Subgroups — #13091718

Order 1458.

2130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624943	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#92404	C₃	1	1	yes	maximal, characteristic
3	C₃⋊#4208	—	3	40	no	maximal
4	3₋¹⁺⁴	—	2	40	no	—
5	H(5,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	C₃×#737	D₃	1	40	yes	complemented
7	C₃⋊#272	—	3	40	no	—
8	#4208	—	9	90	no	—
9	C₉×C₃⋊D₃	—	9	40	no	—
10	#737	—	2	360	no	—
11	#737	C₃⋊D₃	1	90	yes	complemented
12	C₃×3₋¹⁺²	—	2	160	no	—
13	C₃×H(3,𝔽₃)	C₃×D₃	1	40	yes	—
14	C₃²×C₉	C₃⋊D₃	1	40	yes	complemented
15	C₃×C₃⋊D₃	—	9	40	no	—
16	#272	—	9	90	no	—
17	D₃×C₉	—	27	40	no	—
18	C₃³	C₃×C₃⋊D₃	1	40	yes	—
19	3₋¹⁺²	—	2	360	no	—
20	H(3,𝔽₃)	C₃×C₃⋊D₃	1	90	yes	—
21	C₃×C₉	—	2	160	no	—
22	C₃×C₉	C₃⋊(C₃⋊D₃)	1	40	yes	—
23	C₃⋊D₃	—	9	40	no	—
24	C₃×D₃	—	27	40	no	—
25	C₂×C₉	—	81	1	no	—
26	C₃²	—	9	40	no	—
27	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	40	yes	—
28	C₉	—	2	40	no	—
29	C₉	C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
30	C₂×C₃	—	81	1	no	—
31	D₃	—	27	40	no	—
32	C₃	—	3	40	no	—
33	C₃	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
34	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉	C₃⋊(C₃⋊(C₃⋊D₃))
commutator, cosocle, hypocenter	H(5,𝔽₃)	C₂×C₃
Frattini, socle	C₃	C₃×C₃⋊(C₃⋊(C₃⋊D₃))
Fitting	#10624943	C₂
prime radical	#92404	C₃
LCS	G ▷ H(5,𝔽₃)
UCS	C₁ ◁ C₉

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

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