Subgroups — C₂×D₈₀₄₁ #44565504

Order 32164.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₀₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₇×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₇×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇₃₁	—	11	1	no	maximal, Hall
5	C₂×D₄₇₃	—	17	1	no	maximal, Hall
6	C₂×C₁₇×C₄₃	D₁₁	1	1	yes	characteristic, complemented
7	D₇₃₁	—	11	2	no	—
8	C₂×C₁₁×C₄₃	D₁₇	1	1	yes	characteristic, complemented
9	D₄₇₃	—	17	2	no	—
10	C₂×D₁₈₇	—	43	1	no	maximal, Hall
11	C₁₇×C₄₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₄₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁×C₁₇	D₄₃	1	1	yes	characteristic, complemented
14	D₁₈₇	—	43	2	no	—
15	C₁₁×C₁₇	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₄₃	—	187	1	no	Hall
17	C₂×C₄₃	D₁₈₇	1	1	yes	characteristic, complemented
18	D₄₃	—	187	2	no	—
19	C₂×D₁₇	—	473	1	no	Hall
20	C₂×D₁₁	—	731	1	no	Hall
21	C₄₃	C₂×D₁₈₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₇	D₄₇₃	1	1	yes	characteristic, complemented
23	D₁₇	—	473	2	no	—
24	C₂×C₁₁	D₇₃₁	1	1	yes	characteristic, complemented
25	D₁₁	—	731	2	no	—
26	C₁₇	C₂×D₄₇₃	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₂×D₇₃₁	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	8041	1	no	Sylow
29	C₂	—	8041	2	no	—
30	C₂	D₈₀₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₀₄₁
commutator, cosocle, hypocenter	C₁₁×C₁₇×C₄₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₇×C₄₃	C₂
LCS	G ▷ C₁₁×C₁₇×C₄₃
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.