Subgroups — A₄×C₃₂ #68043

Order 384.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₂	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₈×A₄	C₄	1	1	yes	characteristic
4	C₃×C₃₂	—	4	1	no	maximal
5	C₂²×C₁₆	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃₂	—	3	1	no	—
7	C₂×C₃₂	—	3	1	no	—
8	C₄×A₄	C₈	1	1	yes	characteristic
9	C₃×C₁₆	—	4	1	no	—
10	C₂²×C₈	C₃×C₄	1	1	yes	characteristic
11	C₂×C₁₆	—	3	1	no	—
12	C₂×C₁₆	—	3	1	no	—
13	C₃₂	—	3	1	no	—
14	C₃₂	A₄	1	1	yes	characteristic, direct product factor
15	C₂×A₄	C₁₆	1	1	yes	characteristic
16	C₃×C₈	—	4	1	no	—
17	C₂²×C₄	C₃×C₈	1	1	yes	characteristic
18	C₂×C₈	—	3	1	no	—
19	C₂×C₈	—	3	1	no	—
20	C₁₆	—	3	1	no	—
21	C₁₆	C₂×A₄	1	1	yes	characteristic
22	A₄	C₃₂	1	1	yes	characteristic, direct product factor
23	C₃×C₄	—	4	1	no	—
24	C₂³	C₃×C₁₆	1	1	yes	characteristic
25	C₂×C₄	—	3	1	no	—
26	C₂×C₄	—	3	1	no	—
27	C₈	—	3	1	no	—
28	C₈	C₄×A₄	1	1	yes	characteristic
29	C₂×C₃	—	4	1	no	—
30	C₂²	—	3	1	no	—
31	C₂²	—	3	1	no	—
32	C₂²	C₃×C₃₂	1	1	yes	characteristic, complemented
33	C₄	—	3	1	no	—
34	C₄	C₈×A₄	1	1	yes	characteristic
35	C₃	—	4	1	no	Sylow
36	C₂	—	3	1	no	—
37	C₂	—	3	1	no	—
38	C₂	A₄×C₁₆	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.