Subgroups — A₄×Q₁₆ #5457

Order 192.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×A₄	C₂	1	2	yes	maximal
2	C₈×A₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×Q₁₆	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₄×A₄	—	2	2	no	—
5	C₄×A₄	C₂²	1	1	yes	characteristic
6	C₃×Q₁₆	—	4	1	no	maximal
7	C₂²×Q₈	C₂×C₃	1	2	yes	—
8	C₂×Q₁₆	—	3	1	no	—
9	C₂×Q₁₆	—	3	1	no	—
10	C₂×Q₁₆	—	3	2	no	—
11	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
12	C₂×A₄	D₄	1	1	yes	characteristic
13	C₃×Q₈	—	4	2	no	—
14	C₃×C₈	—	4	1	no	—
15	C₂×Q₈	—	3	2	no	—
16	C₂×Q₈	—	3	2	no	—
17	C₂×Q₈	—	6	2	no	—
18	C₂²×C₄	—	2	2	no	—
19	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
20	Q₁₆	—	3	2	no	—
21	Q₁₆	—	3	2	no	—
22	Q₁₆	—	3	1	no	—
23	Q₁₆	A₄	1	1	yes	characteristic, direct product factor
24	C₂×C₈	—	3	1	no	—
25	C₂×C₈	—	3	1	no	—
26	A₄	Q₁₆	1	1	yes	characteristic, direct product factor
27	C₃×C₄	—	4	1	no	—
28	C₃×C₄	—	8	2	no	—
29	C₂³	C₃×D₄	1	1	yes	characteristic
30	Q₈	—	3	2	no	—
31	Q₈	—	6	2	no	—
32	Q₈	—	6	2	no	—
33	Q₈	C₂×A₄	1	2	yes	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	3	1	no	—
36	C₂×C₄	—	6	2	no	—
37	C₂×C₄	—	6	2	no	—
38	C₈	—	3	1	no	—
39	C₈	C₂×A₄	1	1	yes	characteristic
40	C₂×C₃	—	4	1	no	—
41	C₂²	—	3	1	no	—
42	C₂²	—	3	1	no	—
43	C₂²	C₃×Q₁₆	1	1	yes	characteristic, complemented
44	C₄	—	2	2	no	—
45	C₄	—	3	1	no	—
46	C₄	—	6	2	no	—
47	C₄	C₂²×A₄	1	1	yes	characteristic
48	C₃	—	4	1	no	Sylow
49	C₂	—	3	1	no	—
50	C₂	—	3	1	no	—
51	C₂	D₄×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.