1	1	yes	characteristic
62	C₃	#22582523	1	2	yes	—

	subgroup	G/H
center	C₃²	#15688519
commutator, cosocle	C₃²×C₉×C₃₇	C₃²
Frattini	C₃²×C₉	C₃×C₃₇⋊C₃
Fitting	C₃₇×#6855	C₃
socle	C₃²×C₃₇	#732
prime radical	C₃³×C₃₇	H(3,𝔽₃)
hypercenter	#6855	C₃₇⋊C₃
hypocenter	C₃₇	#10624492
LCS	G ▷ C₃²×C₉×C₃₇ ▷ C₃³×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ #6855

Complements

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

N	H ≅ G/N	type
39. C₃₇	#10624492	semidirect

Maximal subgroups

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

subgroup	index
#22582472	3
C₃₇×#6855	3
#10624492	37