Subgroups — Dic₉⋊C₄ #3669

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	1	yes	maximal, characteristic
3	C₂×Dic₉	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊C₄	—	3	1	no	maximal
5	C₂²×C₉	C₂²	1	1	yes	characteristic
6	C₄×C₉	—	2	1	no	—
7	Dic₉	—	2	1	no	—
8	Dic₉	C₄	1	2	yes	complemented
9	C₂×C₃×C₄	D₃	1	1	yes	characteristic
10	C₂×Dic₃	—	3	1	no	—
11	C₂×Dic₃	—	3	1	no	—
12	C₂×C₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₉	D₄	1	1	yes	characteristic
14	C₂×C₉	Q₈	1	1	yes	characteristic
15	C₄⋊C₄	—	9	1	no	Sylow
16	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
17	C₃×C₄	—	2	1	no	—
18	Dic₃	—	3	2	no	—
19	Dic₃	—	6	1	no	—
20	C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₄	—	9	1	no	—
22	C₂×C₄	—	9	1	no	—
23	C₂×C₄	D₉	1	1	yes	characteristic
24	C₂×C₃	Dic₆	1	1	yes	characteristic
25	C₂×C₃	C₄×D₃	1	1	yes	characteristic
26	C₂×C₃	#67	1	1	yes	characteristic
27	C₂²	C₂×D₉	1	1	yes	characteristic
28	C₄	—	2	1	no	—
29	C₄	—	9	2	no	—
30	C₄	—	18	1	no	—
31	C₃	Dic₃⋊C₄	1	1	yes	characteristic
32	C₂	Dic₁₈	1	1	yes	characteristic
33	C₂	C₄×D₉	1	1	yes	characteristic
34	C₂	#611	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.

N	H ≅ G/N	type
8. Dic₉	C₄	semidirect
20. C₉	C₄⋊C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.