Subgroups — C₃²⋊#15688534 #41008358

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	C₃²×#11758601	C₃	1	1	yes	maximal, characteristic
3	#15688534	—	3	3	no	—
4	C₃×#11758601	—	3	1	no	—
5	C₃×#11758601	—	3	2	no	—
6	C₃×#11758601	C₉	1	2	yes	—
7	C₃×#11758601	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
9	C₃³×C₃₇	C₂₇	1	1	yes	characteristic
10	C₃×C₉×C₃₇	—	3	1	no	—
11	C₃×C₉×C₃₇	—	3	2	no	—
12	C₃×C₉×C₃₇	C₂₇	1	2	yes	—
13	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
14	#11758601	—	3	2	no	—
15	#11758601	H(3,𝔽₃)	1	1	yes	characteristic
16	#11758601	3₋¹⁺²	1	2	yes	—
17	C₃²⋊C₈₁	—	37	1	no	maximal, Sylow
18	C₃²×C₃₇	—	3	1	no	—
19	C₃²×C₃₇	—	3	2	no	—
20	C₃²×C₃₇	C₈₁	1	3	yes	complemented
21	C₃²×C₃₇	C₃×C₂₇	1	1	yes	characteristic
22	C₉×C₃₇	—	3	2	no	—
23	C₉×C₃₇	C₃²⋊C₉	1	1	yes	characteristic
24	C₉×C₃₇	C₂₇⋊C₃	1	2	yes	—
25	C₃²×C₂₇	—	37	1	no	—
26	C₃×C₈₁	—	37	3	no	—
27	C₃×C₃₇	—	3	3	no	—
28	C₃×C₃₇	C₃²⋊C₂₇	1	1	yes	characteristic
29	C₃×C₃₇	C₃×C₈₁	1	1	yes	characteristic
30	C₃×C₃₇	C₈₁⋊C₃	1	2	yes	—
31	C₃²×C₉	#66526	1	1	yes	characteristic
32	C₃×C₂₇	—	37	1	no	—
33	C₃×C₂₇	—	37	2	no	—
34	C₃×C₂₇	—	111	1	no	—
35	C₃×C₂₇	—	111	2	no	—
36	C₈₁	—	111	3	no	—
37	C₃₇	C₃²⋊C₈₁	1	1	yes	characteristic, complemented, Sylow
38	C₃³	#11758603	1	1	yes	characteristic
39	C₃×C₉	—	3	1	no	—
40	C₃×C₉	—	3	2	no	—
41	C₃×C₉	#11758603	1	2	yes	—
42	C₃×C₉	C₃×#66526	1	1	yes	characteristic
43	C₂₇	—	37	1	no	—
44	C₂₇	—	37	2	no	—
45	C₂₇	—	111	2	no	—
46	C₃²	—	3	1	no	—
47	C₃²	—	3	2	no	—
48	C₃²	#15688534	1	3	yes	complemented
49	C₃²	C₃×#11758603	1	1	yes	characteristic
50	C₉	—	3	2	no	—
51	C₉	C₃²⋊#66526	1	1	yes	characteristic
52	C₉	#15688541	1	2	yes	—
53	C₃	—	3	3	no	—
54	C₃	C₃²⋊#11758603	1	1	yes	characteristic
55	C₃	C₃×#15688534	1	1	yes	characteristic
56	C₃	#22582715	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×#66526
commutator	C₃×C₃₇	C₃×C₈₁
Fitting	C₃²×C₉×C₃₇	C₉
socle	C₃²×C₃₇	C₃×C₂₇
prime radical	C₃³×C₃₇	C₂₇
cosocle	C₃×#11758601	C₃²
hypercenter	C₃²×C₉	#66526
hypocenter	C₃₇	C₃²⋊C₈₁
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×#15688534	C₃	semidirect
20. C₃²×C₃₇	C₈₁	semidirect
37. C₃₇	C₃²⋊C₈₁	semidirect
48. C₃²	#15688534	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
C₃²×#11758601	3
C₃²⋊C₈₁	37

Subgroups — C32⋊#15688534 #41008358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²⋊#15688534 #41008358