Subgroups — Dic₃₃₉₇ #28331120

Order 13588.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₄₃×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₉	—	43	1	no	maximal, Hall
4	Dic₄₃	—	79	1	no	maximal, Hall
5	C₂×C₇₉	D₄₃	1	1	yes	characteristic
6	C₂×C₄₃	D₇₉	1	1	yes	characteristic
7	C₇₉	Dic₄₃	1	1	yes	characteristic, complemented, Sylow
8	C₄₃	Dic₇₉	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	3397	1	no	Sylow
10	C₂	D₃₃₉₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₃₉₇
commutator, hypocenter	C₄₃×C₇₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₄₃×C₇₉	C₂
LCS	G ▷ C₄₃×C₇₉
UCS	C₁ ◁ C₂

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.