Subgroups — C₉×#127 #63529

Order 288.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₉	C₂	1	6	yes	maximal, complemented
2	C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#127	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₉	C₂²	1	4	yes	—
5	D₄×C₉	—	2	12	no	—
6	C₂×C₄×C₉	C₂²	1	3	yes	—
7	C₂×C₃×D₄	C₂×C₃	1	6	yes	—
8	C₃×C₄²	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₉	—	2	12	no	—
10	C₂²×C₉	C₂³	1	1	yes	characteristic
11	C₄×C₉	D₄	1	6	yes	complemented
12	#127	C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂³×C₃	C₂²×C₃	1	4	yes	—
14	C₃×D₄	—	2	12	no	—
15	C₂×C₃×C₄	C₂²×C₃	1	3	yes	—
16	C₂×C₉	—	4	4	no	—
17	C₂×C₉	C₂×D₄	1	3	yes	—
18	C₂×D₄	C₂×C₉	1	6	yes	complemented
19	C₄²	C₂×C₉	1	1	yes	characteristic, complemented
20	C₂²×C₃	—	2	12	no	—
21	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
22	C₃×C₄	C₃×D₄	1	6	yes	—
23	C₉	#127	1	1	yes	characteristic, direct product factor, Sylow
24	C₂³	C₂²×C₉	1	4	yes	—
25	D₄	—	2	12	no	—
26	C₂×C₄	C₂²×C₉	1	3	yes	—
27	C₂×C₃	—	4	4	no	—
28	C₂×C₃	C₂×C₃×D₄	1	3	yes	—
29	C₂²	—	2	12	no	—
30	C₂²	C₂³×C₉	1	1	yes	characteristic
31	C₄	D₄×C₉	1	6	yes	complemented
32	C₃	C₃×#127	1	1	yes	characteristic
33	C₂	—	4	4	no	—
34	C₂	C₂×D₄×C₉	1	3	yes	—

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.