Subgroups — #92589

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#4247	—	3	1	no	maximal
5	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
6	D₆₃	—	2	1	no	—
7	C₇×D₉	—	2	1	no	—
8	C₂×D₂₁	—	3	1	no	—
9	C₂×D₃×C₇	—	3	1	no	—
10	C₃×Dic₇	D₃	1	1	yes	characteristic
11	D₃₆	—	7	1	no	maximal, Hall
12	C₇×C₉	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂²⋊D₇	—	9	1	no	Hall
14	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
15	D₂₁	—	6	1	no	—
16	D₃×C₇	—	6	1	no	—
17	C₂×D₉	—	7	1	no	—
18	C₂×D₉	D₇	1	1	yes	characteristic, complemented
19	C₄×C₉	—	7	1	no	—
20	C₂²×C₇	—	9	1	no	—
21	C₂×D₇	—	9	1	no	—
22	Dic₇	D₉	1	1	yes	characteristic, complemented
23	D₁₂	—	21	1	no	—
24	C₃×C₇	D₁₂	1	1	yes	characteristic
25	C₂×C₉	C₂×D₇	1	1	yes	characteristic
26	D₉	—	2	1	no	—
27	D₉	—	14	1	no	—
28	C₂×C₇	—	18	1	no	—
29	C₂×C₇	C₂×D₉	1	1	yes	characteristic
30	D₇	—	18	1	no	—
31	C₂×D₃	—	3	1	no	—
32	C₂×D₃	—	21	1	no	—
33	C₃×C₄	—	7	1	no	—
34	C₉	C₂²⋊D₇	1	1	yes	characteristic, complemented, Sylow
35	D₄	—	63	1	no	Sylow
36	C₇	D₃₆	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃	D₃×D₇	1	1	yes	characteristic
38	D₃	—	6	1	no	—
39	D₃	—	42	1	no	—
40	C₂²	—	9	1	no	—
41	C₂²	—	63	1	no	—
42	C₄	—	7	1	no	—
43	C₃	#4247	1	1	yes	characteristic
44	C₂	—	18	1	no	—
45	C₂	—	126	1	no	—
46	C₂	D₇×D₉	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.