Subgroups — #41004932

Order 26973.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582468	C₃	1	1	yes	maximal, characteristic
2	#22582468	C₃	1	2	yes	maximal
3	C₃₇×#6866	C₃	1	1	yes	maximal, characteristic
4	C₃²⋊#66524	—	3	1	no	—
5	C₃²⋊#66524	—	3	2	no	—
6	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
7	C₃₇×C₃²⋊C₉	—	3	1	no	—
8	C₃³×C₃₇	—	3	1	no	—
9	C₃³×C₃₇	—	3	1	no	—
10	C₃³×C₃₇	—	3	2	no	—
11	C₃³×C₃₇	—	9	3	no	—
12	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₃₇	—	9	1	no	—
14	C₃×#66524	—	9	1	no	—
15	C₃×#66524	—	9	2	no	—
16	#10624496	—	37	1	no	maximal, Sylow
17	C₃²×C₃₇	—	9	1	no	—
18	C₃²×C₃₇	—	9	3	no	—
19	C₃²×C₃₇	—	9	6	no	—
20	C₃²×C₃₇	—	9	3	no	—
21	C₃²×C₃₇	—	9	1	no	—
22	C₃²×C₃₇	#731	1	1	yes	characteristic
23	C₃²×C₃₇	#731	1	1	yes	characteristic
24	C₃²×C₃₇	#731	1	2	yes	—
25	C₉×C₃₇	—	27	1	no	—
26	#66524	—	27	1	no	—
27	#66524	—	27	2	no	—
28	#6866	—	37	1	no	—
29	#6866	—	37	2	no	—
30	#6866	C₃₇⋊C₃	1	1	yes	characteristic
31	C₃×C₃₇	—	3	1	no	—
32	C₃×C₃₇	—	3	2	no	—
33	C₃×C₃₇	—	3	1	no	—
34	C₃×C₃₇	—	9	3	no	—
35	C₃×C₃₇	#6862	1	1	yes	characteristic
36	C₃⁴	C₃×C₃₇⋊C₃	1	1	yes	characteristic
37	C₃²⋊C₉	—	3	1	no	—
38	C₃²⋊C₉	—	111	1	no	—
39	C₃²⋊C₉	—	111	2	no	—
40	C₃₇	#10624496	1	1	yes	characteristic, complemented, Sylow
41	C₃³	—	3	1	no	—
42	C₃³	—	3	1	no	—
43	C₃³	—	3	2	no	—
44	C₃³	—	9	3	no	—
45	C₃³	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
46	C₃×C₉	—	9	1	no	—
47	C₃×C₉	—	333	1	no	—
48	C₃×C₉	—	333	2	no	—
49	C₃²	—	9	1	no	—
50	C₃²	—	9	3	no	—
51	C₃²	—	9	3	no	—
52	C₃²	—	9	6	no	—
53	C₃²	—	9	1	no	—
54	C₃²	#15688515	1	1	yes	characteristic
55	C₃²	#15688516	1	1	yes	characteristic
56	C₃²	#15688517	1	2	yes	—
57	C₉	—	27	1	no	—
58	C₉	—	999	1	no	—
59	C₉	—	999	2	no	—
60	C₃	—	3	1	no	—
61	C₃	—	3	1	no	—
62	C₃	—	3	2	no	—
63	C₃	—	9	3	no	—
64	C₃	C₃₇⋊#6862	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃₇⋊#6862
commutator, prime radical, cosocle	C₃⁴×C₃₇	C₃²
Frattini	C₃⁴	C₃×C₃₇⋊C₃
Fitting	C₃₇×#6866	C₃
socle	C₃×C₃₇	#6862
hypercenter	#6866	C₃₇⋊C₃
hypocenter	C₃₇	#10624496
LCS	G ▷ C₃⁴×C₃₇ ▷ C₃³×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃⁴ ◁ #6866

Complements

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

N	H ≅ G/N	type
40. C₃₇	#10624496	semidirect

Maximal subgroups

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

subgroup	index
#22582468	3
C₃₇×#6866	3
#10624496	37