Subgroups — AΣL(1,𝔽₁₆) #351

Order 64.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#120	C₂	1	1	yes	maximal, characteristic
2	#100	C₂	1	1	yes	maximal, characteristic, complemented
3	#99	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴	C₄	1	1	yes	characteristic, complemented
5	C₂×D₄	—	2	1	no	—
6	C₂×D₄	C₂²	1	1	yes	characteristic
7	M₁₆	—	2	1	no	—
8	C₂²⋊C₄	—	2	1	no	—
9	C₂²⋊C₄	—	2	1	no	—
10	C₂²⋊C₄	C₄	1	1	yes	characteristic, complemented
11	C₂³	—	2	1	no	—
12	C₂³	—	4	2	no	—
13	C₂³	—	4	1	no	—
14	C₂³	C₂×C₄	1	1	yes	characteristic
15	C₂³	D₄	1	1	yes	characteristic
16	D₄	—	4	1	no	—
17	D₄	—	4	2	no	—
18	C₂×C₄	—	2	1	no	—
19	C₂×C₄	—	4	1	no	—
20	C₂×C₄	D₄	1	1	yes	characteristic
21	C₈	—	4	1	no	—
22	C₂²	—	2	2	no	—
23	C₂²	—	2	1	no	—
24	C₂²	—	2	1	no	—
25	C₂²	—	4	1	no	—
26	C₂²	—	4	1	no	—
27	C₂²	—	4	1	no	—
28	C₂²	—	4	2	no	—
29	C₂²	—	4	2	no	—
30	C₂²	—	4	1	no	—
31	C₂²	C₂²⋊C₄	1	1	yes	characteristic
32	C₄	—	2	1	no	—
33	C₄	—	4	1	no	—
34	C₄	—	8	1	no	—
35	C₂	—	2	1	no	—
36	C₂	—	4	1	no	—
37	C₂	—	4	2	no	—
38	C₂	—	4	1	no	—
39	C₂	#99	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.