Subgroups — C₃₇×#10624458 #41004247

Order 26973.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic
2	C₃₇×C₃²⋊C₂₇	C₃	1	3	yes	maximal
3	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
4	C₃×C₂₇×C₃₇	—	3	3	no	—
5	C₃₇×C₉⋊C₉	—	3	2	no	—
6	C₃₇×C₃²⋊C₉	C₉	1	3	yes	—
7	C₉²×C₃₇	—	3	1	no	—
8	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
9	C₃×C₉×C₃₇	—	3	1	no	—
10	C₃×C₉×C₃₇	—	3	2	no	—
11	C₃×C₉×C₃₇	—	3	3	no	—
12	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
14	C₂₇×C₃₇	—	9	3	no	—
15	#10624458	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃²×C₃₇	—	3	1	no	—
17	C₃²×C₃₇	—	3	3	no	—
18	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
19	C₉×C₃₇	—	3	2	no	—
20	C₉×C₃₇	—	9	3	no	—
21	C₉×C₃₇	#732	1	1	yes	characteristic
22	C₉×C₃₇	#733	1	2	yes	—
23	#6887	C₃×C₃₇	1	1	yes	characteristic
24	C₃²⋊C₂₇	C₃×C₃₇	1	3	yes	—
25	C₃×C₃₇	—	9	1	no	—
26	C₃×C₃₇	#6868	1	1	yes	characteristic
27	C₃×C₃₇	#6872	1	3	yes	—
28	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
29	C₃×C₂₇	—	3	3	no	—
30	C₉⋊C₉	—	3	2	no	—
31	C₃²⋊C₉	C₉×C₃₇	1	3	yes	—
32	C₉²	—	3	1	no	—
33	C₃₇	#10624458	1	1	yes	characteristic, direct product factor, Sylow
34	C₃³	C₃×C₉×C₃₇	1	1	yes	characteristic
35	C₃×C₉	—	3	1	no	—
36	C₃×C₉	—	3	2	no	—
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
39	C₃×C₉	3₋¹⁺²×C₃₇	1	2	yes	—
40	C₂₇	—	9	3	no	—
41	C₃²	—	3	1	no	—
42	C₃²	—	3	3	no	—
43	C₃²	C₃₇×C₃²⋊C₉	1	1	yes	characteristic
44	C₉	—	3	2	no	—
45	C₉	—	9	3	no	—
46	C₉	C₃₇×#732	1	1	yes	characteristic
47	C₉	C₃₇×#733	1	2	yes	—
48	C₃	—	9	1	no	—
49	C₃	C₃₇×#6868	1	1	yes	characteristic
50	C₃	C₃₇×#6872	1	3	yes	—

	subgroup	G/H
center	C₃×C₉×C₃₇	H(3,𝔽₃)
commutator	C₃³	C₃×C₉×C₃₇
Frattini, cosocle	C₃²×C₉	C₃²×C₃₇
socle	C₃²×C₃₇	C₃²⋊C₉
prime radical	C₃³×C₃₇	C₃×C₉
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
15. #10624458	C₃₇	direct (N × H)
33. C₃₇	#10624458	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×#6887	3
C₃₇×C₃²⋊C₂₇	3
#10624458	37

Subgroups — C37×#10624458 #41004247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624458 #41004247