Subgroups — C₃₇×#10624902 #41004691

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×#6896	C₃	1	9	yes	maximal, complemented
3	C₃₇×#6895	C₃	1	12	yes	maximal, complemented
4	C₃₇×#6891	C₃	1	2	yes	maximal
5	C₃₇×#6887	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	12	yes	—
17	C₃₇×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₉²×C₃₇	C₃²	1	9	yes	complemented
19	C₃³×C₃₇	—	3	6	no	—
20	C₃³×C₃₇	—	9	2	no	—
21	C₃³×C₃₇	C₃³	1	1	yes	characteristic
22	C₃³×C₃₇	C₃³	1	1	yes	characteristic
23	C₃³×C₃₇	C₃³	1	2	yes	—
24	3₋¹⁺²×C₃₇	—	9	6	no	—
25	C₃×C₉×C₃₇	—	3	18	no	—
26	C₃×C₉×C₃₇	C₃³	1	6	yes	—
27	C₃×C₉×C₃₇	C₃³	1	18	yes	—
28	C₃×C₉×C₃₇	C₃³	1	12	yes	—
29	#10624902	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₃²×C₃₇	—	3	2	no	—
31	C₃²×C₃₇	—	3	4	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	—	9	9	no	—
37	C₃²×C₃₇	#737	1	6	yes	—
38	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
39	C₉×C₃₇	—	3	6	no	—
40	C₉×C₃₇	—	3	12	no	—
41	C₉×C₃₇	—	3	18	no	—
42	#6898	C₃×C₃₇	1	9	yes	complemented
43	#6896	C₃×C₃₇	1	9	yes	complemented
44	#6895	C₃×C₃₇	1	12	yes	complemented
45	#6891	C₃×C₃₇	1	2	yes	—
46	#6887	C₃×C₃₇	1	6	yes	complemented
47	C₃×C₃²⋊C₉	C₃×C₃₇	1	2	yes	—
48	C₃×C₃₇	—	3	6	no	—
49	C₃×C₃₇	—	9	1	no	—
50	C₃×C₃₇	—	9	1	no	—
51	C₃×C₃₇	C₃×#737	1	2	yes	—
52	C₃×C₃₇	3₋¹⁺⁴	1	2	yes	—
53	C₃⁴	C₃²×C₃₇	1	1	yes	characteristic
54	C₃×3₋¹⁺²	C₃²×C₃₇	1	6	yes	—
55	C₃²×C₉	C₃²×C₃₇	1	6	yes	—
56	C₉⋊C₉	C₃²×C₃₇	1	36	yes	complemented
57	C₉⋊C₉	C₃²×C₃₇	1	36	yes	complemented
58	C₃²⋊C₉	C₃²×C₃₇	1	2	yes	—
59	C₃²⋊C₉	C₃²×C₃₇	1	4	yes	—
60	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
61	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
62	C₃²⋊C₉	C₃²×C₃₇	1	12	yes	—
63	C₃²⋊C₉	C₃²×C₃₇	1	6	yes	—
64	C₉²	C₃²×C₃₇	1	9	yes	complemented
65	C₃₇	#10624902	1	1	yes	characteristic, direct product factor, Sylow
66	C₃³	—	3	6	no	—
67	C₃³	—	9	2	no	—
68	C₃³	C₃³×C₃₇	1	1	yes	characteristic
69	C₃³	C₃³×C₃₇	1	1	yes	characteristic
70	C₃³	C₃³×C₃₇	1	2	yes	—
71	3₋¹⁺²	—	9	6	no	—
72	C₃×C₉	—	3	18	no	—
73	C₃×C₉	C₃³×C₃₇	1	6	yes	—
74	C₃×C₉	C₃³×C₃₇	1	18	yes	—
75	C₃×C₉	C₃³×C₃₇	1	12	yes	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	4	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	9	9	no	—
83	C₃²	C₃₇×#737	1	6	yes	—
84	C₃²	C₃⁴×C₃₇	1	1	yes	characteristic
85	C₉	—	3	6	no	—
86	C₉	—	3	12	no	—
87	C₉	—	3	18	no	—
88	C₃	—	3	6	no	—
89	C₃	—	9	1	no	—
90	C₃	—	9	1	no	—
91	C₃	C₃×C₃₇×#737	1	2	yes	—
92	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×#6896	C₃	semidirect
3. C₃₇×#6895	C₃	semidirect
5. C₃₇×#6887	C₃	semidirect
10. C₃₇×C₉⋊C₉	C₃²	semidirect
11. C₃₇×C₉⋊C₉	C₃²	semidirect
18. C₉²×C₃₇	C₃²	semidirect
29. #10624902	C₃₇	direct (N × H)
42. #6898	C₃×C₃₇	semidirect
43. #6896	C₃×C₃₇	semidirect
44. #6895	C₃×C₃₇	semidirect
46. #6887	C₃×C₃₇	semidirect
56. C₉⋊C₉	C₃²×C₃₇	semidirect
57. C₉⋊C₉	C₃²×C₃₇	semidirect
64. C₉²	C₃²×C₃₇	semidirect
65. C₃₇	#10624902	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×#6896	3
C₃₇×#6895	3
C₃₇×#6891	3
C₃₇×#6887	3
C₃×C₃₇×C₃²⋊C₉	3
#10624902	37

Subgroups — C37×#10624902 #41004691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624902 #41004691