Subgroups — C₃×C₃²⋊#11758601 #41006209

Order 26973.

464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758601	C₃	1	3	yes	maximal, complemented
2	C₃²⋊#11758601	C₃	1	9	yes	maximal, direct product factor
3	C₃³×C₉×C₃₇	C₃	1	1	yes	maximal, characteristic
4	C₃×#11758601	—	3	9	no	—
5	C₃×#11758601	C₃²	1	9	yes	complemented
6	C₃⁴×C₃₇	C₉	1	1	yes	characteristic
7	C₃²×C₉×C₃₇	—	3	3	no	—
8	C₃²×C₉×C₃₇	—	3	6	no	—
9	C₃²×C₉×C₃₇	C₉	1	2	yes	—
10	C₃²×C₉×C₃₇	C₉	1	6	yes	—
11	C₃²×C₉×C₃₇	C₃²	1	3	yes	—
12	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
13	C₃³×C₃₇	—	3	3	no	—
14	C₃³×C₃₇	—	3	6	no	—
15	C₃³×C₃₇	C₂₇	1	9	yes	complemented
16	C₃³×C₃₇	C₃×C₉	1	3	yes	—
17	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₃₇	—	3	6	no	—
19	C₃×C₉×C₃₇	—	3	18	no	—
20	C₃×C₉×C₃₇	—	3	3	no	—
21	C₃×C₉×C₃₇	—	3	6	no	—
22	C₃×C₉×C₃₇	C₃×C₉	1	6	yes	—
23	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
24	C₃×C₉×C₃₇	H(3,𝔽₃)	1	3	yes	—
25	C₃×C₉×C₃₇	3₋¹⁺²	1	6	yes	—
26	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
27	#11758601	—	3	9	no	—
28	C₃×C₃²⋊C₂₇	—	37	1	no	maximal, Sylow
29	C₃²×C₃₇	—	3	27	no	—
30	C₃²×C₃₇	—	3	3	no	—
31	C₃²×C₃₇	—	3	6	no	—
32	C₃²×C₃₇	C₃²⋊C₉	1	3	yes	—
33	C₃²×C₃₇	C₃×C₂₇	1	3	yes	—
34	C₃²×C₃₇	C₃×C₂₇	1	9	yes	complemented
35	C₃²×C₃₇	C₂₇⋊C₃	1	6	yes	—
36	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
37	C₉×C₃₇	—	3	6	no	—
38	C₉×C₃₇	C₃²⋊C₉	1	6	yes	—
39	C₉×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₉×C₃₇	C₃×3₋¹⁺²	1	2	yes	—
41	C₃³×C₉	C₃₇⋊C₃	1	1	yes	characteristic
42	C₃²×C₂₇	—	37	3	no	—
43	C₃²⋊C₂₇	—	37	9	no	—
44	C₃×C₃₇	—	3	9	no	—
45	C₃×C₃₇	C₃²⋊C₂₇	1	9	yes	complemented
46	C₃×C₃₇	C₃×C₃²⋊C₉	1	1	yes	characteristic
47	C₃×C₃₇	C₃²×C₂₇	1	1	yes	characteristic
48	C₃×C₃₇	C₃×C₂₇⋊C₃	1	2	yes	—
49	C₃⁴	#66524	1	1	yes	characteristic
50	C₃²×C₉	—	3	6	no	—
51	C₃²×C₉	—	3	3	no	—
52	C₃²×C₉	#66524	1	2	yes	—
53	C₃²×C₉	#66524	1	6	yes	—
54	C₃²×C₉	C₃×C₃₇⋊C₃	1	3	yes	—
55	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
56	C₃×C₂₇	—	37	9	no	—
57	C₃×C₂₇	—	111	9	no	—
58	C₃₇	C₃×C₃²⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
59	C₃³	—	3	3	no	—
60	C₃³	—	3	6	no	—
61	C₃³	#11758601	1	9	yes	complemented
62	C₃³	C₃×#66524	1	3	yes	—
63	C₃³	C₃×#66524	1	1	yes	characteristic
64	C₃×C₉	—	3	6	no	—
65	C₃×C₉	—	3	18	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	C₃×#66524	1	6	yes	—
69	C₃×C₉	C₃×#66524	1	2	yes	—
70	C₃×C₉	#11758608	1	6	yes	—
71	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	3	yes	—
72	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
73	C₂₇	—	111	9	no	—
74	C₃²	—	3	3	no	—
75	C₃²	—	3	6	no	—
76	C₃²	—	3	27	no	—
77	C₃²	C₃²⋊#66524	1	3	yes	—
78	C₃²	C₃×#11758601	1	3	yes	—
79	C₃²	C₃×#11758601	1	9	yes	complemented
80	C₃²	#15688511	1	6	yes	—
81	C₃²	C₃²×#66524	1	1	yes	characteristic
82	C₉	—	3	6	no	—
83	C₉	C₃²⋊#66524	1	6	yes	—
84	C₉	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
85	C₉	C₃×#11758608	1	2	yes	—
86	C₃	—	3	9	no	—
87	C₃	C₃²⋊#11758601	1	9	yes	direct product factor
88	C₃	C₃×C₃²⋊#66524	1	1	yes	characteristic
89	C₃	C₃²×#11758601	1	1	yes	characteristic
90	C₃	C₃×#15688511	1	2	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃²×C₂₇
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃³×C₉×C₃₇	C₃
socle	C₃³×C₃₇	C₃×C₉
prime radical	C₃⁴×C₃₇	C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₃³×C₉	C₃₇⋊C₃
hypocenter	C₃₇	C₃×C₃²⋊C₂₇
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃²×C₉ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
1. C₃²×#11758601	C₃	semidirect
2. C₃²⋊#11758601	C₃	direct (N × H)
5. C₃×#11758601	C₃²	semidirect
15. C₃³×C₃₇	C₂₇	semidirect
34. C₃²×C₃₇	C₃×C₂₇	semidirect
45. C₃×C₃₇	C₃²⋊C₂₇	semidirect
58. C₃₇	C₃×C₃²⋊C₂₇	semidirect
61. C₃³	#11758601	semidirect
79. C₃²	C₃×#11758601	semidirect
87. C₃	C₃²⋊#11758601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#11758601	3
C₃²⋊#11758601	3
C₃³×C₉×C₃₇	3
C₃×C₃²⋊C₂₇	37

Subgroups — C3×C32⋊#11758601 #41006209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃²⋊#11758601 #41006209