Subgroups — C₂×C₃₇⋊C₃×C₁₂₁ #41001728

Order 26862.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊C₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃₇×C₁₂₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₇×C₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₃₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic
5	C₁₁×C₃₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₃₇	C₃×C₁₁	1	1	yes	characteristic
7	C₂×C₃×C₁₂₁	—	37	1	no	maximal, Hall
8	C₁₁×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic
9	C₃×C₁₂₁	—	37	1	no	Hall
10	C₂×C₁₂₁	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃₇⋊C₃	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₂₁	C₂×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃₇⋊C₃	C₂×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₇	C₃×C₁₂₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₁	—	37	1	no	—
16	C₃₇	C₂×C₃×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₁	—	37	1	no	—
18	C₂×C₁₁	C₁₁×C₃₇⋊C₃	1	1	yes	characteristic
19	C₁₁	C₂×C₁₁×C₃₇⋊C₃	1	1	yes	characteristic
20	C₂×C₃	—	37	1	no	Hall
21	C₃	—	37	1	no	Sylow
22	C₂	C₃₇⋊C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, 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.