Subgroups — C₈×C₉⋊C₉ #10619515

Order 648.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

subgroup	index
C₄×C₉⋊C₉	2
C₃×C₈×C₉	3