Subgroups — C₃₇×#10624575 #41004364

Order 26973.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₉⋊C₉	C₃	1	3	yes	maximal
2	C₃×C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃₇×#6855	C₃	1	3	yes	maximal
4	C₃₇×#6855	C₃	1	3	yes	maximal
5	C₃₇×#6855	C₃	1	3	yes	maximal
6	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
7	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
8	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
9	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
11	C₃₇×C₉⋊C₉	—	3	9	no	—
12	C₃₇×C₉⋊C₉	—	3	3	no	—
13	C₃³×C₃₇	C₃³	1	1	yes	characteristic
14	C₃×C₉×C₃₇	—	3	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	—	3	3	no	—
20	C₃×C₉×C₃₇	—	3	3	no	—
21	C₃×C₉×C₃₇	—	3	3	no	—
22	C₃×C₉×C₃₇	—	3	3	no	—
23	C₃×C₉×C₃₇	—	3	3	no	—
24	C₃×C₉×C₃₇	—	3	6	no	—
25	C₃×C₉×C₃₇	—	3	3	no	—
26	C₃×C₉×C₃₇	—	3	3	no	—
27	C₃×C₉×C₃₇	—	3	6	no	—
28	C₃×C₉×C₃₇	3₋¹⁺²	1	9	yes	—
29	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
30	#10624575	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₃²×C₃₇	C₃×3₋¹⁺²	1	3	yes	—
32	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
33	C₃²×C₃₇	#737	1	3	yes	—
34	C₃²×C₃₇	#737	1	3	yes	—
35	C₃²×C₃₇	#737	1	3	yes	—
36	C₉×C₃₇	—	3	9	no	—
37	C₉×C₃₇	—	3	3	no	—
38	C₉×C₃₇	—	9	3	no	—
39	C₉×C₃₇	—	9	3	no	—
40	C₉×C₃₇	—	9	3	no	—
41	C₃×C₉⋊C₉	C₃×C₃₇	1	3	yes	—
42	C₃×C₉⋊C₉	C₃×C₃₇	1	1	yes	characteristic
43	#6855	C₃×C₃₇	1	3	yes	—
44	#6855	C₃×C₃₇	1	3	yes	—
45	#6855	C₃×C₃₇	1	3	yes	—
46	C₃×C₃₇	#6894	1	3	yes	—
47	C₃×C₃₇	#6895	1	1	yes	characteristic
48	C₃×C₃₇	#6896	1	3	yes	—
49	C₃×C₃₇	#6897	1	3	yes	—
50	C₃×C₃₇	#6899	1	3	yes	—
51	C₃²×C₉	C₃²×C₃₇	1	3	yes	—
52	C₃²×C₉	C₃²×C₃₇	1	3	yes	—
53	C₃²×C₉	C₃²×C₃₇	1	3	yes	—
54	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
55	C₃²×C₉	C₃²×C₃₇	1	3	yes	—
56	C₉⋊C₉	—	3	9	no	—
57	C₉⋊C₉	—	3	3	no	—
58	C₃₇	#10624575	1	1	yes	characteristic, direct product factor, Sylow
59	C₃³	C₃³×C₃₇	1	1	yes	characteristic
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	—	3	3	no	—
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	3	no	—
69	C₃×C₉	—	3	3	no	—
70	C₃×C₉	—	3	6	no	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	3	3	no	—
73	C₃×C₉	—	3	6	no	—
74	C₃×C₉	3₋¹⁺²×C₃₇	1	9	yes	—
75	C₃×C₉	3₋¹⁺²×C₃₇	1	3	yes	—
76	C₃²	C₃×3₋¹⁺²×C₃₇	1	3	yes	—
77	C₃²	C₃×3₋¹⁺²×C₃₇	1	1	yes	characteristic
78	C₃²	C₃₇×#737	1	3	yes	—
79	C₃²	C₃₇×#737	1	3	yes	—
80	C₃²	C₃₇×#737	1	3	yes	—
81	C₉	—	3	9	no	—
82	C₉	—	3	3	no	—
83	C₉	—	9	3	no	—
84	C₉	—	9	3	no	—
85	C₉	—	9	3	no	—
86	C₃	C₃₇×#6894	1	3	yes	—
87	C₃	C₃₇×#6895	1	1	yes	characteristic
88	C₃	C₃₇×#6896	1	3	yes	—
89	C₃	C₃₇×#6897	1	3	yes	—
90	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
30. #10624575	C₃₇	direct (N × H)
58. C₃₇	#10624575	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
#10624575	37

Subgroups — C37×#10624575 #41004364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624575 #41004364