Subgroups — A₄×C₁₆ #4644

Order 192.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₆	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₄×A₄	C₄	1	1	yes	characteristic
4	C₃×C₁₆	—	4	1	no	maximal
5	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₆	—	3	1	no	—
7	C₂×C₁₆	—	3	1	no	—
8	C₂×A₄	C₈	1	1	yes	characteristic
9	C₃×C₈	—	4	1	no	—
10	C₂²×C₄	C₃×C₄	1	1	yes	characteristic
11	C₂×C₈	—	3	1	no	—
12	C₂×C₈	—	3	1	no	—
13	C₁₆	—	3	1	no	—
14	C₁₆	A₄	1	1	yes	characteristic, direct product factor
15	A₄	C₁₆	1	1	yes	characteristic, direct product factor
16	C₃×C₄	—	4	1	no	—
17	C₂³	C₃×C₈	1	1	yes	characteristic
18	C₂×C₄	—	3	1	no	—
19	C₂×C₄	—	3	1	no	—
20	C₈	—	3	1	no	—
21	C₈	C₂×A₄	1	1	yes	characteristic
22	C₂×C₃	—	4	1	no	—
23	C₂²	—	3	1	no	—
24	C₂²	—	3	1	no	—
25	C₂²	C₃×C₁₆	1	1	yes	characteristic, complemented
26	C₄	—	3	1	no	—
27	C₄	C₄×A₄	1	1	yes	characteristic
28	C₃	—	4	1	no	Sylow
29	C₂	—	3	1	no	—
30	C₂	—	3	1	no	—
31	C₂	C₈×A₄	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.