Subgroups — C₃₇⋊C₃×#6879 #41007325

Order 26973.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#732×C₃₇⋊C₃	C₃	1	3	yes	maximal, complemented
2	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#22582507	C₃	1	2	yes	maximal, complemented
4	#22582506	C₃	1	6	yes	maximal, complemented
5	C₃₇×#6879	C₃	1	1	yes	maximal, characteristic, complemented
6	H(3,𝔽₃)×C₃₇⋊C₃	—	3	3	no	—
7	C₃×C₉×C₃₇⋊C₃	—	3	1	no	—
8	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
9	#15688519	C₃²	1	6	yes	complemented
10	#15688518	—	3	6	no	—
11	C₉×#66524	—	3	2	no	—
12	C₉×#66524	C₃²	1	2	yes	complemented
13	C₃₇×#732	C₃²	1	3	yes	complemented
14	C₉²×C₃₇	C₃²	1	1	yes	characteristic, complemented
15	C₃²×C₃₇⋊C₃	—	9	3	no	—
16	C₃²×C₃₇⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
17	H(3,𝔽₃)×C₃₇	—	3	3	no	—
18	C₃×C₉×C₃₇	—	3	1	no	—
19	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
20	C₃²⋊(C₃₇⋊C₃)	—	3	6	no	—
21	C₃²⋊(C₃₇⋊C₃)	—	9	6	no	—
22	C₃×#66524	—	3	2	no	—
23	C₃×#66524	H(3,𝔽₃)	1	2	yes	—
24	C₉×C₃₇⋊C₃	—	3	9	no	—
25	C₉×C₃₇⋊C₃	—	3	2	no	—
26	C₉×C₃₇⋊C₃	—	3	1	no	—
27	C₃×#6879	—	37	1	no	maximal, Sylow
28	C₃²×C₃₇	—	9	3	no	—
29	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
30	C₃×C₃₇⋊C₃	—	3	3	no	—
31	C₃×C₃₇⋊C₃	—	9	6	no	—
32	C₃×C₃₇⋊C₃	—	27	9	no	—
33	C₃×C₃₇⋊C₃	#732	1	2	yes	—
34	C₃×C₃₇⋊C₃	#732	1	1	yes	characteristic
35	C₉×C₃₇	—	3	3	no	—
36	C₉×C₃₇	—	3	1	no	—
37	#66524	—	3	6	no	—
38	#66524	—	3	2	no	—
39	C₃×#732	—	37	3	no	—
40	C₃×C₉²	—	37	1	no	—
41	#6879	—	37	6	no	—
42	#6879	—	37	2	no	—
43	#6879	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
44	C₃×C₃₇	—	3	1	no	—
45	C₃×C₃₇	—	27	3	no	—
46	C₃×C₃₇	C₃×#732	1	1	yes	characteristic
47	C₃₇⋊C₃	—	3	2	no	—
48	C₃₇⋊C₃	—	27	6	no	—
49	C₃₇⋊C₃	#6879	1	3	yes	direct product factor
50	C₃×H(3,𝔽₃)	—	111	3	no	—
51	C₃²×C₉	—	37	1	no	—
52	C₃²×C₉	—	111	1	no	—
53	#732	—	37	6	no	—
54	#732	—	111	6	no	—
55	#732	C₃×C₃₇⋊C₃	1	3	yes	complemented
56	C₉²	—	37	2	no	—
57	C₉²	—	111	2	no	—
58	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented
59	C₃₇	C₃×#6879	1	1	yes	characteristic, complemented, Sylow
60	C₃³	—	37	1	no	—
61	C₃³	—	333	3	no	—
62	H(3,𝔽₃)	—	3	3	no	—
63	H(3,𝔽₃)	—	333	6	no	—
64	H(3,𝔽₃)	—	111	6	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	37	2	no	—
67	C₃×C₉	—	111	1	no	—
68	C₃×C₉	—	111	2	no	—
69	C₃×C₉	—	111	9	no	—
70	C₃×C₉	—	111	2	no	—
71	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
72	C₃²	—	9	3	no	—
73	C₃²	—	37	1	no	—
74	C₃²	—	37	2	no	—
75	C₃²	—	333	6	no	—
76	C₃²	—	111	3	no	—
77	C₃²	—	999	9	no	—
78	C₃²	H(3,𝔽₃)×C₃₇⋊C₃	1	1	yes	characteristic
79	C₉	—	3	3	no	—
80	C₉	—	3	1	no	—
81	C₉	—	111	6	no	—
82	C₉	—	111	2	no	—
83	C₃	—	3	1	no	—
84	C₃	—	27	3	no	—
85	C₃	—	37	3	no	—
86	C₃	—	111	2	no	—
87	C₃	—	999	6	no	—
88	C₃	#732×C₃₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#732×C₃₇⋊C₃
commutator, cosocle	C₃×C₉×C₃₇	C₃³
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃₇×#6879	C₃
socle	C₃×C₃₇	C₃×#732
hypercenter	#6879	C₃₇⋊C₃
hypocenter	C₃₇	C₃×#6879
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ #6879

Complements

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

N	H ≅ G/N	type
1. #732×C₃₇⋊C₃	C₃	semidirect
2. C₉²×C₃₇⋊C₃	C₃	semidirect
3. #22582507	C₃	semidirect
4. #22582506	C₃	semidirect
5. C₃₇×#6879	C₃	semidirect
9. #15688519	C₃²	semidirect
12. C₉×#66524	C₃²	semidirect
13. C₃₇×#732	C₃²	semidirect
14. C₉²×C₃₇	C₃²	semidirect
43. #6879	C₃₇⋊C₃	direct (N × H)
49. C₃₇⋊C₃	#6879	direct (N × H)
55. #732	C₃×C₃₇⋊C₃	semidirect
58. C₉²	C₃×C₃₇⋊C₃	semidirect
59. C₃₇	C₃×#6879	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#732×C₃₇⋊C₃	3
C₉²×C₃₇⋊C₃	3
#22582507	3
#22582506	3
C₃₇×#6879	3
C₃×#6879	37

Subgroups — C37⋊C3×#6879 #41007325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇⋊C₃×#6879 #41007325