Subgroups — Dic₆₆₀₁ #40995987

Order 26404.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₉₄₃	—	7	1	no	maximal, Hall
4	C₂×C₂₃×C₄₁	D₇	1	1	yes	characteristic
5	Dic₂₈₇	—	23	1	no	maximal, Hall
6	C₂₃×C₄₁	Dic₇	1	1	yes	characteristic, complemented, Hall
7	Dic₁₆₁	—	41	1	no	maximal, Hall
8	C₂×C₇×C₄₁	D₂₃	1	1	yes	characteristic
9	C₂×C₇×C₂₃	D₄₁	1	1	yes	characteristic
10	C₇×C₄₁	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	Dic₄₁	—	161	1	no	Hall
12	C₇×C₂₃	Dic₄₁	1	1	yes	characteristic, complemented, Hall
13	Dic₂₃	—	287	1	no	Hall
14	C₂×C₄₁	D₁₆₁	1	1	yes	characteristic
15	C₂×C₂₃	D₂₈₇	1	1	yes	characteristic
16	C₄₁	Dic₁₆₁	1	1	yes	characteristic, complemented, Sylow
17	Dic₇	—	943	1	no	Hall
18	C₂₃	Dic₂₈₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₇	D₉₄₃	1	1	yes	characteristic
20	C₇	Dic₉₄₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6601	1	no	Sylow
22	C₂	D₆₆₀₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₆₀₁
commutator, hypocenter	C₇×C₂₃×C₄₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₂₃×C₄₁	C₂
LCS	G ▷ C₇×C₂₃×C₄₁
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.