Subgroups — C₄₁×SL(2,ℤ/4) #14520177

Order 1968.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×A₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₄×C₄₁	—	3	1	no	maximal, Hall
3	A₄×C₄₁	C₄	1	1	yes	characteristic, complemented
4	Dic₃×C₄₁	—	4	1	no	maximal
5	C₂³×C₄₁	D₃	1	1	yes	characteristic
6	C₂×C₄×C₄₁	—	3	1	no	—
7	C₂×C₄×C₄₁	—	3	1	no	—
8	C₂×C₃×C₄₁	—	4	1	no	—
9	C₂²×C₄₁	—	3	1	no	—
10	C₂²×C₄₁	—	3	1	no	—
11	C₂²×C₄₁	Dic₃	1	1	yes	characteristic, complemented
12	C₄×C₄₁	—	6	1	no	—
13	C₄×C₄₁	—	6	1	no	—
14	C₃×C₄₁	—	4	1	no	Hall
15	C₂×C₄₁	—	3	1	no	—
16	C₂×C₄₁	—	3	1	no	—
17	C₂×C₄₁	S₄	1	1	yes	characteristic
18	SL(2,ℤ/4)	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₄₁	SL(2,ℤ/4)	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×A₄	C₂×C₄₁	1	1	yes	characteristic
21	C₂²⋊C₄	—	3	1	no	Sylow
22	A₄	C₄×C₄₁	1	1	yes	characteristic, complemented
23	Dic₃	—	4	1	no	—
24	C₂³	D₃×C₄₁	1	1	yes	characteristic
25	C₂×C₄	—	3	1	no	—
26	C₂×C₄	—	3	1	no	—
27	C₂×C₃	—	4	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	Dic₃×C₄₁	1	1	yes	characteristic, complemented
31	C₄	—	6	1	no	—
32	C₄	—	6	1	no	—
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	3	1	no	—
36	C₂	S₄×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.