Subgroups — #41007339

Order 26973.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688521	C₃	1	2	yes	maximal, complemented
2	#22582538	C₃	1	1	yes	maximal, characteristic, complemented
3	#22582501	C₃	1	9	yes	maximal, complemented
4	C₃×C₃₇×#732	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758608	—	3	2	no	—
6	#15688521	—	3	2	no	—
7	#15688521	—	3	2	no	—
8	#15688521	C₃²	1	6	yes	complemented
9	#15688506	—	3	1	no	—
10	#15688505	—	3	1	no	—
11	C₃²⋊#66524	—	3	1	no	—
12	C₉×#66524	C₃²	1	3	yes	complemented
13	C₃×H(3,𝔽₃)×C₃₇	—	3	1	no	—
14	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
15	C₃₇×#732	—	3	1	no	—
16	C₃₇×#732	—	3	1	no	—
17	C₃₇×#732	C₃²	1	3	yes	—
18	C₃³×C₃₇	—	9	1	no	—
19	C₃³×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
20	H(3,𝔽₃)×C₃₇	—	3	3	no	—
21	H(3,𝔽₃)×C₃₇	—	9	2	no	—
22	C₃×C₉×C₃₇	—	3	2	no	—
23	C₃×C₉×C₃₇	—	3	1	no	—
24	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
27	#11758608	—	3	6	no	—
28	#11758608	—	9	2	no	—
29	#11758608	—	9	2	no	—
30	C₃×#66524	—	3	3	no	—
31	C₃×#66524	—	9	2	no	—
32	#10624838	—	37	1	no	maximal, Sylow
33	C₃²×C₃₇	—	9	1	no	—
34	C₃²×C₃₇	—	9	3	no	—
35	C₃²×C₃₇	—	27	3	no	—
36	C₃²×C₃₇	#732	1	2	yes	—
37	C₃²×C₃₇	#732	1	1	yes	characteristic
38	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₉×C₃₇	—	3	1	no	—
40	C₉×C₃₇	—	3	1	no	—
41	C₉×C₃₇	—	3	1	no	—
42	#66524	—	9	3	no	—
43	#66524	—	9	6	no	—
44	C₃×#733	—	37	2	no	—
45	C₃×#732	C₃₇⋊C₃	1	1	yes	characteristic
46	#6887	—	37	1	no	—
47	#6878	—	37	9	no	—
48	C₃×C₃₇	—	3	1	no	—
49	C₃×C₃₇	—	3	1	no	—
50	C₃×C₃₇	—	3	2	no	—
51	C₃×C₃₇	—	27	3	no	—
52	C₃×C₃₇	C₃×#732	1	1	yes	characteristic
53	C₃×3₋¹⁺²	—	111	2	no	—
54	C₃×H(3,𝔽₃)	—	3	1	no	—
55	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
56	#733	—	37	6	no	—
57	#733	—	111	2	no	—
58	#733	—	111	2	no	—
59	#732	—	3	1	no	—
60	#732	—	3	1	no	—
61	#732	C₃×C₃₇⋊C₃	1	3	yes	—
62	C₉⋊C₉	—	111	1	no	—
63	C₉⋊C₉	—	111	1	no	—
64	C₃²⋊C₉	—	111	1	no	—
65	C₉²	—	37	3	no	—
66	C₃₇	#10624838	1	1	yes	characteristic, complemented, Sylow
67	C₃³	—	9	1	no	—
68	C₃³	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
69	3₋¹⁺²	—	333	2	no	—
70	3₋¹⁺²	—	333	2	no	—
71	3₋¹⁺²	—	111	6	no	—
72	H(3,𝔽₃)	—	3	3	no	—
73	H(3,𝔽₃)	—	9	2	no	—
74	C₃×C₉	—	3	2	no	—
75	C₃×C₉	—	3	1	no	—
76	C₃×C₉	—	333	2	no	—
77	C₃×C₉	—	111	3	no	—
78	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
79	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
80	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
81	C₃²	—	9	1	no	—
82	C₃²	—	9	3	no	—
83	C₃²	—	27	3	no	—
84	C₃²	#15688518	1	2	yes	—
85	C₃²	#15688518	1	1	yes	characteristic
86	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
87	C₉	—	3	1	no	—
88	C₉	—	3	1	no	—
89	C₉	—	3	1	no	—
90	C₉	—	333	3	no	—
91	C₉	—	333	6	no	—
92	C₃	—	3	1	no	—
93	C₃	—	3	1	no	—
94	C₃	—	3	2	no	—
95	C₃	—	27	3	no	—
96	C₃	C₃×#15688518	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#15688518
commutator, cosocle	C₃×C₉×C₃₇	C₃³
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting, prime radical	C₃×C₃₇×#732	C₃
socle	C₃×C₃₇	C₃×#732
hypercenter	C₃×#732	C₃₇⋊C₃
hypocenter	C₃₇	#10624838
LCS	G ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#732

Complements

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

N	H ≅ G/N	type
1. C₃×#15688521	C₃	semidirect
2. #22582538	C₃	semidirect
3. #22582501	C₃	semidirect
8. #15688521	C₃²	semidirect
12. C₉×#66524	C₃²	semidirect
66. C₃₇	#10624838	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688521	3
#22582538	3
#22582501	3
C₃×C₃₇×#732	3
#10624838	37