Subgroups — C₉×D₂₈ #92600

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	2	yes	maximal, complemented
2	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₈	C₃	1	1	yes	maximal, characteristic
4	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
5	C₉×D₇	—	2	2	no	—
6	C₂×C₃×D₇	C₂×C₃	1	2	yes	—
7	C₃×C₄×C₇	C₂×C₃	1	1	yes	characteristic
8	D₄×C₉	—	7	1	no	maximal, Hall
9	C₇×C₉	D₄	1	1	yes	characteristic, complemented, Hall
10	D₂₈	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
12	C₃×D₇	—	2	2	no	—
13	C₂²×C₉	—	7	2	no	—
14	C₄×C₉	D₇	1	1	yes	characteristic, complemented
15	C₂×D₇	C₂×C₉	1	2	yes	complemented
16	C₄×C₇	C₂×C₉	1	1	yes	characteristic, complemented
17	C₃×D₄	—	7	1	no	—
18	C₃×C₇	C₃×D₄	1	1	yes	characteristic
19	C₂×C₉	—	14	2	no	—
20	C₂×C₉	C₂×D₇	1	1	yes	characteristic
21	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
22	D₇	—	2	2	no	—
23	C₂²×C₃	—	7	2	no	—
24	C₃×C₄	C₃×D₇	1	1	yes	characteristic
25	C₉	D₂₈	1	1	yes	characteristic, direct product factor, Sylow
26	D₄	—	7	1	no	Sylow
27	C₇	D₄×C₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	14	2	no	—
29	C₂×C₃	C₂×C₃×D₇	1	1	yes	characteristic
30	C₂²	—	7	2	no	—
31	C₄	C₉×D₇	1	1	yes	characteristic, complemented
32	C₃	C₃×D₂₈	1	1	yes	characteristic
33	C₂	—	14	2	no	—
34	C₂	C₂×C₉×D₇	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.