Subgroups — C₂×C₇×Dic₉ #92606

Order 504.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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