Subgroups — C₃₇×#10624846 #41004635

Order 26973.

210 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, complemented
2	C₃×C₃₇×#732	C₃	1	2	yes	maximal, complemented
3	C₃₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#6881	C₃	1	9	yes	maximal, complemented
5	C₃×3₋¹⁺²×C₃₇	—	3	1	no	—
6	C₃×H(3,𝔽₃)×C₃₇	—	3	2	no	—
7	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
8	C₃₇×#733	—	3	1	no	—
9	C₃₇×#733	—	3	1	no	—
10	C₃₇×#733	C₃²	1	3	yes	complemented
11	C₃₇×#732	—	3	2	no	—
12	C₃₇×#732	—	3	2	no	—
13	C₃₇×#732	C₃²	1	6	yes	complemented
14	C₃₇×C₉⋊C₉	—	3	1	no	—
15	C₃₇×C₉⋊C₉	C₃²	1	3	yes	complemented
16	C₃₇×C₃²⋊C₉	—	3	1	no	—
17	C₉²×C₃₇	—	3	1	no	—
18	C₃³×C₃₇	—	9	2	no	—
19	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
20	3₋¹⁺²×C₃₇	—	3	3	no	—
21	3₋¹⁺²×C₃₇	—	9	2	no	—
22	H(3,𝔽₃)×C₃₇	—	3	6	no	—
23	H(3,𝔽₃)×C₃₇	—	9	2	no	—
24	H(3,𝔽₃)×C₃₇	—	9	2	no	—
25	C₃×C₉×C₃₇	—	3	1	no	—
26	C₃×C₉×C₃₇	—	3	2	no	—
27	C₃×C₉×C₃₇	—	3	3	no	—
28	C₃×C₉×C₃₇	—	9	1	no	—
29	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
30	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
31	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
32	#10624846	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₃²×C₃₇	—	9	1	no	—
34	C₃²×C₃₇	—	9	6	no	—
35	C₃²×C₃₇	—	27	6	no	—
36	C₃²×C₃₇	#732	1	1	yes	characteristic
37	C₃²×C₃₇	#732	1	2	yes	—
38	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₉×C₃₇	—	3	1	no	—
40	C₉×C₃₇	—	3	1	no	—
41	C₉×C₃₇	—	3	1	no	—
42	C₉×C₃₇	—	9	3	no	—
43	C₉×C₃₇	—	9	3	no	—
44	C₃×#733	C₃×C₃₇	1	1	yes	characteristic, complemented
45	C₃×#732	C₃×C₃₇	1	2	yes	complemented
46	#6887	C₃×C₃₇	1	1	yes	characteristic, complemented
47	#6881	C₃×C₃₇	1	9	yes	complemented
48	C₃×C₃₇	—	3	1	no	—
49	C₃×C₃₇	—	3	2	no	—
50	C₃×C₃₇	—	3	1	no	—
51	C₃×C₃₇	—	27	6	no	—
52	C₃×C₃₇	C₃×#732	1	1	yes	characteristic
53	C₃×3₋¹⁺²	—	3	1	no	—
54	C₃×H(3,𝔽₃)	—	3	2	no	—
55	C₃²×C₉	C₃²×C₃₇	1	1	yes	characteristic
56	#733	—	3	1	no	—
57	#733	—	3	1	no	—
58	#733	C₃²×C₃₇	1	3	yes	complemented
59	#732	—	3	2	no	—
60	#732	—	3	2	no	—
61	#732	C₃²×C₃₇	1	6	yes	complemented
62	C₉⋊C₉	—	3	1	no	—
63	C₉⋊C₉	C₃²×C₃₇	1	3	yes	complemented
64	C₃²⋊C₉	—	3	1	no	—
65	C₉²	—	3	1	no	—
66	C₃₇	#10624846	1	1	yes	characteristic, direct product factor, Sylow
67	C₃³	—	9	2	no	—
68	C₃³	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
69	3₋¹⁺²	—	3	3	no	—
70	3₋¹⁺²	—	9	2	no	—
71	H(3,𝔽₃)	—	3	6	no	—
72	H(3,𝔽₃)	—	9	2	no	—
73	H(3,𝔽₃)	—	9	2	no	—
74	C₃×C₉	—	3	1	no	—
75	C₃×C₉	—	3	2	no	—
76	C₃×C₉	—	3	3	no	—
77	C₃×C₉	—	9	1	no	—
78	C₃×C₉	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
79	C₃×C₉	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
80	C₃×C₉	C₃³×C₃₇	1	1	yes	characteristic
81	C₃²	—	9	1	no	—
82	C₃²	—	9	6	no	—
83	C₃²	—	27	6	no	—
84	C₃²	C₃₇×#732	1	1	yes	characteristic
85	C₃²	C₃₇×#732	1	2	yes	—
86	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
87	C₉	—	3	1	no	—
88	C₉	—	3	1	no	—
89	C₉	—	3	1	no	—
90	C₉	—	9	3	no	—
91	C₉	—	9	3	no	—
92	C₃	—	3	1	no	—
93	C₃	—	3	2	no	—
94	C₃	—	3	1	no	—
95	C₃	—	27	6	no	—
96	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 ◁ C₃³×C₃₇ ◁ C₃²×C₉×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₇×#733	C₃	semidirect
2. C₃×C₃₇×#732	C₃	semidirect
3. C₃₇×#6887	C₃	semidirect
4. C₃₇×#6881	C₃	semidirect
10. C₃₇×#733	C₃²	semidirect
13. C₃₇×#732	C₃²	semidirect
15. C₃₇×C₉⋊C₉	C₃²	semidirect
32. #10624846	C₃₇	direct (N × H)
44. C₃×#733	C₃×C₃₇	semidirect
45. C₃×#732	C₃×C₃₇	semidirect
46. #6887	C₃×C₃₇	semidirect
47. #6881	C₃×C₃₇	semidirect
58. #733	C₃²×C₃₇	semidirect
61. #732	C₃²×C₃₇	semidirect
63. C₉⋊C₉	C₃²×C₃₇	semidirect
66. C₃₇	#10624846	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
C₃×C₃₇×#732	3
C₃₇×#6887	3
C₃₇×#6881	3
#10624846	37

Subgroups — C37×#10624846 #41004635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#10624846 #41004635