Subgroups — #41008359

Order 26973.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688534	C₃	1	3	yes	maximal, complemented
2	C₃×C₂₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#15688534	—	3	3	no	—
4	C₃×C₉×C₃₇⋊C₃	C₉	1	1	yes	characteristic
5	C₃×#11758601	C₉	1	1	yes	characteristic
6	C₃×#11758601	C₃²	1	1	yes	characteristic
7	C₂₇×C₃₇⋊C₃	—	3	1	no	—
8	C₂₇×C₃₇⋊C₃	—	3	2	no	—
9	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
10	C₃²×C₃₇⋊C₃	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
12	C₃×#66524	C₂₇	1	2	yes	—
13	C₉×C₃₇⋊C₃	—	3	1	no	—
14	C₉×C₃₇⋊C₃	—	3	1	no	—
15	C₉×C₃₇⋊C₃	—	3	1	no	—
16	C₂₇×C₃₇	—	3	1	no	—
17	#11758601	—	3	1	no	—
18	#11758601	H(3,𝔽₃)	1	1	yes	characteristic
19	#11758601	3₋¹⁺²	1	2	yes	—
20	C₃²⋊C₈₁	—	37	1	no	maximal, Sylow
21	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
22	C₃×C₃₇⋊C₃	—	3	1	no	—
23	C₃×C₃₇⋊C₃	—	3	1	no	—
24	C₃×C₃₇⋊C₃	—	3	1	no	—
25	C₃×C₃₇⋊C₃	C₈₁	1	3	yes	complemented
26	C₉×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
27	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
28	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
29	#66524	—	3	2	no	—
30	C₃²×C₂₇	—	37	1	no	—
31	C₃×C₈₁	—	37	3	no	—
32	C₃×C₃₇	C₃²⋊C₂₇	1	1	yes	characteristic
33	C₃×C₃₇	C₃×C₈₁	1	1	yes	characteristic
34	C₃×C₃₇	C₈₁⋊C₃	1	1	yes	characteristic
35	C₃×C₃₇	C₈₁⋊C₃	1	1	yes	characteristic
36	C₃₇⋊C₃	—	3	3	no	—
37	C₃²×C₉	—	37	1	no	—
38	C₃×C₂₇	—	37	1	no	—
39	C₃×C₂₇	—	37	1	no	—
40	C₃×C₂₇	—	111	1	no	—
41	C₃×C₂₇	—	111	2	no	—
42	C₃×C₂₇	#66526	1	1	yes	characteristic
43	C₈₁	—	111	3	no	—
44	C₃₇	C₃²⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
45	C₃³	—	37	1	no	—
46	C₃×C₉	—	37	2	no	—
47	C₃×C₉	—	111	1	no	—
48	C₃×C₉	—	111	1	no	—
49	C₃×C₉	—	111	1	no	—
50	C₃×C₉	C₃×#66526	1	1	yes	characteristic
51	C₂₇	—	3	1	no	—
52	C₂₇	—	37	1	no	—
53	C₂₇	—	37	2	no	—
54	C₂₇	—	111	1	no	—
55	C₃²	—	37	3	no	—
56	C₃²	—	111	1	no	—
57	C₃²	—	111	1	no	—
58	C₃²	—	111	1	no	—
59	C₃²	(C₃₇⋊C₃)⋊C₂₇	1	1	yes	characteristic
60	C₉	—	111	2	no	—
61	C₉	C₃²⋊#66526	1	1	yes	characteristic
62	C₉	#15688542	1	1	yes	characteristic
63	C₉	#15688543	1	1	yes	characteristic
64	C₃	—	111	3	no	—
65	C₃	#22582690	1	1	yes	characteristic
66	C₃	(C₃₇⋊C₃)⋊C₈₁	1	1	yes	characteristic
67	C₃	#22582716	1	1	yes	characteristic
68	C₃	#22582717	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×#66526
commutator	C₃×C₃₇	C₃×C₈₁
Fitting	C₃×C₂₇×C₃₇	C₉
socle	C₃²×C₃₇	C₃×C₂₇
prime radical	C₃²×C₃₇⋊C₃	C₂₇
cosocle	C₃×#11758601	C₃²
hypercenter	C₃×C₂₇	#66526
hypocenter	C₃₇	C₃²⋊C₈₁
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×#15688534	C₃	semidirect
25. C₃×C₃₇⋊C₃	C₈₁	semidirect
44. C₃₇	C₃²⋊C₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688534	3
C₃×C₂₇×C₃₇⋊C₃	3
C₃²⋊C₈₁	37