Subgroups — #41006461

Order 26973.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758601	C₃	1	1	yes	maximal, characteristic
2	#22582490	C₃	1	3	yes	maximal, complemented
3	#22582489	C₃	1	3	yes	maximal, complemented
4	C₃²⋊#11758601	C₃	1	2	yes	maximal
5	#22582464	C₃	1	3	yes	maximal, complemented
6	C₉×3₋¹⁺²×C₃₇	C₃	1	1	yes	maximal, characteristic
7	C₃×#11758601	—	3	3	no	—
8	C₃×#11758601	C₃²	1	1	yes	characteristic
9	C₃×#11758601	C₃²	1	1	yes	characteristic
10	C₃×#11758601	C₃²	1	6	yes	—
11	C₃×#11758601	C₃²	1	1	yes	characteristic
12	C₃×3₋¹⁺²×C₃₇	C₉	1	1	yes	characteristic
13	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
14	C₃₇×C₉⋊C₉	C₉	1	6	yes	—
15	C₃₇×C₃²⋊C₉	C₉	1	2	yes	—
16	C₉²×C₃₇	C₃²	1	3	yes	—
17	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
18	3₋¹⁺²×C₃₇	—	3	3	no	—
19	C₃×C₉×C₃₇	—	3	1	no	—
20	C₃×C₉×C₃₇	—	3	2	no	—
21	C₃×C₉×C₃₇	C₃×C₉	1	6	yes	—
22	C₃×C₉×C₃₇	C₃×C₉	1	3	yes	—
23	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
25	#11758601	—	3	1	no	—
26	#11758601	—	3	1	no	—
27	#11758601	—	3	6	no	—
28	#11758601	3₋¹⁺²	1	3	yes	complemented
29	#10624727	—	37	1	no	maximal, Sylow
30	C₃²×C₃₇	—	3	1	no	—
31	C₃²×C₃₇	—	3	2	no	—
32	C₃²×C₃₇	C₂₇⋊C₃	1	3	yes	—
33	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
34	C₉×C₃₇	—	3	2	no	—
35	C₉×C₃₇	—	3	3	no	—
36	C₉×C₃₇	—	3	6	no	—
37	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
38	C₉×C₃₇	#737	1	2	yes	—
39	C₃²×C₂₇	—	37	1	no	—
40	C₉×3₋¹⁺²	C₃₇⋊C₃	1	1	yes	characteristic
41	C₉⋊C₂₇	—	37	3	no	—
42	C₉⋊C₂₇	—	37	3	no	—
43	C₃²⋊C₂₇	—	37	2	no	—
44	#6864	—	37	3	no	—
45	C₃×C₃₇	—	3	3	no	—
46	C₃×C₃₇	C₉×3₋¹⁺²	1	1	yes	characteristic
47	C₃×C₃₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
48	C₃×C₃₇	#6903	1	2	yes	—
49	C₃×3₋¹⁺²	#66524	1	1	yes	characteristic
50	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
51	C₃×C₂₇	—	37	1	no	—
52	C₃×C₂₇	—	37	6	no	—
53	C₃×C₂₇	—	37	1	no	—
54	C₃×C₂₇	—	37	1	no	—
55	C₃×C₂₇	—	111	3	no	—
56	C₉⋊C₉	#66524	1	6	yes	—
57	C₃²⋊C₉	#66524	1	2	yes	—
58	C₉²	C₃×C₃₇⋊C₃	1	3	yes	—
59	C₃₇	#10624727	1	1	yes	characteristic, complemented, Sylow
60	C₃³	C₃×#66524	1	1	yes	characteristic
61	3₋¹⁺²	—	3	3	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	3	2	no	—
64	C₃×C₉	C₃×#66524	1	6	yes	—
65	C₃×C₉	C₃×#66524	1	3	yes	—
66	C₃×C₉	C₃×#66524	1	2	yes	—
67	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
68	C₂₇	—	37	3	no	—
69	C₂₇	—	111	1	no	—
70	C₂₇	—	111	1	no	—
71	C₂₇	—	111	6	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	3	2	no	—
74	C₃²	#15688511	1	3	yes	—
75	C₃²	C₃²×#66524	1	1	yes	characteristic
76	C₉	—	3	2	no	—
77	C₉	—	3	3	no	—
78	C₉	—	3	6	no	—
79	C₉	3₋¹⁺²×C₃₇⋊C₃	1	1	yes	characteristic
80	C₉	#15688532	1	2	yes	—
81	C₃	—	3	3	no	—
82	C₃	3₋¹⁺²×#66524	1	1	yes	characteristic
83	C₃	C₃×#15688511	1	1	yes	characteristic
84	C₃	#22582613	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
commutator, socle	C₃²×C₃₇	C₃²×C₉
Fitting	C₉×3₋¹⁺²×C₃₇	C₃
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₉×3₋¹⁺²	C₃₇⋊C₃
hypocenter	C₃₇	#10624727
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₉×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #22582490	C₃	semidirect
3. #22582489	C₃	semidirect
5. #22582464	C₃	semidirect
28. #11758601	3₋¹⁺²	semidirect
59. C₃₇	#10624727	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#11758601	3
#22582490	3
#22582489	3
C₃²⋊#11758601	3
#22582464	3
C₉×3₋¹⁺²×C₃₇	3
#10624727	37