Subgroups — C₂×D₈₉₆₁ #49089484

Order 35844.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₉₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₂₉×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₉₈₇	—	3	1	no	maximal, Hall
4	C₃×C₂₉×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₉×C₁₀₃	D₃	1	1	yes	characteristic, complemented
6	D₂₉₈₇	—	3	2	no	—
7	C₂₉×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃₀₉	—	29	1	no	maximal, Hall
9	C₂×C₃×C₁₀₃	D₂₉	1	1	yes	characteristic, complemented
10	D₃₀₉	—	29	2	no	—
11	C₂×D₁₀₃	—	87	1	no	Hall
12	C₂×D₈₇	—	103	1	no	maximal, Hall
13	C₃×C₁₀₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₀₃	D₈₇	1	1	yes	characteristic, complemented
15	D₁₀₃	—	87	2	no	—
16	C₂×C₃×C₂₉	D₁₀₃	1	1	yes	characteristic, complemented
17	D₈₇	—	103	2	no	—
18	C₂×D₂₉	—	309	1	no	Hall
19	C₁₀₃	C₂×D₈₇	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₂₉	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₉	D₃₀₉	1	1	yes	characteristic, complemented
22	D₂₉	—	309	2	no	—
23	C₂₉	C₂×D₃₀₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	2987	1	no	Hall
25	C₂×C₃	D₂₉₈₇	1	1	yes	characteristic, complemented
26	D₃	—	2987	2	no	—
27	C₂²	—	8961	1	no	Sylow
28	C₃	C₂×D₂₉₈₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	8961	2	no	—
30	C₂	D₈₉₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₉₆₁
commutator, cosocle, hypocenter	C₃×C₂₉×C₁₀₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₉×C₁₀₃	C₂
LCS	G ▷ C₃×C₂₉×C₁₀₃
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.