Subgroups — #41008291

Order 26973.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688541	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊#11758603	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊#11758603	C₃	1	1	yes	maximal, characteristic
4	#22582548	C₃	1	1	yes	maximal, characteristic
5	#15688541	—	3	3	no	—
6	C₃×#11758603	—	3	1	no	—
7	C₃×#11758603	—	3	1	no	—
8	C₃×#11758603	—	3	1	no	—
9	C₃×#11758608	C₉	1	1	yes	characteristic
10	C₃²×#66524	C₃²	1	1	yes	characteristic
11	#15688504	—	3	2	no	—
12	C₃²⋊#66524	C₉	1	1	yes	characteristic
13	C₉×#66524	—	3	1	no	—
14	C₃₇×C₃²⋊C₉	C₉	1	1	yes	characteristic
15	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₃₇	—	3	1	no	—
17	#11758608	—	3	3	no	—
18	C₃×#66524	—	3	1	no	—
19	C₃×#66524	—	3	1	no	—
20	C₃×#66524	—	3	1	no	—
21	C₃×#66524	—	3	1	no	—
22	C₃×#66524	—	3	1	no	—
23	C₃×#66524	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×#66524	3₋¹⁺²	1	2	yes	—
25	#11758603	—	3	3	no	—
26	#11758603	—	9	1	no	—
27	#11758603	—	9	1	no	—
28	#10624455	—	37	1	no	maximal, Sylow
29	C₃²×C₃₇	—	3	1	no	—
30	C₃²×C₃₇	—	3	1	no	—
31	C₃²×C₃₇	—	3	1	no	—
32	C₃²×C₃₇	—	3	1	no	—
33	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
34	C₉×C₃₇	—	9	1	no	—
35	#66524	—	3	3	no	—
36	#66524	—	3	2	no	—
37	#66524	—	9	1	no	—
38	#66524	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	#66524	#731	1	1	yes	characteristic
40	#66524	#733	1	1	yes	characteristic
41	C₃×C₂₇⋊C₃	—	37	1	no	—
42	C₉×3₋¹⁺²	—	37	1	no	—
43	C₃²⋊C₂₇	—	37	1	no	—
44	C₃²⋊C₂₇	—	37	1	no	—
45	C₃×C₃₇	—	9	1	no	—
46	C₃×C₃₇	#6869	1	1	yes	characteristic
47	C₃×C₃₇	3₋¹⁺²⋊C₉	1	1	yes	characteristic
48	C₃×C₃₇	#6872	1	1	yes	characteristic
49	C₃×C₃₇	#6873	1	1	yes	characteristic
50	C₃×3₋¹⁺²	—	37	1	no	—
51	C₃²×C₉	—	37	1	no	—
52	C₂₇⋊C₃	—	111	3	no	—
53	C₃×C₂₇	—	111	1	no	—
54	C₃×C₂₇	—	111	1	no	—
55	C₃×C₂₇	—	111	1	no	—
56	C₉⋊C₉	—	111	2	no	—
57	C₃²⋊C₉	—	37	1	no	—
58	C₃²⋊C₉	#66526	1	1	yes	characteristic
59	C₉²	—	111	1	no	—
60	C₃₇	#10624455	1	1	yes	characteristic, complemented, Sylow
61	C₃³	C₃×#66526	1	1	yes	characteristic
62	3₋¹⁺²	—	111	3	no	—
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	37	1	no	—
65	C₃×C₉	—	37	2	no	—
66	C₃×C₉	—	111	1	no	—
67	C₃×C₉	—	111	1	no	—
68	C₃×C₉	—	111	1	no	—
69	C₃×C₉	—	111	1	no	—
70	C₃×C₉	—	111	1	no	—
71	C₂₇	—	333	1	no	—
72	C₂₇	—	333	1	no	—
73	C₂₇	—	111	3	no	—
74	C₃²	—	3	1	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	1	no	—
78	C₃²	C₃²⋊#66526	1	1	yes	characteristic
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	3	no	—
85	C₉	—	111	2	no	—
86	C₃	—	9	1	no	—
87	C₃	#22582696	1	1	yes	characteristic
88	C₃	3₋¹⁺²⋊#66526	1	1	yes	characteristic
89	C₃	#22582699	1	1	yes	characteristic
90	C₃	#22582702	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊#66526
commutator, prime radical	C₃³×C₃₇	C₃×C₉
Frattini	C₃³	C₃×#66526
Fitting	C₃₇×C₃²⋊C₉	C₉
socle	C₃²×C₃₇	C₃²⋊C₉
cosocle	C₃²×#66524	C₃²
hypercenter	C₃²⋊C₉	#66526
hypocenter	C₃₇	#10624455
LCS	G ▷ C₃³×C₃₇ ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
60. C₃₇	#10624455	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688541	3
C₃²⋊#11758603	3
#22582548	3
#10624455	37