Subgroups — D₉×Dic₇ #92587

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₉	C₂	1	1	yes	maximal, characteristic
2	Dic₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×Dic₇	—	3	1	no	maximal
5	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
6	C₇×D₉	C₄	1	2	yes	complemented
7	C₂×D₃×C₇	—	3	1	no	—
8	Dic₂₁	—	3	1	no	—
9	C₃×Dic₇	D₃	1	1	yes	characteristic
10	C₄×D₉	—	7	1	no	maximal, Hall
11	C₇×C₉	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×Dic₇	—	9	1	no	Hall
13	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
14	D₃×C₇	—	3	2	no	—
15	C₂×D₉	D₇	1	1	yes	characteristic
16	C₄×C₉	—	7	1	no	—
17	Dic₉	—	7	1	no	—
18	C₂²×C₇	—	9	1	no	—
19	Dic₇	—	9	1	no	—
20	Dic₇	D₉	1	1	yes	characteristic, direct product factor
21	C₄×D₃	—	21	1	no	—
22	C₃×C₇	C₄×D₃	1	1	yes	characteristic
23	C₂×C₉	C₂×D₇	1	1	yes	characteristic
24	D₉	Dic₇	1	2	yes	direct product factor
25	C₂×C₇	—	9	2	no	—
26	C₂×C₇	C₂×D₉	1	1	yes	characteristic
27	C₂×D₃	—	3	1	no	—
28	C₃×C₄	—	7	1	no	—
29	Dic₃	—	21	1	no	—
30	C₉	C₂×Dic₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄	—	63	1	no	Sylow
32	C₇	C₄×D₉	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	D₃×D₇	1	1	yes	characteristic
34	D₃	—	3	2	no	—
35	C₂²	—	9	1	no	—
36	C₄	—	7	1	no	—
37	C₄	—	63	1	no	—
38	C₃	D₃×Dic₇	1	1	yes	characteristic
39	C₂	—	9	2	no	—
40	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.