Subgroups — C₄×C₂²⋊C₉ #3691

Order 144.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄	C₃	1	1	yes	maximal, characteristic
3	C₂²⋊C₉	C₄	1	1	yes	characteristic, direct product factor
4	C₄×C₉	—	4	1	no	maximal
5	C₂³×C₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₄	—	3	1	no	—
7	C₂×C₃×C₄	—	3	1	no	—
8	C₂×C₉	—	4	1	no	—
9	C₂²×C₄	C₉	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₃	—	3	1	no	—
11	C₂²×C₃	—	3	1	no	—
12	C₂²×C₃	C₃×C₄	1	1	yes	characteristic
13	C₃×C₄	—	3	1	no	—
14	C₃×C₄	A₄	1	1	yes	characteristic
15	C₉	—	4	1	no	Sylow
16	C₂³	C₂×C₉	1	1	yes	characteristic
17	C₂×C₄	—	3	1	no	—
18	C₂×C₄	—	3	1	no	—
19	C₂×C₃	—	3	1	no	—
20	C₂×C₃	—	3	1	no	—
21	C₂×C₃	C₂×A₄	1	1	yes	characteristic
22	C₂²	—	3	1	no	—
23	C₂²	—	3	1	no	—
24	C₂²	C₄×C₉	1	1	yes	characteristic, complemented
25	C₄	—	3	1	no	—
26	C₄	C₂²⋊C₉	1	1	yes	characteristic, direct product factor
27	C₃	C₄×A₄	1	1	yes	characteristic
28	C₂	—	3	1	no	—
29	C₂	—	3	1	no	—
30	C₂	C₂×C₂²⋊C₉	1	1	yes	characteristic

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.