Subgroups — C₃₇×#10624850 #41004639

Order 26973.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6908	C₃	1	3	yes	maximal, complemented
2	C₃×C₃₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#6883	C₃	1	3	yes	maximal, complemented
4	C₃₇×#6882	C₃	1	3	yes	maximal, complemented
5	C₃₇×#6881	C₃	1	3	yes	maximal, complemented
6	C₃₇×#737	—	3	3	no	—
7	C₃²×C₉×C₃₇	—	3	1	no	—
8	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
9	C₃₇×#733	C₃²	1	3	yes	—
10	C₃₇×#733	C₃²	1	3	yes	—
11	C₃₇×#732	C₃²	1	3	yes	—
12	C₃₇×#731	—	3	3	no	—
13	C₃₇×AΣL(1,𝔽₂₇)	—	3	3	no	—
14	C₃₇×C₉⋊C₉	—	3	1	no	—
15	C₃₇×C₉⋊C₉	—	3	1	no	—
16	C₃₇×C₉⋊C₉	C₃²	1	3	yes	—
17	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
18	3₋¹⁺²×C₃₇	—	3	3	no	—
19	3₋¹⁺²×C₃₇	—	3	3	no	—
20	3₋¹⁺²×C₃₇	—	9	6	no	—
21	H(3,𝔽₃)×C₃₇	—	3	3	no	—
22	C₃×C₉×C₃₇	—	3	3	no	—
23	C₃×C₉×C₃₇	—	3	3	no	—
24	C₃×C₉×C₃₇	—	9	3	no	—
25	C₃×C₉×C₃₇	—	9	3	no	—
26	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
29	#10624850	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₃²×C₃₇	—	3	3	no	—
31	C₃²×C₃₇	—	3	1	no	—
32	C₃²×C₃₇	—	9	3	no	—
33	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₉×C₃₇	—	3	1	no	—
35	C₉×C₃₇	—	3	1	no	—
36	C₉×C₃₇	—	9	3	no	—
37	C₉×C₃₇	—	9	3	no	—
38	C₉×C₃₇	—	9	3	no	—
39	C₉×C₃₇	#732	1	3	yes	—
40	#6908	C₃×C₃₇	1	3	yes	complemented
41	C₃×C₉⋊C₉	C₃×C₃₇	1	1	yes	characteristic, complemented
42	#6883	C₃×C₃₇	1	3	yes	complemented
43	#6882	C₃×C₃₇	1	3	yes	complemented
44	#6881	C₃×C₃₇	1	3	yes	complemented
45	C₃×C₃₇	—	3	1	no	—
46	C₃×C₃₇	—	3	3	no	—
47	C₃×C₃₇	—	27	3	no	—
48	C₃×C₃₇	C₃×#732	1	1	yes	characteristic
49	#737	—	3	3	no	—
50	C₃²×C₉	—	3	1	no	—
51	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
52	#733	C₃²×C₃₇	1	3	yes	—
53	#733	C₃²×C₃₇	1	3	yes	—
54	#732	C₃²×C₃₇	1	3	yes	—
55	#731	—	3	3	no	—
56	AΣL(1,𝔽₂₇)	—	3	3	no	—
57	C₉⋊C₉	—	3	1	no	—
58	C₉⋊C₉	—	3	1	no	—
59	C₉⋊C₉	C₃²×C₃₇	1	3	yes	—
60	C₃₇	#10624850	1	1	yes	characteristic, direct product factor, Sylow
61	C₃³	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
62	3₋¹⁺²	—	3	3	no	—
63	3₋¹⁺²	—	3	3	no	—
64	3₋¹⁺²	—	9	6	no	—
65	H(3,𝔽₃)	—	3	3	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	9	3	no	—
69	C₃×C₉	—	9	3	no	—
70	C₃×C₉	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
71	C₃×C₉	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
72	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
73	C₃²	—	3	3	no	—
74	C₃²	—	3	1	no	—
75	C₃²	—	9	3	no	—
76	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
77	C₉	—	3	1	no	—
78	C₉	—	3	1	no	—
79	C₉	—	9	3	no	—
80	C₉	—	9	3	no	—
81	C₉	—	9	3	no	—
82	C₉	C₃₇×#732	1	3	yes	—
83	C₃	—	3	1	no	—
84	C₃	—	3	3	no	—
85	C₃	—	27	3	no	—
86	C₃	C₃×C₃₇×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₃₇	C₃×#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₃₇
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₃₇ ◁ C₃×C₉×C₃₇ ◁ C₃²×C₉×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#6908	C₃	semidirect
2. C₃×C₃₇×C₉⋊C₉	C₃	semidirect
3. C₃₇×#6883	C₃	semidirect
4. C₃₇×#6882	C₃	semidirect
5. C₃₇×#6881	C₃	semidirect
29. #10624850	C₃₇	direct (N × H)
40. #6908	C₃×C₃₇	semidirect
41. C₃×C₉⋊C₉	C₃×C₃₇	semidirect
42. #6883	C₃×C₃₇	semidirect
43. #6882	C₃×C₃₇	semidirect
44. #6881	C₃×C₃₇	semidirect
60. C₃₇	#10624850	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×#6908	3
C₃×C₃₇×C₉⋊C₉	3
C₃₇×#6883	3
C₃₇×#6882	3
C₃₇×#6881	3
#10624850	37

Subgroups — C37×#10624850 #41004639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624850 #41004639