Subgroups — D₃×C₄₉×C₈₉ #39908577

Order 26166.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₄₉×C₈₉	—	3	1	no	maximal, Hall
3	C₄₉×C₈₉	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₇×C₈₉	C₇	1	1	yes	maximal, characteristic
5	C₃×C₇×C₈₉	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₈₉	—	3	1	no	—
7	C₇×C₈₉	D₃×C₇	1	1	yes	characteristic
8	D₃×C₈₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
9	D₃×C₄₉	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₈₉	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₈₉	—	3	1	no	Hall
12	C₃×C₄₉	C₂×C₈₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₉	—	3	1	no	Hall
14	C₈₉	D₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₄₉	D₃×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
16	D₃×C₇	C₇×C₈₉	1	1	yes	characteristic
17	C₃×C₇	C₂×C₇×C₈₉	1	1	yes	characteristic
18	C₂×C₇	—	3	1	no	—
19	C₇	D₃×C₇×C₈₉	1	1	yes	characteristic
20	D₃	C₄₉×C₈₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₄₉×C₈₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

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.