Subgroups — #41006322

Order 26973.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688511	C₃	1	1	yes	maximal, characteristic
2	C₃×#15688511	C₃	1	1	yes	maximal, characteristic
3	#22582538	C₃	1	1	yes	maximal, characteristic
4	#22582488	C₃	1	9	yes	maximal, complemented
5	C₃²×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
6	#15688511	—	3	3	no	—
7	#15688511	—	3	3	no	—
8	C₃×#11758601	C₃²	1	3	yes	—
9	C₃×#11758601	C₃²	1	3	yes	—
10	#15688506	C₉	1	3	yes	—
11	#15688505	C₉	1	3	yes	—
12	C₃²⋊#66524	C₉	1	3	yes	—
13	C₉×#66524	C₃²	1	3	yes	—
14	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
15	C₃×C₂₇×C₃₇	—	3	3	no	—
16	C₃×C₂₇×C₃₇	C₃²	1	3	yes	—
17	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
19	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
21	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
22	C₃×C₉×C₃₇	3₋¹⁺²	1	3	yes	—
23	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
24	C₃×#66524	C₃×C₉	1	9	yes	—
25	C₂₇×C₃₇	—	3	3	no	—
26	#11758601	—	3	3	no	—
27	#11758601	—	3	3	no	—
28	#10624707	—	37	1	no	maximal, Sylow
29	C₃²×C₃₇	—	3	3	no	—
30	C₃²×C₃₇	C₉⋊C₉	1	3	yes	—
31	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
32	C₉×C₃₇	C₉⋊C₉	1	3	yes	—
33	C₉×C₃₇	C₉⋊C₉	1	3	yes	—
34	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
37	#66524	—	3	9	no	—
38	C₃×C₂₇⋊C₃	—	37	1	no	—
39	C₃×C₂₇⋊C₃	—	37	1	no	—
40	C₃²×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
41	#6887	—	37	1	no	—
42	C₉⋊C₂₇	—	37	9	no	—
43	C₃×C₃₇	—	3	3	no	—
44	C₃×C₃₇	C₃×C₉⋊C₉	1	1	yes	characteristic
45	C₃×C₃₇	#6903	1	3	yes	—
46	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
47	C₂₇⋊C₃	—	111	3	no	—
48	C₂₇⋊C₃	—	111	3	no	—
49	C₃×C₂₇	—	3	3	no	—
50	C₃×C₂₇	—	37	3	no	—
51	C₃×C₂₇	—	37	3	no	—
52	C₃×C₂₇	C₃×C₃₇⋊C₃	1	3	yes	—
53	C₉⋊C₉	—	37	3	no	—
54	C₉⋊C₉	—	37	3	no	—
55	C₃²⋊C₉	—	37	3	no	—
56	C₉²	—	37	3	no	—
57	C₃₇	#10624707	1	1	yes	characteristic, complemented, Sylow
58	C₃³	C₉×C₃₇⋊C₃	1	1	yes	characteristic
59	C₃×C₉	—	37	9	no	—
60	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
61	C₃×C₉	C₉×C₃₇⋊C₃	1	1	yes	characteristic
62	C₃×C₉	#11758605	1	3	yes	—
63	C₃×C₉	#11758606	1	3	yes	—
64	C₃×C₉	#11758608	1	3	yes	—
65	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
66	C₂₇	—	3	3	no	—
67	C₂₇	—	111	3	no	—
68	C₂₇	—	111	3	no	—
69	C₃²	—	3	3	no	—
70	C₃²	#15688504	1	3	yes	—
71	C₃²	C₃×C₉×C₃₇⋊C₃	1	1	yes	characteristic
72	C₉	—	111	9	no	—
73	C₉	#15688504	1	3	yes	—
74	C₉	#15688504	1	3	yes	—
75	C₉	C₃×#11758606	1	1	yes	characteristic
76	C₉	C₃×#11758605	1	1	yes	characteristic
77	C₉	C₃×#11758608	1	1	yes	characteristic
78	C₃	—	3	3	no	—
79	C₃	C₃×#15688504	1	1	yes	characteristic
80	C₃	#22582612	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
commutator, socle	C₃²×C₃₇	C₃²×C₉
Fitting	C₃²×C₂₇×C₃₇	C₃
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₃²×C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	#10624707
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
4. #22582488	C₃	semidirect
57. C₃₇	#10624707	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688511	3
#22582538	3
#22582488	3
C₃²×C₂₇×C₃₇	3
#10624707	37