Subgroups — C₆₁×(C₄₃⋊C₃)⋊C₄ #44538342

Order 31476.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₆₁×Dic₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₁×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₃×C₆₁	C₂×C₃	1	1	yes	characteristic
5	C₄₃×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₆₁	—	43	1	no	maximal, Hall
7	(C₄₃⋊C₃)⋊C₄	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₆₁	—	43	1	no	—
9	C₂×C₄₃⋊C₃	C₂×C₆₁	1	1	yes	characteristic
10	C₄×C₆₁	—	43	1	no	Hall
11	C₃×C₆₁	—	43	1	no	Hall
12	Dic₄₃	C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
13	C₄₃⋊C₃	C₄×C₆₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₆₁	D₄₃⋊C₃	1	1	yes	characteristic
15	C₂×C₄₃	C₂×C₃×C₆₁	1	1	yes	characteristic
16	C₆₁	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₃	C₃×C₄×C₆₁	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	43	1	no	Hall
19	C₂×C₃	—	43	1	no	—
20	C₄	—	43	1	no	Sylow
21	C₃	—	43	1	no	Sylow
22	C₂	C₆₁×D₄₃⋊C₃	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.