Subgroups — C₄₁×D₂₄ #14520129

Order 1968.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₂×C₄₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×C₄₁	—	3	1	no	maximal, Hall
4	C₂×D₃×C₄₁	—	2	2	no	—
5	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	D₄×C₄₁	—	3	2	no	—
7	C₈×C₄₁	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₄₁	D₄	1	1	yes	characteristic
9	D₃×C₄₁	—	4	2	no	—
10	C₂²×C₄₁	—	6	2	no	—
11	C₄×C₄₁	C₂×D₃	1	1	yes	characteristic
12	C₃×C₄₁	D₈	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₁	—	12	2	no	—
14	C₂×C₄₁	D₁₂	1	1	yes	characteristic
15	D₂₄	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₄₁	D₂₄	1	1	yes	characteristic, direct product factor, Sylow
17	D₁₂	C₂×C₄₁	1	2	yes	complemented
18	C₃×C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
19	D₈	—	3	1	no	Sylow
20	C₂×D₃	—	2	2	no	—
21	C₃×C₄	C₂²×C₄₁	1	1	yes	characteristic
22	D₄	—	3	2	no	—
23	C₈	D₃×C₄₁	1	1	yes	characteristic, complemented
24	C₂×C₃	D₄×C₄₁	1	1	yes	characteristic
25	D₃	—	4	2	no	—
26	C₂²	—	6	2	no	—
27	C₄	C₂×D₃×C₄₁	1	1	yes	characteristic
28	C₃	D₈×C₄₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	12	2	no	—
30	C₂	D₁₂×C₄₁	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.