Subgroups — C₄⋊Dic₉ #3670

Order 144.

39 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	—	2	2	no	—
7	C₂×C₃×C₄	D₃	1	1	yes	characteristic
8	C₂×Dic₃	—	3	2	no	—
9	C₂×C₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₉	D₄	1	1	yes	characteristic
11	C₂×C₉	Q₈	1	1	yes	characteristic
12	C₄⋊C₄	—	9	1	no	Sylow
13	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
14	C₃×C₄	Dic₃	1	2	yes	—
15	Dic₃	—	6	2	no	—
16	C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₄	—	9	2	no	—
18	C₂×C₄	D₉	1	1	yes	characteristic
19	C₂×C₃	Dic₆	1	1	yes	characteristic
20	C₂×C₃	D₁₂	1	1	yes	characteristic
21	C₂×C₃	C₂×Dic₃	1	1	yes	characteristic
22	C₂²	C₂×D₉	1	1	yes	characteristic
23	C₄	—	18	2	no	—
24	C₄	Dic₉	1	2	yes	complemented
25	C₃	C₄⋊Dic₃	1	1	yes	characteristic
26	C₂	Dic₁₈	1	1	yes	characteristic
27	C₂	D₃₆	1	1	yes	characteristic
28	C₂	C₂×Dic₉	1	1	yes	characteristic

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