Subgroups — D₄×A₄ #990

Order 96.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×A₄	C₂	1	2	yes	maximal, complemented
2	C₄×A₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₄	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×A₄	—	2	2	no	—
5	C₂×A₄	C₂²	1	1	yes	characteristic
6	C₃×D₄	—	4	1	no	maximal
7	C₂⁴	C₂×C₃	1	2	yes	complemented
8	C₂×D₄	—	3	1	no	—
9	C₂×D₄	—	3	1	no	—
10	C₂×D₄	—	3	2	no	—
11	C₂²×C₄	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂²×C₃	—	4	2	no	—
13	A₄	D₄	1	1	yes	characteristic, direct product factor
14	C₃×C₄	—	4	1	no	—
15	C₂³	—	2	2	no	—
16	C₂³	—	3	2	no	—
17	C₂³	—	3	2	no	—
18	C₂³	—	6	2	no	—
19	C₂³	C₂²×C₃	1	1	yes	characteristic
20	D₄	—	3	2	no	—
21	D₄	—	3	2	no	—
22	D₄	—	3	1	no	—
23	D₄	A₄	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	1	no	—
26	C₂×C₃	—	4	1	no	—
27	C₂×C₃	—	8	2	no	—
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	—	3	2	no	—
31	C₂²	—	6	2	no	—
32	C₂²	—	6	2	no	—
33	C₂²	—	6	2	no	—
34	C₂²	—	6	2	no	—
35	C₂²	C₃×D₄	1	1	yes	characteristic, complemented
36	C₂²	C₂×A₄	1	2	yes	complemented
37	C₄	—	3	1	no	—
38	C₄	C₂×A₄	1	1	yes	characteristic, complemented
39	C₃	—	4	1	no	Sylow
40	C₂	—	2	2	no	—
41	C₂	—	3	1	no	—
42	C₂	—	3	1	no	—
43	C₂	—	6	2	no	—
44	C₂	C₂²×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.