Subgroups — C₂×#6881 #92243

Order 486.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6881	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#733	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#732	C₃	1	2	yes	maximal, complemented
4	C₂×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
5	#733	C₂×C₃	1	1	yes	characteristic, complemented
6	#732	C₂×C₃	1	2	yes	complemented
7	C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×3₋¹⁺²	—	3	1	no	—
9	C₂×H(3,𝔽₃)	—	3	2	no	—
10	C₂×C₃×C₉	—	3	1	no	—
11	C₂×C₃×C₉	C₃²	1	1	yes	characteristic
12	3₋¹⁺²	—	3	1	no	—
13	H(3,𝔽₃)	—	3	2	no	—
14	C₃×C₉	—	3	1	no	—
15	C₃×C₉	C₂×C₃²	1	1	yes	characteristic
16	C₂×C₃²	—	9	2	no	—
17	C₂×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
18	C₂×C₉	—	3	1	no	—
19	C₂×C₉	—	9	1	no	—
20	C₂×C₉	—	9	1	no	—
21	C₃²	—	9	2	no	—
22	C₃²	C₂×H(3,𝔽₃)	1	1	yes	characteristic
23	C₉	—	3	1	no	—
24	C₉	—	9	1	no	—
25	C₉	—	9	1	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	—	27	2	no	—
28	C₂×C₃	#732	1	1	yes	characteristic
29	C₃	—	3	1	no	—
30	C₃	—	27	2	no	—
31	C₃	C₂×#732	1	1	yes	characteristic
32	C₂	#6881	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃	#732
commutator, Frattini, cosocle	C₃×C₉	C₂×C₃²
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃² ◁ C₂×C₃×C₉ ◁ G

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.