Subgroups — 3₋¹⁺²⋊#11758601 #41004749

Order 26973.

126 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	C₃²⋊#11758601	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊#11758601	C₃	1	1	yes	maximal, characteristic
4	C₉×3₋¹⁺²×C₃₇	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758601	—	3	1	no	—
6	C₃×#11758601	—	3	3	no	—
7	C₃×#11758601	—	3	1	no	—
8	C₃×#11758601	—	3	1	no	—
9	C₃×3₋¹⁺²×C₃₇	C₉	1	1	yes	characteristic
10	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
11	C₃₇×C₉⋊C₉	—	3	2	no	—
12	C₃₇×C₃²⋊C₉	C₉	1	1	yes	characteristic
13	C₃₇×C₃²⋊C₉	C₉	1	1	yes	characteristic
14	C₉²×C₃₇	—	3	1	no	—
15	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
16	3₋¹⁺²×C₃₇	—	3	2	no	—
17	3₋¹⁺²×C₃₇	C₂₇	1	3	yes	complemented
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	—	3	1	no	—
22	C₃×C₉×C₃₇	—	3	1	no	—
23	C₃×C₉×C₃₇	—	3	1	no	—
24	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃×C₉×C₃₇	3₋¹⁺²	1	2	yes	—
26	#11758601	—	3	3	no	—
27	#11758601	—	9	1	no	—
28	#11758601	—	9	1	no	—
29	3₋¹⁺²⋊C₂₇	—	37	1	no	maximal, Sylow
30	C₃²×C₃₇	—	3	1	no	—
31	C₃²×C₃₇	—	3	1	no	—
32	C₃²×C₃₇	—	3	1	no	—
33	C₃²×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
34	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
35	C₃²×C₃₇	C₂₇⋊C₃	1	2	yes	—
36	C₉×C₃₇	—	3	3	no	—
37	C₉×C₃₇	—	3	2	no	—
38	C₉×C₃₇	—	9	1	no	—
39	C₉×C₃₇	—	9	1	no	—
40	C₉×C₃₇	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
41	C₉×C₃₇	#731	1	1	yes	characteristic
42	C₉×C₃₇	#733	1	1	yes	characteristic
43	C₃²×C₂₇	—	37	1	no	—
44	C₉×3₋¹⁺²	C₃₇⋊C₃	1	1	yes	characteristic
45	C₃²⋊C₂₇	—	37	1	no	—
46	C₃²⋊C₂₇	—	37	1	no	—
47	C₃×C₃₇	—	3	1	no	—
48	C₃×C₃₇	—	3	2	no	—
49	C₃×C₃₇	C₃²⋊C₂₇	1	1	yes	characteristic
50	C₃×C₃₇	3₋¹⁺²⋊C₉	1	1	yes	characteristic
51	C₃×C₃₇	#6872	1	1	yes	characteristic
52	C₃×C₃₇	#6873	1	1	yes	characteristic
53	C₃×3₋¹⁺²	#66524	1	1	yes	characteristic
54	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
55	C₃×C₂₇	—	111	1	no	—
56	C₃×C₂₇	—	111	1	no	—
57	C₃×C₂₇	—	111	1	no	—
58	C₃×C₂₇	—	111	3	no	—
59	C₉⋊C₉	—	3	2	no	—
60	C₃²⋊C₉	#66524	1	1	yes	characteristic
61	C₃²⋊C₉	#66524	1	1	yes	characteristic
62	C₉²	—	3	1	no	—
63	C₃₇	3₋¹⁺²⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
64	C₃³	C₃×#66524	1	1	yes	characteristic
65	3₋¹⁺²	—	3	2	no	—
66	3₋¹⁺²	#11758601	1	3	yes	complemented
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	3	1	no	—
71	C₃×C₉	—	3	1	no	—
72	C₃×C₉	—	3	1	no	—
73	C₃×C₉	#11758608	1	2	yes	—
74	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
75	C₂₇	—	333	1	no	—
76	C₂₇	—	333	1	no	—
77	C₂₇	—	111	3	no	—
78	C₃²	—	3	1	no	—
79	C₃²	—	3	1	no	—
80	C₃²	—	3	1	no	—
81	C₃²	C₃²⋊#66524	1	1	yes	characteristic
82	C₃²	C₃×#11758601	1	1	yes	characteristic
83	C₃²	#15688511	1	2	yes	—
84	C₉	—	3	3	no	—
85	C₉	—	3	2	no	—
86	C₉	—	9	1	no	—
87	C₉	—	9	1	no	—
88	C₉	#15688514	1	1	yes	characteristic
89	C₉	#15688517	1	1	yes	characteristic
90	C₉	#15688520	1	1	yes	characteristic
91	C₃	—	3	1	no	—
92	C₃	—	3	2	no	—
93	C₃	C₃²⋊#11758601	1	1	yes	characteristic
94	C₃	3₋¹⁺²⋊#66524	1	1	yes	characteristic
95	C₃	#22582483	1	1	yes	characteristic
96	C₃	#22582486	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₃₇⋊C₃)
commutator	C₃²×C₃₇	C₃×C₂₇
Frattini	C₃²×C₉	C₃×C₃₇⋊C₃
Fitting	C₉×3₋¹⁺²×C₃₇	C₃
socle	C₃²×C₃₇	C₃²⋊C₉
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃²×C₉×C₃₇	C₃²
hypercenter	C₉×3₋¹⁺²	C₃₇⋊C₃
hypocenter	C₃₇	3₋¹⁺²⋊C₂₇
LCS	G ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₉×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
17. 3₋¹⁺²×C₃₇	C₂₇	semidirect
63. C₃₇	3₋¹⁺²⋊C₂₇	semidirect
66. 3₋¹⁺²	#11758601	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
C₃²⋊#11758601	3
C₉×3₋¹⁺²×C₃₇	3
3₋¹⁺²⋊C₂₇	37

Subgroups — 3−1+2⋊#11758601 #41004749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 3₋¹⁺²⋊#11758601 #41004749