Subgroups — C₂×#6859 #92221

Order 486.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6859	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₃×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃²⋊C₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₃³	—	3	1	no	—
9	C₂×C₃³	C₃²	1	1	yes	characteristic
10	C₂×H(3,𝔽₃)	—	3	3	no	—
11	C₂×C₃×C₉	—	3	1	no	—
12	C₂×C₃×C₉	—	3	2	no	—
13	C₃³	—	3	1	no	—
14	C₃³	C₂×C₃²	1	1	yes	characteristic
15	H(3,𝔽₃)	—	3	3	no	—
16	C₃×C₉	—	3	1	no	—
17	C₃×C₉	—	3	2	no	—
18	C₂×C₃²	—	3	1	no	—
19	C₂×C₃²	—	3	3	no	—
20	C₂×C₃²	—	3	2	no	—
21	C₂×C₃²	—	3	1	no	—
22	C₂×C₃²	—	9	2	no	—
23	C₂×C₃²	—	9	1	no	—
24	C₂×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
25	C₂×C₉	—	9	1	no	—
26	C₂×C₉	—	9	2	no	—
27	C₃²	—	3	1	no	—
28	C₃²	—	3	3	no	—
29	C₃²	—	3	2	no	—
30	C₃²	—	3	1	no	—
31	C₃²	—	9	2	no	—
32	C₃²	—	9	1	no	—
33	C₃²	C₂×H(3,𝔽₃)	1	1	yes	characteristic
34	C₉	—	9	1	no	—
35	C₉	—	9	2	no	—
36	C₂×C₃	—	9	1	no	—
37	C₂×C₃	—	9	3	no	—
38	C₂×C₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	C₂×C₃	#731	1	2	yes	—
40	C₂×C₃	#732	1	1	yes	characteristic
41	C₃	—	9	1	no	—
42	C₃	—	9	3	no	—
43	C₃	C₂×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
44	C₃	C₂×#731	1	2	yes	—
45	C₃	C₂×#732	1	1	yes	characteristic
46	C₂	#6859	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₂×C₃²
prime radical	C₂×C₃×H(3,𝔽₃)	C₃
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃³ ◁ 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.