Subgroups — C₄²×C₂₃×C₆₁ #72199846

Order 22448.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₃×C₆₁	C₂	1	3	yes	maximal
2	C₂²×C₂₃×C₆₁	C₂²	1	1	yes	characteristic
3	C₄×C₂₃×C₆₁	C₄	1	6	yes	direct product factor
4	C₂×C₂₃×C₆₁	C₂×C₄	1	3	yes	—
5	C₂₃×C₆₁	C₄²	1	1	yes	characteristic, direct product factor, Hall
6	C₄²×C₆₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄×C₆₁	C₂×C₂₃	1	3	yes	—
8	C₄²×C₂₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₆₁	C₂²×C₂₃	1	1	yes	characteristic
10	C₄×C₆₁	C₄×C₂₃	1	6	yes	direct product factor
11	C₂×C₄×C₂₃	C₂×C₆₁	1	3	yes	—
12	C₂×C₆₁	C₂×C₄×C₂₃	1	3	yes	—
13	C₂²×C₂₃	C₂²×C₆₁	1	1	yes	characteristic
14	C₄×C₂₃	C₄×C₆₁	1	6	yes	direct product factor
15	C₆₁	C₄²×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₃	C₂×C₄×C₆₁	1	3	yes	—
17	C₂₃	C₄²×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₄²	C₂₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₄	C₂×C₂₃×C₆₁	1	3	yes	—
20	C₂²	C₂²×C₂₃×C₆₁	1	1	yes	characteristic
21	C₄	C₄×C₂₃×C₆₁	1	6	yes	direct product factor
22	C₂	C₂×C₄×C₂₃×C₆₁	1	3	yes	—

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.