Subgroups — C₃₇×#10624491 #41004280

Order 26973.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×#733	C₃	1	1	yes	maximal, characteristic
2	C₃₇×#6868	C₃	1	2	yes	maximal
3	C₃₇×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃×3₋¹⁺²×C₃₇	—	3	1	no	—
5	C₃²×C₉×C₃₇	—	3	1	no	—
6	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
7	C₃₇×#733	—	3	3	no	—
8	C₃₇×C₃²⋊C₉	—	3	2	no	—
9	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
10	3₋¹⁺²×C₃₇	—	3	3	no	—
11	3₋¹⁺²×C₃₇	—	9	2	no	—
12	C₃×C₉×C₃₇	—	3	3	no	—
13	C₃×C₉×C₃₇	—	3	1	no	—
14	C₃×C₉×C₃₇	—	3	2	no	—
15	C₃×C₉×C₃₇	—	3	1	no	—
16	C₃×C₉×C₃₇	—	9	1	no	—
17	C₃×C₉×C₃₇	—	9	1	no	—
18	C₃×C₉×C₃₇	—	9	1	no	—
19	C₃×C₉×C₃₇	—	9	1	no	—
20	C₃×C₉×C₃₇	—	9	2	no	—
21	#10624491	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃²×C₃₇	—	3	1	no	—
23	C₃²×C₃₇	—	3	1	no	—
24	C₃²×C₃₇	—	3	1	no	—
25	C₃²×C₃₇	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
26	C₃²×C₃₇	#731	1	2	yes	—
27	C₃²×C₃₇	#732	1	1	yes	characteristic
28	C₉×C₃₇	—	9	3	no	—
29	C₉×C₃₇	—	9	1	no	—
30	C₉×C₃₇	—	9	3	no	—
31	C₉×C₃₇	—	27	2	no	—
32	C₃×#733	C₃×C₃₇	1	1	yes	characteristic
33	#6868	C₃×C₃₇	1	2	yes	—
34	#6855	C₃×C₃₇	1	1	yes	characteristic
35	C₃×C₃₇	—	3	1	no	—
36	C₃×C₃₇	—	3	2	no	—
37	C₃×C₃₇	#6859	1	1	yes	characteristic
38	C₃×C₃₇	#6880	1	1	yes	characteristic
39	C₃×C₃₇	#6881	1	1	yes	characteristic
40	C₃×C₃₇	#6882	1	1	yes	characteristic
41	C₃×3₋¹⁺²	—	3	1	no	—
42	C₃²×C₉	—	3	1	no	—
43	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
44	#733	—	3	3	no	—
45	C₃²⋊C₉	—	3	2	no	—
46	C₃₇	#10624491	1	1	yes	characteristic, direct product factor, Sylow
47	C₃³	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
48	3₋¹⁺²	—	3	3	no	—
49	3₋¹⁺²	—	9	2	no	—
50	C₃×C₉	—	3	3	no	—
51	C₃×C₉	—	3	1	no	—
52	C₃×C₉	—	3	2	no	—
53	C₃×C₉	—	3	1	no	—
54	C₃×C₉	—	9	1	no	—
55	C₃×C₉	—	9	1	no	—
56	C₃×C₉	—	9	1	no	—
57	C₃×C₉	—	9	1	no	—
58	C₃×C₉	—	9	2	no	—
59	C₃²	—	3	1	no	—
60	C₃²	—	3	1	no	—
61	C₃²	—	3	1	no	—
62	C₃²	C₃₇×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
63	C₃²	C₃₇×#731	1	2	yes	—
64	C₃²	C₃₇×#732	1	1	yes	characteristic
65	C₉	—	9	3	no	—
66	C₉	—	9	1	no	—
67	C₉	—	9	3	no	—
68	C₉	—	27	2	no	—
69	C₃	—	3	1	no	—
70	C₃	—	3	2	no	—
71	C₃	C₃₇×#6859	1	1	yes	characteristic
72	C₃	C₃₇×#6880	1	1	yes	characteristic
73	C₃	C₃₇×#6881	1	1	yes	characteristic
74	C₃	C₃₇×#6882	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₃₇	#732
commutator, Frattini, cosocle	C₃²×C₉	C₃²×C₃₇
prime radical	C₃³×C₃₇	H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ C₃³×C₃₇ ◁ C₃²×C₉×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
21. #10624491	C₃₇	direct (N × H)
46. C₃₇	#10624491	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×#733	3
C₃₇×#6868	3
C₃₇×#6855	3
#10624491	37

Subgroups — C37×#10624491 #41004280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624491 #41004280