Subgroups — C₂×#4181 #66383

Order 324.

99 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#4181	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₃⋊D₃	—	3	1	no	maximal
4	C₂×C₃×D₉	—	3	3	no	maximal
5	C₃²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃³	D₃	1	1	yes	characteristic
7	C₃×C₃⋊D₃	—	3	2	no	—
8	C₂×C₃×C₉	D₃	1	3	yes	complemented
9	C₃×D₉	—	3	6	no	—
10	C₂×C₃⋊D₃	—	3	1	no	—
11	C₂×C₃×D₃	—	9	3	no	—
12	C₂×C₃×D₃	—	9	1	no	—
13	C₂×D₉	—	3	3	no	—
14	C₃³	C₂×D₃	1	1	yes	characteristic
15	C₃×C₉	C₂×D₃	1	3	yes	complemented
16	C₂×C₃²	—	3	1	no	—
17	C₂×C₃²	—	6	1	no	—
18	C₂×C₃²	D₉	1	3	yes	complemented
19	C₂×C₃²	C₃⋊D₃	1	1	yes	characteristic
20	C₃⋊D₃	—	3	2	no	—
21	C₃×D₃	—	9	6	no	—
22	C₃×D₃	—	9	2	no	—
23	C₂×C₉	—	3	3	no	—
24	D₉	—	3	6	no	—
25	C₂²×C₃	—	27	1	no	—
26	C₂×D₃	—	9	3	no	—
27	C₂×D₃	—	9	1	no	—
28	C₃²	—	3	1	no	—
29	C₃²	—	6	1	no	—
30	C₃²	C₂×D₉	1	3	yes	complemented
31	C₃²	C₂×C₃⋊D₃	1	1	yes	characteristic
32	C₉	—	3	3	no	—
33	C₂×C₃	—	2	1	no	—
34	C₂×C₃	—	3	3	no	—
35	C₂×C₃	—	27	2	no	—
36	C₂×C₃	C₃⋊D₉	1	1	yes	characteristic
37	C₂×C₃	#272	1	1	yes	characteristic
38	D₃	—	9	6	no	—
39	D₃	—	9	2	no	—
40	C₂²	—	27	1	no	Sylow
41	C₃	—	2	1	no	—
42	C₃	—	3	3	no	—
43	C₃	C₂×C₃⋊D₉	1	1	yes	characteristic
44	C₃	C₂×#272	1	1	yes	characteristic
45	C₂	—	27	2	no	—
46	C₂	#4181	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊D₉
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂²
Frattini	C₃²	C₂×C₃⋊D₃
Fitting	C₂×C₃²⋊C₉	C₂
socle	C₂×C₃²	C₃⋊D₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂×C₃

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.