Subgroups — D₇×C₁₉×C₁₂₁ #44565678

Order 32186.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₉×C₁₂₁	—	7	1	no	maximal, Hall
3	C₁₁×D₇×C₁₉	C₁₁	1	1	yes	maximal, characteristic
4	C₁₉×C₁₂₁	D₇	1	1	yes	characteristic, direct product factor, Hall
5	D₇×C₁₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₁×C₁₉	C₂×C₁₁	1	1	yes	characteristic
7	C₇×C₁₂₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₁₉	—	7	1	no	—
9	D₇×C₁₉	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₂₁	—	7	1	no	Hall
11	C₁₁×C₁₉	C₁₁×D₇	1	1	yes	characteristic
12	C₁₁×D₇	C₁₁×C₁₉	1	1	yes	characteristic
13	C₇×C₁₉	C₂×C₁₂₁	1	1	yes	characteristic, complemented, Hall
14	C₁₂₁	D₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₇×C₁₁	C₂×C₁₁×C₁₉	1	1	yes	characteristic
16	C₂×C₁₉	—	7	1	no	Hall
17	C₂×C₁₁	—	7	1	no	—
18	C₁₉	D₇×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
19	D₇	C₁₉×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
20	C₁₁	C₁₁×D₇×C₁₉	1	1	yes	characteristic
21	C₇	C₂×C₁₉×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	7	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.