Subgroups — C₃₇×#10624906 #41004695

Order 26973.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6898	C₃	1	9	yes	maximal, complemented
2	C₃₇×#6897	C₃	1	9	yes	maximal, complemented
3	C₃₇×#6894	C₃	1	12	yes	maximal, complemented
4	C₃₇×#6891	C₃	1	2	yes	maximal
5	C₉×3₋¹⁺²×C₃₇	C₃	1	6	yes	maximal, complemented
6	C₃×C₃₇×C₃²⋊C₉	C₃	1	2	yes	maximal
7	C₃⁴×C₃₇	C₃²	1	1	yes	characteristic
8	C₃×3₋¹⁺²×C₃₇	C₃²	1	6	yes	—
9	C₃²×C₉×C₃₇	C₃²	1	6	yes	—
10	C₃₇×C₉⋊C₉	C₃²	1	36	yes	complemented
11	C₃₇×C₉⋊C₉	C₃²	1	36	yes	complemented
12	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
13	C₃₇×C₃²⋊C₉	C₃²	1	4	yes	—
14	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
15	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
16	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
17	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
19	C₉²×C₃₇	C₃²	1	9	yes	complemented
20	C₃³×C₃₇	—	3	6	no	—
21	C₃³×C₃₇	—	9	2	no	—
22	C₃³×C₃₇	C₃³	1	1	yes	characteristic
23	C₃³×C₃₇	C₃³	1	1	yes	characteristic
24	C₃³×C₃₇	C₃³	1	2	yes	—
25	3₋¹⁺²×C₃₇	—	3	18	no	—
26	C₃×C₉×C₃₇	—	9	6	no	—
27	C₃×C₉×C₃₇	C₃³	1	6	yes	—
28	C₃×C₉×C₃₇	C₃³	1	18	yes	—
29	C₃×C₉×C₃₇	C₃³	1	12	yes	—
30	#10624906	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₃²×C₃₇	—	3	2	no	—
32	C₃²×C₃₇	—	3	2	no	—
33	C₃²×C₃₇	—	3	2	no	—
34	C₃²×C₃₇	—	3	2	no	—
35	C₃²×C₃₇	—	3	2	no	—
36	C₃²×C₃₇	—	3	2	no	—
37	C₃²×C₃₇	—	3	2	no	—
38	C₃²×C₃₇	—	9	9	no	—
39	C₃²×C₃₇	#737	1	6	yes	—
40	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
41	C₉×C₃₇	—	3	18	no	—
42	C₉×C₃₇	—	3	6	no	—
43	C₉×C₃₇	—	3	12	no	—
44	#6898	C₃×C₃₇	1	9	yes	complemented
45	#6897	C₃×C₃₇	1	9	yes	complemented
46	#6894	C₃×C₃₇	1	12	yes	complemented
47	#6891	C₃×C₃₇	1	2	yes	—
48	C₉×3₋¹⁺²	C₃×C₃₇	1	6	yes	complemented
49	C₃×C₃²⋊C₉	C₃×C₃₇	1	2	yes	—
50	C₃×C₃₇	—	3	6	no	—
51	C₃×C₃₇	—	9	1	no	—
52	C₃×C₃₇	—	9	1	no	—
53	C₃×C₃₇	C₃×#737	1	2	yes	—
54	C₃×C₃₇	3₋¹⁺⁴	1	2	yes	—
55	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
56	C₃×3₋¹⁺²	C₃²×C₃₇	1	6	yes	—
57	C₃²×C₉	C₃²×C₃₇	1	6	yes	—
58	C₉⋊C₉	C₃²×C₃₇	1	36	yes	complemented
59	C₉⋊C₉	C₃²×C₃₇	1	36	yes	complemented
60	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
61	C₃²⋊C₉	C₃²×C₃₇	1	4	yes	—
62	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
63	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
64	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
65	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
66	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
67	C₉²	C₃²×C₃₇	1	9	yes	complemented
68	C₃₇	#10624906	1	1	yes	characteristic, direct product factor, Sylow
69	C₃³	—	3	6	no	—
70	C₃³	—	9	2	no	—
71	C₃³	C₃³×C₃₇	1	1	yes	characteristic
72	C₃³	C₃³×C₃₇	1	1	yes	characteristic
73	C₃³	C₃³×C₃₇	1	2	yes	—
74	3₋¹⁺²	—	3	18	no	—
75	C₃×C₉	—	9	6	no	—
76	C₃×C₉	C₃³×C₃₇	1	6	yes	—
77	C₃×C₉	C₃³×C₃₇	1	18	yes	—
78	C₃×C₉	C₃³×C₃₇	1	12	yes	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	3	2	no	—
83	C₃²	—	3	2	no	—
84	C₃²	—	3	2	no	—
85	C₃²	—	3	2	no	—
86	C₃²	—	9	9	no	—
87	C₃²	C₃₇×#737	1	6	yes	—
88	C₃²	C₃⁴×C₃₇	1	1	yes	characteristic
89	C₉	—	3	18	no	—
90	C₉	—	3	6	no	—
91	C₉	—	3	12	no	—
92	C₃	—	3	6	no	—
93	C₃	—	9	1	no	—
94	C₃	—	9	1	no	—
95	C₃	C₃×C₃₇×#737	1	2	yes	—
96	C₃	C₃₇×3₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₃₇	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₃₇
prime radical	C₃⁴×C₃₇	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#6898	C₃	semidirect
2. C₃₇×#6897	C₃	semidirect
3. C₃₇×#6894	C₃	semidirect
5. C₉×3₋¹⁺²×C₃₇	C₃	semidirect
10. C₃₇×C₉⋊C₉	C₃²	semidirect
11. C₃₇×C₉⋊C₉	C₃²	semidirect
19. C₉²×C₃₇	C₃²	semidirect
30. #10624906	C₃₇	direct (N × H)
44. #6898	C₃×C₃₇	semidirect
45. #6897	C₃×C₃₇	semidirect
46. #6894	C₃×C₃₇	semidirect
48. C₉×3₋¹⁺²	C₃×C₃₇	semidirect
58. C₉⋊C₉	C₃²×C₃₇	semidirect
59. C₉⋊C₉	C₃²×C₃₇	semidirect
67. C₉²	C₃²×C₃₇	semidirect
68. C₃₇	#10624906	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×#6898	3
C₃₇×#6897	3
C₃₇×#6894	3
C₃₇×#6891	3
C₉×3₋¹⁺²×C₃₇	3
C₃×C₃₇×C₃²⋊C₉	3
#10624906	37

Subgroups — C37×#10624906 #41004695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624906 #41004695