Subgroups — #41008474

Order 26973.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688541	C₃	1	2	yes	maximal
2	C₃²×#11758603	C₃	1	1	yes	maximal, characteristic
3	#22582688	C₃	1	6	yes	maximal, complemented
4	C₉×#11758603	C₃	1	3	yes	maximal, complemented
5	#22582535	C₃	1	1	yes	maximal, characteristic
6	#15688541	C₉	1	18	yes	complemented
7	C₃×#11758603	C₉	1	9	yes	complemented
8	C₃×#11758603	C₃²	1	1	yes	characteristic
9	C₃×#11758603	C₃²	1	6	yes	—
10	C₃×#11758603	C₃²	1	2	yes	—
11	C₃²×#66524	C₃²	1	1	yes	characteristic
12	#15688504	C₉	1	6	yes	—
13	C₃²⋊#66524	C₉	1	2	yes	—
14	C₉×#66524	C₃²	1	3	yes	—
15	C₃₇×C₃²⋊C₉	C₉	1	1	yes	characteristic
16	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
18	C₃×#66524	C₃×C₉	1	6	yes	—
19	C₃×#66524	C₃×C₉	1	2	yes	—
20	C₃×#66524	C₃×C₉	1	3	yes	—
21	C₃×#66524	C₃×C₉	1	6	yes	—
22	C₃×#66524	C₃³	1	1	yes	characteristic
23	#11758603	C₃×C₉	1	3	yes	—
24	#11758603	C₃×C₉	1	6	yes	—
25	#11758603	C₃×C₉	1	18	yes	—
26	#10624681	—	37	1	no	maximal, Sylow
27	C₃²×C₃₇	—	3	1	no	—
28	C₃²×C₃₇	—	3	2	no	—
29	C₃²×C₃₇	C₉²	1	3	yes	—
30	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
31	C₉×C₃₇	—	3	3	no	—
32	#66524	—	3	6	no	—
33	#66524	C₉²	1	6	yes	—
34	#66524	C₃²×C₉	1	1	yes	characteristic
35	#66524	C₃²×C₉	1	2	yes	—
36	C₃×C₂₇⋊C₃	—	37	2	no	—
37	C₃²×C₂₇	—	37	1	no	—
38	#6887	—	37	1	no	—
39	#6864	—	37	6	no	—
40	C₉×C₂₇	—	37	3	no	—
41	C₃×C₃₇	—	3	3	no	—
42	C₃×C₃₇	C₃×C₉²	1	1	yes	characteristic
43	C₃×C₃₇	#6903	1	1	yes	characteristic
44	C₃×C₃₇	#6903	1	2	yes	—
45	C₃²×C₉	—	37	1	no	—
46	C₂₇⋊C₃	—	37	18	no	—
47	C₃×C₂₇	—	37	9	no	—
48	C₃×C₂₇	—	37	1	no	—
49	C₃×C₂₇	—	37	6	no	—
50	C₃×C₂₇	—	37	2	no	—
51	C₉⋊C₉	—	37	6	no	—
52	C₃²⋊C₉	—	37	2	no	—
53	C₃²⋊C₉	#66526	1	1	yes	characteristic
54	C₉²	—	37	3	no	—
55	C₃₇	#10624681	1	1	yes	characteristic, complemented, Sylow
56	C₃³	C₃×#66526	1	1	yes	characteristic
57	C₃×C₉	—	37	3	no	—
58	C₃×C₉	—	37	6	no	—
59	C₃×C₉	—	37	2	no	—
60	C₃×C₉	—	37	1	no	—
61	C₃×C₉	—	37	6	no	—
62	C₃×C₉	C₃×#66526	1	3	yes	—
63	C₂₇	—	37	3	no	—
64	C₂₇	—	37	6	no	—
65	C₂₇	—	37	18	no	—
66	C₃²	—	3	1	no	—
67	C₃²	—	3	2	no	—
68	C₃²	C₉×#66526	1	3	yes	—
69	C₃²	C₃²×#66526	1	1	yes	characteristic
70	C₉	—	3	3	no	—
71	C₉	—	37	1	no	—
72	C₉	—	37	2	no	—
73	C₉	—	37	6	no	—
74	C₉	—	111	6	no	—
75	C₃	—	3	3	no	—
76	C₃	C₃×C₉×#66526	1	1	yes	characteristic
77	C₃	#22582731	1	1	yes	characteristic
78	C₃	#22582732	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#66526
commutator	C₃×C₃₇	C₃×C₉²
Fitting	C₃₇×C₃²⋊C₉	C₉
socle	C₃²×C₃₇	C₃²×C₉
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×#66524	C₃³
hypercenter	C₃²⋊C₉	#66526
hypocenter	C₃₇	#10624681
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. #22582688	C₃	semidirect
4. C₉×#11758603	C₃	semidirect
6. #15688541	C₉	semidirect
7. C₃×#11758603	C₉	semidirect
55. C₃₇	#10624681	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
#22582688	3
C₉×#11758603	3
#22582535	3
#10624681	37