Subgroups — C₉×#41 #3707

Order 144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₉	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×C₉	C₂	1	3	yes	maximal, complemented
4	C₃×#41	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₉	C₂²	1	3	yes	—
6	C₄×C₉	C₂²	1	3	yes	—
7	C₄×C₉	C₂²	1	1	yes	characteristic
8	C₃×Q₈	C₂×C₃	1	1	yes	characteristic
9	C₃×D₄	C₂×C₃	1	3	yes	—
10	C₂×C₃×C₄	C₂×C₃	1	3	yes	—
11	C₂×C₉	—	2	3	no	—
12	C₂×C₉	C₂³	1	1	yes	characteristic
13	#41	C₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₃	C₂²×C₃	1	3	yes	—
15	C₃×C₄	C₂²×C₃	1	1	yes	characteristic
16	C₃×C₄	C₂²×C₃	1	3	yes	—
17	C₉	#41	1	1	yes	characteristic, direct product factor, Sylow
18	Q₈	C₂×C₉	1	1	yes	characteristic, complemented
19	D₄	C₂×C₉	1	3	yes	complemented
20	C₂×C₄	C₂×C₉	1	3	yes	complemented
21	C₂×C₃	—	2	3	no	—
22	C₂×C₃	C₂³×C₃	1	1	yes	characteristic
23	C₂²	C₂²×C₉	1	3	yes	—
24	C₄	C₂²×C₉	1	1	yes	characteristic
25	C₄	C₂²×C₉	1	3	yes	—
26	C₃	C₃×#41	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂³×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.