Subgroups — C₁₁×C₂₉×C₆₄ #72197993

Order 20416.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₆×C₂₉	C₄	1	1	yes	characteristic
3	C₈×C₁₁×C₂₉	C₈	1	1	yes	characteristic
4	C₂₉×C₆₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₁₁×C₂₉	C₁₆	1	1	yes	characteristic
6	C₂₉×C₃₂	C₂×C₁₁	1	1	yes	characteristic
7	C₁₁×C₆₄	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₁×C₂₉	C₃₂	1	1	yes	characteristic
9	C₁₆×C₂₉	C₄×C₁₁	1	1	yes	characteristic
10	C₁₁×C₃₂	C₂×C₂₉	1	1	yes	characteristic
11	C₁₁×C₂₉	C₆₄	1	1	yes	characteristic, direct product factor, Hall
12	C₈×C₂₉	C₈×C₁₁	1	1	yes	characteristic
13	C₁₁×C₁₆	C₄×C₂₉	1	1	yes	characteristic
14	C₄×C₂₉	C₁₁×C₁₆	1	1	yes	characteristic
15	C₈×C₁₁	C₈×C₂₉	1	1	yes	characteristic
16	C₆₄	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₂₉	C₁₁×C₃₂	1	1	yes	characteristic
18	C₄×C₁₁	C₁₆×C₂₉	1	1	yes	characteristic
19	C₃₂	C₂×C₁₁×C₂₉	1	1	yes	characteristic
20	C₂₉	C₁₁×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₁₁	C₂₉×C₃₂	1	1	yes	characteristic
22	C₁₆	C₄×C₁₁×C₂₉	1	1	yes	characteristic
23	C₁₁	C₂₉×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
24	C₈	C₈×C₁₁×C₂₉	1	1	yes	characteristic
25	C₄	C₁₁×C₁₆×C₂₉	1	1	yes	characteristic
26	C₂	C₁₁×C₂₉×C₃₂	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.