Subgroups — #41008417

Order 26973.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688543	C₃	1	1	yes	maximal, characteristic, complemented
2	#22582695	C₃	1	2	yes	maximal, complemented
3	#22582634	C₃	1	1	yes	maximal, characteristic
4	#15688543	—	3	3	no	—
5	#15688541	—	3	2	no	—
6	C₃×#11758603	—	3	1	no	—
7	#15688532	—	3	1	no	—
8	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
9	#15688521	C₉	1	1	yes	characteristic
10	#15688519	C₉	1	1	yes	characteristic
11	#15688517	—	3	1	no	—
12	#15688514	—	3	1	no	—
13	C₃₇×#733	C₉	1	1	yes	characteristic
14	C₃²×C₃₇⋊C₃	3₋¹⁺²	1	1	yes	characteristic
15	3₋¹⁺²×C₃₇	—	3	1	no	—
16	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃²⋊(C₃₇⋊C₃)	—	3	1	no	—
18	#11758608	—	3	1	no	—
19	C₃×#66524	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×#66524	3₋¹⁺²	1	1	yes	characteristic
21	#11758606	—	9	1	no	—
22	#11758605	—	9	1	no	—
23	C₉×C₃₇⋊C₃	—	3	1	no	—
24	C₉×C₃₇⋊C₃	—	3	1	no	—
25	C₉×C₃₇⋊C₃	—	3	1	no	—
26	C₉×C₃₇⋊C₃	—	9	1	no	—
27	#11758603	—	3	3	no	—
28	#11758603	—	9	2	no	—
29	#10624530	—	37	1	no	maximal, Sylow
30	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
31	C₃×C₃₇⋊C₃	—	3	1	no	—
32	C₃×C₃₇⋊C₃	—	9	1	no	—
33	C₃×C₃₇⋊C₃	—	9	1	no	—
34	C₉×C₃₇	—	3	1	no	—
35	C₉×C₃₇	—	9	1	no	—
36	#66524	—	3	1	no	—
37	#66524	—	9	1	no	—
38	#66524	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	#66524	#731	1	1	yes	characteristic
40	#66524	#732	1	1	yes	characteristic
41	#6908	—	37	1	no	—
42	C₃×C₂₇⋊C₃	—	37	1	no	—
43	#6869	—	37	2	no	—
44	C₃×C₃₇	—	3	1	no	—
45	C₃×C₃₇	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
46	C₃₇⋊C₃	—	9	1	no	—
47	C₃₇⋊C₃	—	27	1	no	—
48	#737	—	111	1	no	—
49	C₃²×C₉	—	37	1	no	—
50	#733	—	37	1	no	—
51	#733	#66526	1	1	yes	characteristic
52	#732	—	37	1	no	—
53	#731	—	111	1	no	—
54	AΣL(1,𝔽₂₇)	—	111	1	no	—
55	C₂₇⋊C₃	—	111	2	no	—
56	C₂₇⋊C₃	—	111	3	no	—
57	C₃×C₂₇	—	111	1	no	—
58	C₃₇	#10624530	1	1	yes	characteristic, complemented, Sylow
59	C₃³	—	37	1	no	—
60	3₋¹⁺²	—	3	1	no	—
61	3₋¹⁺²	—	333	1	no	—
62	3₋¹⁺²	—	333	1	no	—
63	3₋¹⁺²	—	111	1	no	—
64	H(3,𝔽₃)	—	111	1	no	—
65	C₃×C₉	—	37	1	no	—
66	C₃×C₉	—	37	1	no	—
67	C₃×C₉	—	333	1	no	—
68	C₃×C₉	—	111	1	no	—
69	C₃×C₉	—	111	1	no	—
70	C₃×C₉	—	111	1	no	—
71	C₃×C₉	C₃×#66526	1	1	yes	characteristic
72	C₂₇	—	333	2	no	—
73	C₂₇	—	111	3	no	—
74	C₃²	—	333	1	no	—
75	C₃²	—	333	1	no	—
76	C₃²	—	111	1	no	—
77	C₃²	C₃²⋊#66526	1	1	yes	characteristic
78	C₉	—	3	1	no	—
79	C₉	—	9	1	no	—
80	C₉	—	37	1	no	—
81	C₉	—	37	1	no	—
82	C₉	—	37	1	no	—
83	C₉	—	333	1	no	—
84	C₉	—	111	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	333	1	no	—
87	C₃	—	999	1	no	—
88	C₃	H(3,𝔽₃)⋊#66526	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)⋊#66526
commutator	C₃×C₉×C₃₇	C₃×C₉
Frattini	C₃×C₉	C₃×#66526
Fitting	C₃₇×#733	C₉
socle	C₃×C₃₇	H(3,𝔽₃)⋊C₉
prime radical	#22582634	C₃
cosocle	C₃×C₉×C₃₇⋊C₃	C₃²
hypercenter	#733	#66526
hypocenter	C₃₇	#10624530
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ #733

Complements

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

N	H ≅ G/N	type
1. C₃×#15688543	C₃	semidirect
2. #22582695	C₃	semidirect
58. C₃₇	#10624530	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688543	3
#22582695	3
#22582634	3
#10624530	37