Subgroups — C₄×Dic₉ #3668

Order 144.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉	C₂	1	2	yes	maximal
3	C₄×Dic₃	—	3	1	no	maximal
4	C₂²×C₉	C₂²	1	1	yes	characteristic
5	C₄×C₉	C₄	1	2	yes	complemented
6	Dic₉	C₄	1	4	yes	direct product factor
7	C₂×C₃×C₄	D₃	1	1	yes	characteristic
8	C₂×Dic₃	—	3	2	no	—
9	C₂×C₉	C₂×C₄	1	2	yes	—
10	C₂×C₉	C₂×C₄	1	1	yes	characteristic
11	C₄²	—	9	1	no	Sylow
12	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
13	C₃×C₄	Dic₃	1	2	yes	—
14	Dic₃	—	3	4	no	—
15	C₉	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₄	—	9	2	no	—
17	C₂×C₄	D₉	1	1	yes	characteristic
18	C₂×C₃	C₄×D₃	1	2	yes	—
19	C₂×C₃	C₂×Dic₃	1	1	yes	characteristic
20	C₂²	C₂×D₉	1	1	yes	characteristic
21	C₄	—	9	4	no	—
22	C₄	Dic₉	1	2	yes	direct product factor
23	C₃	C₄×Dic₃	1	1	yes	characteristic
24	C₂	C₄×D₉	1	2	yes	—
25	C₂	C₂×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₉
commutator, hypocenter	C₉	C₄²
Frattini, socle, prime radical	C₂²×C₃	C₂×D₃
Fitting	C₂×C₄×C₉	C₂
cosocle	C₂²×C₉	C₂²
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₄

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.