Subgroups — Dic₁₄₈₀₁ #72292001

Order 59204.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×C₃₆₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×C₃₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₇₉	—	19	1	no	maximal
4	C₂×C₁₉×C₄₁	D₁₉	1	1	yes	characteristic
5	Dic₃₆₁	—	41	1	no	maximal, Hall
6	C₁₉×C₄₁	Dic₁₉	1	1	yes	characteristic
7	C₂×C₃₆₁	D₄₁	1	1	yes	characteristic
8	C₃₆₁	Dic₄₁	1	1	yes	characteristic, complemented, Sylow
9	Dic₄₁	—	361	1	no	Hall
10	C₂×C₄₁	D₃₆₁	1	1	yes	characteristic
11	Dic₁₉	—	779	1	no	—
12	C₄₁	Dic₃₆₁	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₉	D₇₇₉	1	1	yes	characteristic
14	C₁₉	Dic₇₇₉	1	1	yes	characteristic
15	C₄	—	14801	1	no	Sylow
16	C₂	D₁₄₈₀₁	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.