Subgroups — C₂×D₄₁×C₁₂₁ #34090752

Order 19844.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₁×C₁₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄₁×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₄₁	C₁₁	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄₁	C₂×C₁₁	1	1	yes	characteristic
6	C₁₁×D₄₁	C₂×C₁₁	1	2	yes	—
7	C₂²×C₁₂₁	—	41	1	no	maximal, Hall
8	C₁₁×C₄₁	C₂²×C₁₁	1	1	yes	characteristic
9	C₂×C₁₂₁	—	41	2	no	—
10	C₂×C₁₂₁	D₄₁	1	1	yes	characteristic, direct product factor
11	C₂×D₄₁	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₂₁	C₂×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₄₁	C₂×C₁₂₁	1	1	yes	characteristic, complemented
14	D₄₁	C₂×C₁₂₁	1	2	yes	direct product factor
15	C₂²×C₁₁	—	41	1	no	—
16	C₄₁	C₂²×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₁	—	41	2	no	—
18	C₂×C₁₁	C₁₁×D₄₁	1	1	yes	characteristic
19	C₁₁	C₂×C₁₁×D₄₁	1	1	yes	characteristic
20	C₂²	—	41	1	no	Sylow
21	C₂	—	41	2	no	—
22	C₂	D₄₁×C₁₂₁	1	1	yes	characteristic, direct product factor

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.