Subgroups — #41006463

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	C₉×#11758608	C₃	1	1	yes	maximal, characteristic
3	#22582488	C₃	1	6	yes	maximal, complemented
4	C₃²⋊#11758601	C₃	1	1	yes	maximal, characteristic
5	#22582463	C₃	1	3	yes	maximal, complemented
6	C₃₇×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
7	C₃×#11758608	C₉	1	1	yes	characteristic
8	C₃×#11758601	—	3	3	no	—
9	C₃×#11758601	C₃²	1	2	yes	—
10	C₃×#11758601	C₃²	1	3	yes	—
11	C₃×#11758601	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	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
16	C₃×C₂₇×C₃₇	C₃²	1	3	yes	—
17	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₃₇	—	3	1	no	—
19	C₃×C₉×C₃₇	—	3	1	no	—
20	C₃×C₉×C₃₇	—	3	1	no	—
21	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
22	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
23	#11758608	—	3	3	no	—
24	C₃×#66524	C₃×C₉	1	6	yes	—
25	C₃×#66524	C₃×C₉	1	3	yes	—
26	C₂₇×C₃₇	—	3	3	no	—
27	#11758601	—	3	2	no	—
28	#11758601	—	3	3	no	—
29	#11758601	3₋¹⁺²	1	3	yes	complemented
30	#10624727	—	37	1	no	maximal, Sylow
31	C₃²×C₃₇	—	3	1	no	—
32	C₃²×C₃₇	—	3	2	no	—
33	C₃²×C₃₇	C₂₇⋊C₃	1	3	yes	—
34	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
35	C₉×C₃₇	—	3	2	no	—
36	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
37	C₉×C₃₇	#737	1	1	yes	characteristic
38	C₉×C₃₇	#737	1	1	yes	characteristic
39	#66524	—	3	3	no	—
40	#66524	—	3	6	no	—
41	C₃²×C₂₇	—	37	1	no	—
42	C₉×3₋¹⁺²	—	37	1	no	—
43	C₉⋊C₂₇	—	37	6	no	—
44	C₃²⋊C₂₇	—	37	1	no	—
45	C₃²⋊C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
46	#6864	—	37	3	no	—
47	C₃×C₃₇	—	3	3	no	—
48	C₃×C₃₇	C₉×3₋¹⁺²	1	1	yes	characteristic
49	C₃×C₃₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic
50	C₃×C₃₇	#6903	1	2	yes	—
51	C₃×3₋¹⁺²	—	37	1	no	—
52	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
53	C₃×C₂₇	—	37	1	no	—
54	C₃×C₂₇	—	37	3	no	—
55	C₃×C₂₇	—	37	2	no	—
56	C₃×C₂₇	—	111	3	no	—
57	C₃×C₂₇	C₃×C₃₇⋊C₃	1	3	yes	—
58	C₉⋊C₉	—	37	6	no	—
59	C₃²⋊C₉	—	37	2	no	—
60	C₉²	—	37	3	no	—
61	C₃₇	#10624727	1	1	yes	characteristic, complemented, Sylow
62	C₃³	C₉×C₃₇⋊C₃	1	1	yes	characteristic
63	3₋¹⁺²	—	111	3	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	37	6	no	—
68	C₃×C₉	—	37	3	no	—
69	C₃×C₉	C₉×C₃₇⋊C₃	1	2	yes	—
70	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
71	C₂₇	—	3	3	no	—
72	C₂₇	—	37	3	no	—
73	C₂₇	—	111	2	no	—
74	C₂₇	—	111	3	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	#15688510	1	3	yes	—
78	C₃²	C₃×C₉×C₃₇⋊C₃	1	1	yes	characteristic
79	C₉	—	3	2	no	—
80	C₉	—	111	3	no	—
81	C₉	—	111	6	no	—
82	C₉	3₋¹⁺²×C₃₇⋊C₃	1	1	yes	characteristic
83	C₉	#15688530	1	1	yes	characteristic
84	C₉	#15688532	1	1	yes	characteristic
85	C₃	—	3	3	no	—
86	C₃	#22582548	1	1	yes	characteristic
87	C₃	C₃×#15688510	1	1	yes	characteristic
88	C₃	#22582614	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
commutator, socle	C₃²×C₃₇	C₃²×C₉
Fitting	C₃₇×C₃²⋊C₂₇	C₃
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₃²⋊C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	#10624727
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
3. #22582488	C₃	semidirect
5. #22582463	C₃	semidirect
29. #11758601	3₋¹⁺²	semidirect
61. 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
C₉×#11758608	3
#22582488	3
C₃²⋊#11758601	3
#22582463	3
C₃₇×C₃²⋊C₂₇	3
#10624727	37