Subgroups — D₇×Dic₉ #92590

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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