Subgroups — C₄₉×D₂₄₇ #37564137

Order 24206.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₄₇	C₇	1	1	yes	maximal, characteristic
3	D₁₉×C₄₉	—	13	1	no	maximal, Hall
4	C₇×C₁₃×C₁₉	C₂×C₇	1	1	yes	characteristic
5	D₁₃×C₄₉	—	19	1	no	maximal, Hall
6	C₁₉×C₄₉	D₁₃	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₄₉	D₁₉	1	1	yes	characteristic, complemented, Hall
8	D₂₄₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
9	C₇×D₁₉	—	13	1	no	—
10	C₁₃×C₁₉	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
11	C₇×D₁₃	—	19	1	no	—
12	C₇×C₁₉	C₇×D₁₃	1	1	yes	characteristic
13	C₂×C₄₉	—	247	1	no	Hall
14	C₇×C₁₃	C₇×D₁₉	1	1	yes	characteristic
15	C₄₉	D₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
16	D₁₉	—	13	1	no	Hall
17	D₁₃	—	19	1	no	Hall
18	C₁₉	D₁₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₇	—	247	1	no	—
20	C₁₃	D₁₉×C₄₉	1	1	yes	characteristic, complemented, Sylow
21	C₇	C₇×D₂₄₇	1	1	yes	characteristic
22	C₂	—	247	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.