Subgroups — #63510

Order 288.

93 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#41	C₂	1	1	yes	maximal, characteristic
2	#3667	C₂	1	3	yes	maximal, complemented
3	C₂×C₉⋊C₈	C₂	1	3	yes	maximal, complemented
4	#948	—	3	1	no	maximal
5	Q₈×C₉	C₄	1	1	yes	characteristic
6	D₄×C₉	C₄	1	3	yes	—
7	C₂×C₄×C₉	C₂²	1	3	yes	—
8	C₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₉⋊C₈	C₂²	1	3	yes	—
10	C₃×#41	D₃	1	1	yes	characteristic
11	#208	—	3	3	no	—
12	C₂×C₃⋊C₈	—	3	3	no	—
13	C₂²×C₉	C₂×C₄	1	3	yes	—
14	C₄×C₉	C₂×C₄	1	3	yes	—
15	C₄×C₉	C₂³	1	1	yes	characteristic
16	#131	—	9	1	no	Sylow
17	C₃×Q₈	Dic₃	1	1	yes	characteristic
18	C₃×D₄	Dic₃	1	3	yes	—
19	C₂×C₃×C₄	C₂×D₃	1	3	yes	—
20	C₃⋊C₈	—	3	1	no	—
21	C₃⋊C₈	—	3	3	no	—
22	C₂×C₉	—	2	3	no	—
23	C₂×C₉	C₂²×C₄	1	1	yes	characteristic
24	#41	D₉	1	1	yes	characteristic
25	M₁₆	—	9	3	no	—
26	C₂×C₈	—	9	3	no	—
27	C₂²×C₃	C₂×Dic₃	1	3	yes	—
28	C₃×C₄	C₂×Dic₃	1	3	yes	—
29	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
30	C₉	#131	1	1	yes	characteristic, complemented, Sylow
31	Q₈	Dic₉	1	1	yes	characteristic
32	D₄	Dic₉	1	3	yes	—
33	C₂×C₄	C₂×D₉	1	3	yes	—
34	C₈	—	9	1	no	—
35	C₈	—	9	3	no	—
36	C₂×C₃	—	2	3	no	—
37	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
38	C₂²	C₂×Dic₉	1	3	yes	—
39	C₄	C₂×Dic₉	1	3	yes	—
40	C₄	C₂²×D₉	1	1	yes	characteristic
41	C₃	#948	1	1	yes	characteristic
42	C₂	—	2	3	no	—
43	C₂	C₂²×Dic₉	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.