Subgroups — C₈×#732 #10619520

Order 648.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#732	C₂	1	1	yes	maximal, characteristic
2	C₈×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	C₃×C₈×C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#732	C₄	1	1	yes	characteristic
5	C₄×H(3,𝔽₃)	C₂×C₃	1	3	yes	—
6	C₃×C₄×C₉	C₂×C₃	1	1	yes	characteristic
7	#732	C₈	1	1	yes	characteristic, direct product factor, Sylow
8	C₃²×C₈	—	3	3	no	—
9	C₃²×C₈	C₃²	1	1	yes	characteristic
10	C₈×C₉	—	3	1	no	—
11	C₂×H(3,𝔽₃)	C₃×C₄	1	3	yes	—
12	C₂×C₃×C₉	C₃×C₄	1	1	yes	characteristic
13	C₃²×C₄	—	3	3	no	—
14	C₃²×C₄	C₂×C₃²	1	1	yes	characteristic
15	C₄×C₉	—	3	1	no	—
16	H(3,𝔽₃)	C₃×C₈	1	3	yes	complemented
17	C₃×C₉	C₃×C₈	1	1	yes	characteristic, complemented
18	C₃×C₈	—	3	1	no	—
19	C₃×C₈	—	9	3	no	—
20	C₃×C₈	H(3,𝔽₃)	1	1	yes	characteristic
21	C₂×C₃²	—	3	3	no	—
22	C₂×C₃²	C₃²×C₄	1	1	yes	characteristic
23	C₂×C₉	—	3	1	no	—
24	C₃×C₄	—	3	1	no	—
25	C₃×C₄	—	9	3	no	—
26	C₃×C₄	C₂×H(3,𝔽₃)	1	1	yes	characteristic
27	C₃²	—	3	3	no	—
28	C₃²	C₃²×C₈	1	1	yes	characteristic
29	C₉	—	3	1	no	—
30	C₈	#732	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	3	1	no	—
32	C₂×C₃	—	9	3	no	—
33	C₂×C₃	C₄×H(3,𝔽₃)	1	1	yes	characteristic
34	C₄	C₂×#732	1	1	yes	characteristic
35	C₃	—	3	1	no	—
36	C₃	—	9	3	no	—
37	C₃	C₈×H(3,𝔽₃)	1	1	yes	characteristic
38	C₂	C₄×#732	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.