Subgroups — Dic₇₉₄₃ #44540944

Order 31772.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic
2	C₄₇×C₁₆₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₆₁₁	—	13	1	no	maximal
4	C₂×C₁₃×C₄₇	D₁₃	1	1	yes	characteristic
5	Dic₁₆₉	—	47	1	no	maximal, Hall
6	C₁₃×C₄₇	Dic₁₃	1	1	yes	characteristic
7	C₂×C₁₆₉	D₄₇	1	1	yes	characteristic
8	Dic₄₇	—	169	1	no	Hall
9	C₁₆₉	Dic₄₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₄₇	D₁₆₉	1	1	yes	characteristic
11	Dic₁₃	—	611	1	no	—
12	C₄₇	Dic₁₆₉	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₃	D₆₁₁	1	1	yes	characteristic
14	C₁₃	Dic₆₁₁	1	1	yes	characteristic
15	C₄	—	7943	1	no	Sylow
16	C₂	D₇₉₄₃	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.