Subgroups — C₄²×A₄ #5434

Order 192.

133 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×A₄	C₂	1	3	yes	maximal
2	C₂²×C₄²	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂²×A₄	C₂²	1	1	yes	characteristic
4	C₄×A₄	C₄	1	6	yes	direct product factor
5	C₃×C₄²	—	4	1	no	maximal
6	C₂³×C₄	C₂×C₃	1	3	yes	—
7	C₂×C₄²	—	3	1	no	—
8	C₂×C₄²	—	3	3	no	—
9	C₂×A₄	C₂×C₄	1	3	yes	—
10	C₂×C₃×C₄	—	4	3	no	—
11	C₂⁴	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₄	—	3	3	no	—
13	C₂²×C₄	—	3	3	no	—
14	C₂²×C₄	—	3	6	no	—
15	C₂²×C₄	C₃×C₄	1	6	yes	complemented
16	C₄²	—	3	2	no	—
17	C₄²	—	3	3	no	—
18	C₄²	A₄	1	1	yes	characteristic, direct product factor
19	C₂²×C₃	—	4	1	no	—
20	A₄	C₄²	1	1	yes	characteristic, direct product factor
21	C₃×C₄	—	4	6	no	—
22	C₂³	—	3	3	no	—
23	C₂³	—	3	1	no	—
24	C₂³	C₂×C₃×C₄	1	3	yes	—
25	C₂×C₄	—	3	6	no	—
26	C₂×C₄	—	3	3	no	—
27	C₂×C₄	—	3	6	no	—
28	C₂×C₄	—	3	6	no	—
29	C₂×C₄	—	3	6	no	—
30	C₂×C₄	C₂×A₄	1	3	yes	—
31	C₂×C₃	—	4	3	no	—
32	C₂²	—	3	3	no	—
33	C₂²	—	3	2	no	—
34	C₂²	—	3	3	no	—
35	C₂²	—	3	3	no	—
36	C₂²	C₃×C₄²	1	1	yes	characteristic, complemented
37	C₂²	C₂²×A₄	1	1	yes	characteristic
38	C₄	—	3	6	no	—
39	C₄	C₄×A₄	1	6	yes	direct product factor
40	C₃	—	4	1	no	Sylow
41	C₂	—	3	3	no	—
42	C₂	—	3	1	no	—
43	C₂	C₂×C₄×A₄	1	3	yes	—

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.