Subgroups — C₃₇×#10624674 #41004463

Order 26973.

170 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6895	C₃	1	1	yes	maximal, characteristic
2	C₃₇×#6894	C₃	1	3	yes	maximal
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	9	no	—
9	C₃₇×C₉⋊C₉	—	3	3	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	C₃³×C₃₇	C₃³	1	1	yes	characteristic
14	3₋¹⁺²×C₃₇	—	9	3	no	—
15	C₃×C₉×C₃₇	—	3	3	no	—
16	C₃×C₉×C₃₇	—	3	3	no	—
17	C₃×C₉×C₃₇	—	3	3	no	—
18	C₃×C₉×C₃₇	—	3	3	no	—
19	C₃×C₉×C₃₇	—	9	1	no	—
20	C₃×C₉×C₃₇	H(3,𝔽₃)	1	3	yes	—
21	#10624674	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃²×C₃₇	—	3	1	no	—
23	C₃²×C₃₇	—	3	3	no	—
24	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
25	C₉×C₃₇	—	3	3	no	—
26	C₉×C₃₇	—	9	3	no	—
27	C₉×C₃₇	—	9	3	no	—
28	C₉×C₃₇	—	9	3	no	—
29	C₉×C₃₇	—	9	3	no	—
30	#6895	C₃×C₃₇	1	1	yes	characteristic
31	#6894	C₃×C₃₇	1	3	yes	—
32	#6861	C₃×C₃₇	1	3	yes	—
33	#6860	C₃×C₃₇	1	3	yes	—
34	#6858	C₃×C₃₇	1	3	yes	—
35	C₃×C₃₇	—	9	1	no	—
36	C₃×C₃₇	#6912	1	1	yes	characteristic
37	C₃×C₃₇	#6913	1	3	yes	—
38	C₃×3₋¹⁺²	C₃²×C₃₇	1	3	yes	—
39	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
40	C₉⋊C₉	—	3	9	no	—
41	C₉⋊C₉	—	3	3	no	—
42	C₃²⋊C₉	C₃²×C₃₇	1	3	yes	—
43	C₃²⋊C₉	C₃²×C₃₇	1	3	yes	—
44	C₃²⋊C₉	C₃²×C₃₇	1	3	yes	—
45	C₃₇	#10624674	1	1	yes	characteristic, direct product factor, Sylow
46	C₃³	C₃³×C₃₇	1	1	yes	characteristic
47	3₋¹⁺²	—	9	3	no	—
48	C₃×C₉	—	3	3	no	—
49	C₃×C₉	—	3	3	no	—
50	C₃×C₉	—	3	3	no	—
51	C₃×C₉	—	3	3	no	—
52	C₃×C₉	—	9	1	no	—
53	C₃×C₉	H(3,𝔽₃)×C₃₇	1	3	yes	—
54	C₃²	—	3	1	no	—
55	C₃²	—	3	3	no	—
56	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
57	C₉	—	3	3	no	—
58	C₉	—	9	3	no	—
59	C₉	—	9	3	no	—
60	C₉	—	9	3	no	—
61	C₉	—	9	3	no	—
62	C₃	—	9	1	no	—
63	C₃	C₃₇×#6912	1	1	yes	characteristic
64	C₃	C₃₇×#6913	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
21. #10624674	C₃₇	direct (N × H)
45. C₃₇	#10624674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#6895	3
C₃₇×#6894	3
C₃₇×#6861	3
C₃₇×#6860	3
C₃₇×#6858	3
#10624674	37

Subgroups — C37×#10624674 #41004463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624674 #41004463