Subgroups — C₉×C₄⋊C₄ #3679

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	2	yes	maximal
2	C₂×C₄×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₄	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₉	C₂²	1	1	yes	characteristic
5	C₄×C₉	—	2	2	no	—
6	C₄×C₉	C₄	1	2	yes	complemented
7	C₂×C₃×C₄	C₂×C₃	1	2	yes	—
8	C₂×C₃×C₄	C₂×C₃	1	1	yes	characteristic
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	C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic
14	C₃×C₄	—	2	2	no	—
15	C₃×C₄	C₃×C₄	1	2	yes	—
16	C₉	C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₄	C₂×C₉	1	2	yes	—
18	C₂×C₄	C₂×C₉	1	1	yes	characteristic
19	C₂×C₃	C₂×C₃×C₄	1	1	yes	characteristic
20	C₂×C₃	C₃×D₄	1	1	yes	characteristic
21	C₂×C₃	C₃×Q₈	1	1	yes	characteristic
22	C₂²	C₂²×C₉	1	1	yes	characteristic
23	C₄	—	2	2	no	—
24	C₄	C₄×C₉	1	2	yes	complemented
25	C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
26	C₂	C₂×C₄×C₉	1	1	yes	characteristic
27	C₂	D₄×C₉	1	1	yes	characteristic
28	C₂	Q₈×C₉	1	1	yes	characteristic

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

subgroup	index
C₂×C₄×C₉	2
C₃×C₄⋊C₄	3