Subgroups — C₃₇×#10624588 #41004377

Order 26973.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×3₋¹⁺²×C₃₇	C₃	1	3	yes	maximal
2	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
3	C₃₇×#6861	C₃	1	3	yes	maximal
4	C₃₇×#6860	C₃	1	3	yes	maximal
5	C₃₇×#6858	C₃	1	3	yes	maximal
6	C₃×3₋¹⁺²×C₃₇	C₃²	1	3	yes	—
7	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
8	C₃₇×C₉⋊C₉	—	3	2	no	—
9	C₃₇×C₉⋊C₉	—	3	6	no	—
10	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	—
11	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	—
12	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	—
13	C₉²×C₃₇	—	3	1	no	—
14	C₉²×C₃₇	—	3	3	no	—
15	C₃³×C₃₇	C₃³	1	1	yes	characteristic
16	3₋¹⁺²×C₃₇	—	3	9	no	—
17	C₃×C₉×C₃₇	—	3	3	no	—
18	C₃×C₉×C₃₇	—	3	3	no	—
19	C₃×C₉×C₃₇	—	3	3	no	—
20	C₃×C₉×C₃₇	—	3	3	no	—
21	C₃×C₉×C₃₇	—	3	3	no	—
22	C₃×C₉×C₃₇	H(3,𝔽₃)	1	2	yes	—
23	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
24	#10624588	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃²×C₃₇	—	3	1	no	—
26	C₃²×C₃₇	—	3	3	no	—
27	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₉×C₃₇	—	3	2	no	—
29	C₉×C₃₇	—	3	9	no	—
30	C₉×C₃₇	—	9	3	no	—
31	C₉×C₃₇	—	9	3	no	—
32	C₉×C₃₇	—	9	3	no	—
33	C₉×C₃₇	#733	1	3	yes	—
34	C₉×3₋¹⁺²	C₃×C₃₇	1	3	yes	—
35	#6887	C₃×C₃₇	1	1	yes	characteristic
36	#6861	C₃×C₃₇	1	3	yes	—
37	#6860	C₃×C₃₇	1	3	yes	—
38	#6858	C₃×C₃₇	1	3	yes	—
39	C₃×C₃₇	—	9	1	no	—
40	C₃×C₃₇	C₃×#733	1	1	yes	characteristic
41	C₃×C₃₇	#6908	1	3	yes	—
42	C₃×3₋¹⁺²	C₃²×C₃₇	1	3	yes	—
43	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
44	C₉⋊C₉	—	3	2	no	—
45	C₉⋊C₉	—	3	6	no	—
46	C₃²⋊C₉	C₃²×C₃₇	1	3	yes	—
47	C₃²⋊C₉	C₃²×C₃₇	1	3	yes	—
48	C₃²⋊C₉	C₃²×C₃₇	1	3	yes	—
49	C₉²	—	3	1	no	—
50	C₉²	—	3	3	no	—
51	C₃₇	#10624588	1	1	yes	characteristic, direct product factor, Sylow
52	C₃³	C₃³×C₃₇	1	1	yes	characteristic
53	3₋¹⁺²	—	3	9	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	3	3	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	—	3	3	no	—
59	C₃×C₉	H(3,𝔽₃)×C₃₇	1	2	yes	—
60	C₃×C₉	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
61	C₃²	—	3	1	no	—
62	C₃²	—	3	3	no	—
63	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
64	C₉	—	3	2	no	—
65	C₉	—	3	9	no	—
66	C₉	—	9	3	no	—
67	C₉	—	9	3	no	—
68	C₉	—	9	3	no	—
69	C₉	C₃₇×#733	1	3	yes	—
70	C₃	—	9	1	no	—
71	C₃	C₃×C₃₇×#733	1	1	yes	characteristic
72	C₃	C₃₇×#6908	1	3	yes	—

	subgroup	G/H
center	C₃×C₉×C₃₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
prime radical	C₃³×C₃₇	C₃³
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₃₇ ◁ C₃²×C₉×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
24. #10624588	C₃₇	direct (N × H)
51. C₃₇	#10624588	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×3₋¹⁺²×C₃₇	3
C₃₇×#6887	3
C₃₇×#6861	3
C₃₇×#6860	3
C₃₇×#6858	3
#10624588	37

Subgroups — C37×#10624588 #41004377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624588 #41004377