Subgroups — #10619531

Order 648.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉⋊Dic₉	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₉	C₂	1	2	yes	maximal
3	#6189	—	3	2	no	maximal
4	C₂×C₉²	C₂²	1	1	yes	characteristic
5	C₃⋊Dic₉	—	3	2	no	—
6	C₃⋊Dic₉	—	6	1	no	—
7	C₉×Dic₃	—	3	2	no	—
8	C₃×Dic₉	D₃	1	2	yes	—
9	C₉²	Q₈	1	1	yes	characteristic, complemented, Sylow
10	#627	—	9	1	no	—
11	Dic₁₈	—	9	2	no	—
12	C₂×C₃×C₉	—	2	1	no	—
13	C₂×C₃×C₉	C₂×D₃	1	2	yes	—
14	C₃⋊Dic₃	—	9	1	no	—
15	C₃×Dic₃	—	3	2	no	—
16	C₄×C₉	—	9	2	no	—
17	Dic₉	—	9	2	no	—
18	Dic₉	—	18	2	no	—
19	Dic₉	—	18	3	no	—
20	Dic₉	D₉	1	2	yes	—
21	C₃×C₉	—	2	1	no	—
22	C₃×C₉	Dic₆	1	2	yes	—
23	Dic₆	—	27	2	no	—
24	C₂×C₃²	D₃²	1	1	yes	characteristic
25	C₂×C₉	—	2	3	no	—
26	C₂×C₉	—	2	2	no	—
27	C₂×C₉	C₂×D₉	1	2	yes	—
28	C₃×C₄	—	9	2	no	—
29	Dic₃	—	3	2	no	—
30	Dic₃	—	27	2	no	—
31	Dic₃	—	54	1	no	—
32	C₃²	#627	1	1	yes	characteristic
33	C₉	—	2	3	no	—
34	C₉	—	2	2	no	—
35	C₉	Dic₁₈	1	2	yes	complemented
36	Q₈	—	81	1	no	Sylow
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	D₃×D₉	1	2	yes	—
39	C₄	—	9	2	no	—
40	C₄	—	81	1	no	—
41	C₃	—	2	1	no	—
42	C₃	#6189	1	2	yes	—
43	C₂	D₉²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉²
commutator, Fitting, cosocle	C₂×C₉²	C₂²
Frattini, socle, prime radical	C₂×C₃²	D₃²
hypocenter	C₉²	Q₈
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. C₉²	Q₈	semidirect
35. C₉	Dic₁₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.