Subgroups — C₃₇×#10624576 #41004365

Order 26973.

254 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃₇×#6855	C₃	1	9	yes	maximal
3	C₃₇×#6855	C₃	1	2	yes	maximal
4	C₃₇×#6855	C₃	1	1	yes	maximal, characteristic
5	C₃²×C₉×C₃₇	C₃²	1	6	yes	—
6	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
7	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
8	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
9	C₃₇×C₉⋊C₉	—	3	3	no	—
10	C₃³×C₃₇	C₃³	1	1	yes	characteristic
11	C₃×C₉×C₃₇	—	3	2	no	—
12	C₃×C₉×C₃₇	—	3	1	no	—
13	C₃×C₉×C₃₇	—	3	3	no	—
14	C₃×C₉×C₃₇	—	3	6	no	—
15	C₃×C₉×C₃₇	—	3	18	no	—
16	C₃×C₉×C₃₇	—	3	3	no	—
17	C₃×C₉×C₃₇	—	3	9	no	—
18	C₃×C₉×C₃₇	—	3	9	no	—
19	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
20	#10624576	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
22	C₃²×C₃₇	#737	1	2	yes	—
23	C₃²×C₃₇	#737	1	1	yes	characteristic
24	C₃²×C₃₇	#737	1	9	yes	—
25	C₉×C₃₇	—	3	3	no	—
26	C₉×C₃₇	—	9	6	no	—
27	C₉×C₃₇	—	9	3	no	—
28	C₉×C₃₇	—	9	3	no	—
29	C₃×C₉⋊C₉	C₃×C₃₇	1	1	yes	characteristic
30	#6855	C₃×C₃₇	1	9	yes	—
31	#6855	C₃×C₃₇	1	2	yes	—
32	#6855	C₃×C₃₇	1	1	yes	characteristic
33	C₃×C₃₇	#6895	1	1	yes	characteristic
34	C₃×C₃₇	#6897	1	6	yes	—
35	C₃×C₃₇	#6898	1	3	yes	—
36	C₃×C₃₇	#6899	1	3	yes	—
37	C₃²×C₉	C₃²×C₃₇	1	6	yes	—
38	C₃²×C₉	C₃²×C₃₇	1	3	yes	—
39	C₃²×C₉	C₃²×C₃₇	1	3	yes	—
40	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
41	C₉⋊C₉	—	3	3	no	—
42	C₃₇	#10624576	1	1	yes	characteristic, direct product factor, Sylow
43	C₃³	C₃³×C₃₇	1	1	yes	characteristic
44	C₃×C₉	—	3	2	no	—
45	C₃×C₉	—	3	1	no	—
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	—	3	6	no	—
48	C₃×C₉	—	3	18	no	—
49	C₃×C₉	—	3	3	no	—
50	C₃×C₉	—	3	9	no	—
51	C₃×C₉	—	3	9	no	—
52	C₃×C₉	3₋¹⁺²×C₃₇	1	3	yes	—
53	C₃²	C₃×3₋¹⁺²×C₃₇	1	1	yes	characteristic
54	C₃²	C₃₇×#737	1	2	yes	—
55	C₃²	C₃₇×#737	1	1	yes	characteristic
56	C₃²	C₃₇×#737	1	9	yes	—
57	C₉	—	3	3	no	—
58	C₉	—	9	6	no	—
59	C₉	—	9	3	no	—
60	C₉	—	9	3	no	—
61	C₃	C₃₇×#6895	1	1	yes	characteristic
62	C₃	C₃₇×#6897	1	6	yes	—
63	C₃	C₃₇×#6898	1	3	yes	—
64	C₃	C₃₇×#6899	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₃³×C₃₇	C₃³
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
20. #10624576	C₃₇	direct (N × H)
42. C₃₇	#10624576	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₇×C₉⋊C₉	3
C₃₇×#6855	3
#10624576	37

Subgroups — C37×#10624576 #41004365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624576 #41004365