Subgroups — #10619510

Order 648.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#731	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²⋊C₈	—	3	2	no	maximal
3	(C₃⋊(C₃⋊C₈))⋊C₃	—	3	1	no	maximal
4	C₃×C₉⋊C₈	—	3	1	no	maximal
5	C₂×#731	C₄	1	1	yes	characteristic
6	C₄×3₋¹⁺²	D₃	1	2	yes	—
7	C₄×H(3,𝔽₃)	D₃	1	1	yes	characteristic
8	C₃×C₄×C₉	D₃	1	1	yes	characteristic
9	#731	C₈	1	1	yes	characteristic, complemented, Sylow
10	C₃⋊(C₃⋊C₈)	—	3	1	no	—
11	C₃×C₃⋊C₈	—	9	1	no	—
12	C₉⋊C₈	—	3	1	no	—
13	C₉⋊C₈	—	3	2	no	—
14	C₂×3₋¹⁺²	Dic₃	1	2	yes	—
15	C₂×H(3,𝔽₃)	Dic₃	1	1	yes	characteristic
16	C₂×C₃×C₉	Dic₃	1	1	yes	characteristic
17	C₃²×C₄	—	6	1	no	—
18	C₃²×C₄	C₃⋊D₃	1	1	yes	characteristic
19	C₄×C₉	—	6	1	no	—
20	C₄×C₉	—	6	2	no	—
21	3₋¹⁺²	C₃⋊C₈	1	2	yes	complemented
22	H(3,𝔽₃)	C₃⋊C₈	1	1	yes	characteristic
23	C₃×C₉	C₃⋊C₈	1	1	yes	characteristic, complemented
24	C₃×C₈	—	27	1	no	—
25	C₃⋊C₈	—	9	1	no	—
26	C₃⋊C₈	—	27	1	no	—
27	C₂×C₃²	—	6	1	no	—
28	C₂×C₃²	C₃⋊Dic₃	1	1	yes	characteristic
29	C₂×C₉	—	6	1	no	—
30	C₂×C₉	—	6	2	no	—
31	C₃×C₄	—	3	1	no	—
32	C₃×C₄	—	18	1	no	—
33	C₃×C₄	#272	1	1	yes	characteristic
34	C₃²	—	6	1	no	—
35	C₃²	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
36	C₉	—	6	1	no	—
37	C₉	—	6	2	no	—
38	C₈	—	27	1	no	Sylow
39	C₂×C₃	—	3	1	no	—
40	C₂×C₃	—	18	1	no	—
41	C₂×C₃	#1084	1	1	yes	characteristic
42	C₄	#4184	1	1	yes	characteristic
43	C₃	—	3	1	no	—
44	C₃	—	18	1	no	—
45	C₃	#6180	1	1	yes	characteristic
46	C₂	#66331	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.